Title
stringlengths 14
196
| Abstract
stringlengths 349
1.92k
| Authors
sequencelengths 1
114
| Author_company
sequencelengths 0
2
| Date
unknown | arXiv_id
stringlengths 12
12
|
|---|---|---|---|---|---|
Efficient Noise Mitigation Technique for Quantum Computing | Quantum computers have enabled solving problems beyond the current computers'
capabilities. However, this requires handling noise arising from unwanted
interactions in these systems. Several protocols have been proposed to address
efficient and accurate quantum noise profiling and mitigation. In this work, we
propose a novel protocol that efficiently estimates the average output of a
noisy quantum device to be used for quantum noise mitigation. The multi-qubit
system average behavior is approximated as a special form of a Pauli Channel
where Clifford gates are used to estimate the average output for circuits of
different depths. The characterized Pauli channel error rates, and state
preparation and measurement errors are then used to construct the outputs for
different depths thereby eliminating the need for large simulations and
enabling efficient mitigation. We demonstrate the efficiency of the proposed
protocol on four IBM Q 5-qubit quantum devices. Our method demonstrates
improved accuracy with efficient noise characterization. We report up to 88\%
and 69\% improvement for the proposed approach compared to the unmitigated, and
pure measurement error mitigation approaches, respectively. | [
"Ali Shaib",
"Mohamad H. Naim",
"Mohammed E. Fouda",
"Rouwaida Kanj",
"Fadi Kurdahi"
] | [
"IBM"
] | "2021-09-10T23:23:03Z" | 2109.05136v1 |
Conditionally rigorous mitigation of multiqubit measurement errors | Several techniques have been recently introduced to mitigate errors in
near-term quantum computers without the overhead required by quantum error
correcting codes. While most of the focus has been on gate errors, measurement
errors are significantly larger than gate errors on some platforms. A widely
used {\it transition matrix error mitigation} (TMEM) technique uses measured
transition probabilities between initial and final classical states to correct
subsequently measured data. However from a rigorous perspective, the noisy
measurement should be calibrated with perfectly prepared initial states and the
presence of any state-preparation error corrupts the resulting mitigation. Here
we develop a measurement error mitigation technique, conditionally rigorous
TMEM, that is not sensitive to state-preparation errors and thus avoids this
limitation. We demonstrate the importance of the technique for high-precision
measurement and for quantum foundations experiments by measuring Mermin
polynomials on IBM Q superconducting qubits. An extension of the technique
allows one to correct for both state-preparation and measurement (SPAM) errors
in expectation values as well; we illustrate this by giving a protocol for
fully SPAM-corrected quantum process tomography. | [
"Michael R. Geller"
] | [
"IBM"
] | "2021-09-09T17:49:13Z" | 2109.04449v1 |
A case study of variational quantum algorithms for a job shop scheduling
problem | Combinatorial optimization models a vast range of industrial processes aiming
at improving their efficiency. In general, solving this type of problem exactly
is computationally intractable. Therefore, practitioners rely on heuristic
solution approaches. Variational quantum algorithms are optimization heuristics
that can be demonstrated with available quantum hardware. In this case study,
we apply four variational quantum heuristics running on IBM's superconducting
quantum processors to the job shop scheduling problem. Our problem optimizes a
steel manufacturing process. A comparison on 5 qubits shows that the recent
filtering variational quantum eigensolver (F-VQE) converges faster and samples
the global optimum more frequently than the quantum approximate optimization
algorithm (QAOA), the standard variational quantum eigensolver (VQE), and
variational quantum imaginary time evolution (VarQITE). Furthermore, F-VQE
readily solves problem sizes of up to 23 qubits on hardware without error
mitigation post processing. | [
"David Amaro",
"Matthias Rosenkranz",
"Nathan Fitzpatrick",
"Koji Hirano",
"Mattia Fiorentini"
] | [
"IBM"
] | "2021-09-08T16:05:50Z" | 2109.03745v2 |
Experimental violations of Leggett-Garg's inequalities on a quantum
computer | Leggett-Garg's inequalities predict sharp bounds for some classical
correlation functions that address the quantum or classical nature of real-time
evolutions. We experimentally observe the violations of these bounds on single-
and multi-qubit systems, in different settings, exploiting the IBM Quantum
platform. In the multi-qubit case we introduce the Leggett-Garg-Bell's
inequalities as an alternative to the previous ones. Measuring these
correlation functions, we find quantum error mitigation to be essential to spot
inequalities violations. Accessing only two qubit readouts, we assess
Leggett-Garg-Bell's inequalities to emerge as the most efficient quantum
coherence witnesses to be used for investigating quantum hardware, as the
complexity of their calculation does not scale with the number of constituents
of the system. Our analysis highlights the limits of nowadays quantum
platforms, showing that the above-mentioned correlation functions deviate from
theoretical prediction as the number of qubits and the depth of the circuit
grow. | [
"Alessandro Santini",
"Vittorio Vitale"
] | [
"IBM"
] | "2021-09-06T14:35:15Z" | 2109.02507v2 |
QSSA: An SSA-based IR for Quantum Computing | Quantum computing hardware has progressed rapidly. Simultaneously, there has
been a proliferation of programming languages and program optimization tools
for quantum computing. Existing quantum compilers use intermediate
representations (IRs) where quantum programs are described as circuits. Such
IRs fail to leverage existing work on compiler optimizations. In such IRs, it
is non-trivial to statically check for physical constraints such as the
no-cloning theorem, which states that qubits cannot be copied. We introduce
QSSA, a novel quantum IR based on static single assignment (SSA) that enables
decades of research in compiler optimizations to be applied to quantum
compilation. QSSA models quantum operations as being side-effect-free. The
inputs and outputs of the operation are in one-to-one correspondence; qubits
cannot be created or destroyed. As a result, our IR supports a static analysis
pass that verifies no-cloning at compile-time. The quantum circuit is fully
encoded within the def-use chain of the IR, allowing us to leverage existing
optimization passes on SSA representations such as redundancy elimination and
dead-code elimination. Running our QSSA-based compiler on the QASMBench and IBM
Quantum Challenge datasets, we show that our optimizations perform comparably
to IBM's Qiskit quantum compiler infrastructure. QSSA allows us to represent,
analyze, and transform quantum programs using the robust theory of SSA
representations, bringing quantum compilation into the realm of well-understood
theory and practice. | [
"Anurudh Peduri",
"Siddharth Bhat"
] | [
"IBM"
] | "2021-09-06T12:45:02Z" | 2109.02409v1 |
Multi-party Semi-quantum Secret Sharing Protocol based on Measure-flip
and Reflect Operations | Semi-quantum secret sharing (SQSS) protocols serve as fundamental frameworks
in quantum secure multi-party computations, offering the advantage of not
requiring all users to possess intricate quantum devices. However, the current
landscape of SQSS protocols predominantly caters to bipartite scenarios,
rendering them inadequate for practical multi-party secret sharing
requirements. Addressing this gap, this paper proposes a novel SQSS protocol
based on multi-particle GHZ states. In this protocol, the quantum user
distributes predetermined secret information to multiple classical users with
limited quantum capabilities, necessitating collaborative efforts among all
classical users to reconstruct the correct secret information. By utilizing
measure-flip and reflect operations, the transmitted multi-particle GHZ states
can all contribute keys, thereby improving the utilization of transmitted
particles. Security analysis shows that the protocol's resilience against
prevalent external and internal threats. Additionally, employing IBM Qiskit, we
conduct quantum circuit simulations to validate the protocol's accuracy and
feasibility. Compared with similar studies, the proposed protocol has
advantages in terms of protocol scalability, qubit efficiency, and shared
message types. | [
"Li Jian",
"Chong-Qiang Ye"
] | [
"IBM"
] | "2021-09-03T08:52:17Z" | 2109.01380v4 |
Geometric properties of evolutionary graph states and their detection on
a quantum computer | Geometric properties of evolutionary graph states of spin systems generated
by the operator of evolution with Ising Hamiltonian are examined, using their
relationship with fluctuations of energy. We find that the geometric
characteristics of the graph states depend on properties of the corresponding
graphs. Namely, it is obtained that the fluctuations of energy in graph states
and therefore the velocity of quantum evolution, the curvature and the torsion
of the states are related with the total number of edges, triangles and squares
in the corresponding graphs. The obtained results give a possibility to
quantify the number of edges, triangles and squares in a graph on a quantum
devise and achieve quantum supremacy in solving this problem with the
development of a multi-qubit quantum computer. Geometric characteristics of
graph states corresponding to a chain, a triangle, and a square are detected on
the basis of calculations on IBM's quantum computer ibmq-manila. | [
"Kh. P. Gnatenko",
"H. P. Laba",
"V. M. Tkachuk"
] | [
"IBM"
] | "2021-08-29T20:31:37Z" | 2108.12909v2 |
Step-by-Step HHL Algorithm Walkthrough to Enhance the Understanding of
Critical Quantum Computing Concepts | After learning basic quantum computing concepts, it is desirable to reinforce
the learning using an important and relatively complex algorithm through which
the students can observe and appreciate how the qubits evolve and interact with
each other. Harrow-Hassidim-Lloyd (HHL) quantum algorithm, which can solve
Linear System Problems with exponential speed-up over the classical method and
is the basic of many important quantum computing algorithms, is used to serve
this purpose. The HHL algorithm is explained analytically followed by a 4-qubit
numerical example in bra-ket notation. Matlab code corresponding to the
numerical example is available for students to gain a deeper understanding of
the HHL algorithm from a pure matrix point of view. A quantum circuit
programmed using qiskit is also provided which can be used for real hardware
execution in IBM quantum computers. After going through the material, students
are expected to have a better appreciation of the concepts such as basis
transformation, bra-ket and matrix representations, superposition,
entanglement, controlled operations, measurement, Quantum Fourier
Transformation, Quantum Phase Estimation, and quantum programming. To help
readers review these basic concepts, brief explanations augmented by the HHL
numerical examples in the main text are provided in the Appendix. | [
"Hector Jose Morrell Jr",
"Anika Zaman",
"Hiu Yung Wong"
] | [
"IBM"
] | "2021-08-20T05:24:07Z" | 2108.09004v4 |
Energy levels estimation on a quantum computer by evolution of a
physical quantity | We show that the time dependence of mean value of a physical quantity is
related with the transition energies of a quantum system. In the case when the
operator of a physical quantity anticommutes with the Hamiltonian of a system,
studies of the evolution of its mean value allow determining the energy levels
of the system. On the basis of the result, we propose a method for determining
energy levels of physical systems on a quantum computer. The method opens a
possibility to achieve quantum supremacy in solving the problem of finding
minimal or maximal energy of Ising model with spatially anisotropic interaction
using multi-qubit quantum computers. We apply the method for spin systems (spin
in magnetic field, spin chain, Ising model on squared lattice) and realize it
on IBM's quantum computers. | [
"Kh. P. Gnatenko",
"H. P. Laba",
"V. M. Tkachuk"
] | [
"IBM"
] | "2021-08-19T18:39:54Z" | 2108.08873v1 |
Enhancing entanglement and total correlations dynamics via local
unitaries | The interaction with the environment is one of the main obstacles to be
circumvented in practical implementations of quantum information tasks. The use
of local unitaries, while not changing the initial entanglement present in a
given state, can enormously change its dynamics through a noisy channel, and
consequently its ability to be used as a resource. This way, local unitaries
provide an easy and accessible way to enhance quantum correlations in a variety
of different experimental platforms. Given an initial entangled state and a
certain noisy channel, what are the local unitaries providing the most robust
dynamics? In this paper we solve this question considering two qubits states,
together with paradigmatic and relevant noisy channels, showing its
consequences for teleportation protocols and identifying cases where the most
robust states are not necessarily the ones imprinting the least information
about themselves into the environment. We also derive a general law relating
the interplay between the total correlations in the system and environment with
their mutual information built up over the noisy dynamics. Finally, we employ
the IBM Quantum Experience to provide a proof-of-principle experimental
implementation of our results. | [
"Joab Morais Varela",
"Ranieri Nery",
"George Moreno",
"Alice Caroline de Oliveira Viana",
"Gabriel Landi",
"Rafael Chaves"
] | [
"IBM"
] | "2021-08-18T20:12:34Z" | 2108.08372v1 |
Implementation of a Quantum Algorithm to Estimate the Energy of a
Particle in a Finite Square Well Potential on IBM Quantum Computer | In this paper, we implement a quantum algorithm -on IBM quantum devices, IBM
QASM simulator and PPRC computer cluster -to find the energy values of the
ground state and the first excited state of a particle in a finite square-well
potential. We use the quantum phase estimation technique and the iterative one
to execute the program on PPRC cluster and IBM devices, respectively. Our
results obtained from executing the quantum circuits on the IBM classical
devices show that our circuits succeed at simulating the system. However, duo
to scattered results, we execute only the iterative phase estimation part of
the circuit on the 5 qubit quantum devices to reduce the circuit size and
obtain low-scattered results. | [
"Sina Shokri",
"Shahnoosh Rafibakhsh",
"Faezeh Pooshgan",
"Rita Faeghi"
] | [
"IBM"
] | "2021-08-17T11:06:39Z" | 2108.07561v1 |
Real-time simulation of light-driven spin chains on quantum computers | In this work, we study the real-time evolution of periodically driven
(Floquet) systems on a quantum computer using IBM quantum devices. We consider
a driven Landau-Zener model and compute the transition probability between the
Floquet steady states as a function of time. We find that for this simple
one-qubit model, Floquet states can develop in real-time, as indicated by the
transition probability between Floquet states. Next, we model light-driven spin
chains and compute the time-dependent antiferromagnetic order parameter. We
consider models arising from light coupling to the underlying electrons as well
as those arising from light coupling to phonons. For the two-spin chains, the
quantum devices yield time evolutions that match the effective Floquet
Hamiltonian evolution for both models once readout error mitigation is
included. For three-spin chains, zero-noise extrapolation yields a time
dependence that follows the effective Floquet time evolution. Therefore, the
current IBM quantum devices can provide information on the dynamics of small
Floquet systems arising from light drives once error mitigation procedures are
implemented. | [
"Martin Rodriguez-Vega",
"Ella Carlander",
"Adrian Bahri",
"Ze-Xun Lin",
"Nikolai A. Sinitsyn",
"Gregory A. Fiete"
] | [
"IBM"
] | "2021-08-12T21:29:27Z" | 2108.05975v2 |
Suppression of crosstalk in superconducting qubits using dynamical
decoupling | Currently available superconducting quantum processors with interconnected
transmon qubits are noisy and prone to various errors. The errors can be
attributed to sources such as open quantum system effects and spurious
inter-qubit couplings (crosstalk). The ZZ-coupling between qubits in fixed
frequency transmon architectures is always present and contributes to both
coherent and incoherent crosstalk errors. Its suppression is therefore a key
step towards enhancing the fidelity of quantum computation using transmons.
Here we propose the use of dynamical decoupling to suppress the crosstalk, and
demonstrate the success of this scheme through experiments performed on several
IBM quantum cloud processors. In particular, we demonstrate improvements in
quantum memory as well as the performance of single-qubit and two-qubit gate
operations. We perform open quantum system simulations of the multi-qubit
processors and find good agreement with the experimental results. We analyze
the performance of the protocol based on a simple analytical model and
elucidate the importance of the qubit drive frequency in interpreting the
results. In particular, we demonstrate that the XY4 dynamical decoupling
sequence loses its universality if the drive frequency is not much larger than
the system-bath coupling strength. Our work demonstrates that dynamical
decoupling is an effective and practical way to suppress crosstalk and open
system effects, thus paving the way towards higher-fidelity logic gates in
transmon-based quantum computers. | [
"Vinay Tripathi",
"Huo Chen",
"Mostafa Khezri",
"Ka-Wa Yip",
"E. M. Levenson-Falk",
"Daniel A. Lidar"
] | [
"IBM"
] | "2021-08-10T09:16:05Z" | 2108.04530v2 |
Deterministic one-way logic gates on a cloud quantum computer | One-way quantum computing is a promising candidate for fault-tolerant quantum
computing. Here, we propose new protocols to realize a deterministic one-way
CNOT gate and one-way $X$-rotations on quantum-computing platforms. By applying
a delayed-choice scheme, we overcome a limit of most currently available
quantum computers, which are unable to implement further operations on measured
qubits or operations conditioned on measurement results from other qubits.
Moreover, we decrease the error rate of the one-way logic gates, compared to
the original protocol using local operations and classical communication
(LOCC). In addition, we apply our deterministic one-way CNOT gate in the
Deutsch-Jozsa algorithm to show the feasibility of our proposal. We demonstrate
all these one-way gates and algorithms by running experiments on the cloud
quantum-computing platform IBM Quantum Experience. | [
"Zhi-Peng Yang",
"Alakesh Baishya",
"Huan-Yu Ku",
"Yu-Ran Zhang",
"Anton Frisk Kockum",
"Yueh-Nan Chen",
"Fu-Li Li",
"Jaw-Shen Tsai",
"Franco Nori"
] | [
"IBM"
] | "2021-08-09T08:20:44Z" | 2108.03865v2 |
Quantum machine learning of large datasets using randomized measurements | Quantum computers promise to enhance machine learning for practical
applications. Quantum machine learning for real-world data has to handle
extensive amounts of high-dimensional data. However, conventional methods for
measuring quantum kernels are impractical for large datasets as they scale with
the square of the dataset size. Here, we measure quantum kernels using
randomized measurements. The quantum computation time scales linearly with
dataset size and quadratic for classical post-processing. While our method
scales in general exponentially in qubit number, we gain a substantial speed-up
when running on intermediate-sized quantum computers. Further, we efficiently
encode high-dimensional data into quantum computers with the number of features
scaling linearly with the circuit depth. The encoding is characterized by the
quantum Fisher information metric and is related to the radial basis function
kernel. Our approach is robust to noise via a cost-free error mitigation
scheme. We demonstrate the advantages of our methods for noisy quantum
computers by classifying images with the IBM quantum computer. To achieve
further speedups we distribute the quantum computational tasks between
different quantum computers. Our method enables benchmarking of quantum machine
learning algorithms with large datasets on currently available quantum
computers. | [
"Tobias Haug",
"Chris N. Self",
"M. S. Kim"
] | [
"IBM"
] | "2021-08-02T17:00:18Z" | 2108.01039v3 |
Implementing efficient selective quantum process tomography of
superconducting quantum gates on the IBM quantum processor | The experimental implementation of selective quantum process tomography
(SQPT) involves computing individual elements of the process matrix with the
help of a special set of states called quantum 2-design states. However, the
number of experimental settings required to prepare input states from quantum
2-design states to selectively and precisely compute a desired element of the
process matrix is still high, and hence constructing the corresponding unitary
operations in the lab is a daunting task. In order to reduce the experimental
complexity, we mathematically reformulated the standard SQPT problem, which we
term the modified SQPT (MSQPT) method. We designed the generalized quantum
circuit to prepare the required set of input states and formulated an efficient
measurement strategy aimed at minimizing the experimental cost of SQPT. We
experimentally demonstrated the MSQPT protocol on the IBM QX2 cloud quantum
processor and selectively characterized various two- and three-qubit quantum
gates. | [
"Akshay Gaikwad",
"Krishna Shende",
" Arvind",
"Kavita Dorai"
] | [
"IBM"
] | "2021-07-15T17:04:24Z" | 2107.07462v1 |
Scalable estimation of pure multi-qubit states | We introduce an inductive $n$-qubit pure-state estimation method. This is
based on projective measurements on states of $2n+1$ separable bases or $2$
entangled bases plus the computational basis. Thus, the total number of
measurement bases scales as $O(n)$ and $O(1)$, respectively. Thereby, the
proposed method exhibits a very favorable scaling in the number of qubits when
compared to other estimation methods. Monte Carlo numerical experiments show
that the method can achieve a high estimation fidelity. For instance, an
average fidelity of $0.88$ on the Hilbert space of $10$ qubits is achieved with
$21$ separable bases. The use of separable bases makes our estimation method
particularly well suited for applications in noisy intermediate-scale quantum
computers, where entangling gates are much less accurate than local gates. We
experimentally demonstrate the proposed method in one of IBM's quantum
processors by estimating 4-qubit Greenberger-Horne-Zeilinger states with a
fidelity close to $0.875$ via separable bases. Other $10$-qubit separable and
entangled states achieve an estimation fidelity in the order of $0.85$ and
$0.7$, respectively. | [
"L. Pereira",
"L. Zambrano",
"A. Delgado"
] | [
"IBM"
] | "2021-07-12T19:02:56Z" | 2107.05691v1 |
Machine-Learning-Derived Entanglement Witnesses | In this work, we show a correspondence between linear support vector machines
(SVMs) and entanglement witnesses, and use this correspondence to generate
entanglement witnesses for bipartite and tripartite qubit (and qudit) target
entangled states. An SVM allows for the construction of a hyperplane that
clearly delineates between separable states and the target entangled state;
this hyperplane is a weighted sum of observables ('features') whose
coefficients are optimized during the training of the SVM. We demonstrate with
this method the ability to obtain witnesses that require only local
measurements even when the target state is a non-stabilizer state. Furthermore,
we show that SVMs are flexible enough to allow us to rank features, and to
reduce the number of features systematically while bounding the inference
error. This allows us to derive W state witnesses capable of detecting
entanglement with fewer measurement terms than the fidelity method dominant in
today's literature. The utility of this approach is demonstrated on quantum
hardware furnished through the IBM Quantum Experience. | [
"Alexander C. B. Greenwood",
"Larry T. H. Wu",
"Eric Y. Zhu",
"Brian T. Kirby",
"Li Qian"
] | [
"IBM"
] | "2021-07-05T22:28:02Z" | 2107.02301v3 |
Convergence of reconstructed density matrix to a pure state using
maximal entropy approach | Impressive progress has been made in the past decade in the study of
technological applications of varied types of quantum systems. With industry
giants like IBM laying down their roadmap for scalable quantum devices with
more than 1000-qubits by the end of 2023, efficient validation techniques are
also being developed for testing quantum processing on these devices. The
characterization of a quantum state is done by experimental measurements
through the process called quantum state tomography (QST) which scales
exponentially with the size of the system. However, QST performed using
incomplete measurements is aptly suited for characterizing these quantum
technologies especially with the current nature of noisy intermediate-scale
quantum (NISQ) devices where not all mean measurements are available with high
fidelity. We, hereby, propose an alternative approach to QST for the complete
reconstruction of the density matrix of a quantum system in a pure state for
any number of qubits by applying the maximal entropy formalism on the pairwise
combinations of the known mean measurements. This approach provides the best
estimate of the target state when we know the complete set of observables which
is the case of convergence of the reconstructed density matrix to a pure state.
Our goal is to provide a practical inference of a quantum system in a pure
state that can find its applications in the field of quantum error mitigation
on a real quantum computer that we intend to investigate further. | [
"Rishabh Gupta",
"Sabre Kais",
"Raphael D. Levine"
] | [
"IBM"
] | "2021-07-02T16:58:26Z" | 2107.01191v1 |
Quantum simulation of non-equilibrium dynamics and thermalization in the
Schwinger model | We present simulations of non-equilibrium dynamics of quantum field theories
on digital quantum computers. As a representative example, we consider the
Schwinger model, a 1+1 dimensional U(1) gauge theory, coupled through a
Yukawa-type interaction to a thermal environment described by a scalar field
theory. We use the Hamiltonian formulation of the Schwinger model discretized
on a spatial lattice. With the thermal scalar fields traced out, the Schwinger
model can be treated as an open quantum system and its real-time dynamics are
governed by a Lindblad equation in the Markovian limit. The interaction with
the environment ultimately drives the system to thermal equilibrium. In the
quantum Brownian motion limit, the Lindblad equation is related to a field
theoretical Caldeira-Leggett equation. By using the Stinespring dilation
theorem with ancillary qubits, we perform studies of both the non-equilibrium
dynamics and the preparation of a thermal state in the Schwinger model using
IBM's simulator and quantum devices. The real-time dynamics of field theories
as open quantum systems and the thermal state preparation studied here are
relevant for a variety of applications in nuclear and particle physics, quantum
information and cosmology. | [
"Wibe A. de Jong",
"Kyle Lee",
"James Mulligan",
"Mateusz Płoskoń",
"Felix Ringer",
"Xiaojun Yao"
] | [
"IBM"
] | "2021-06-15T19:48:05Z" | 2106.08394v4 |
Variational Quantum Eigensolver with Reduced Circuit Complexity | The variational quantum eigensolver (VQE) is one of the most promising
algorithms to find eigenvalues and eigenvectors of a given Hamiltonian on noisy
intermediate-scale quantum (NISQ) devices. A particular application is to
obtain ground or excited states of molecules. The practical realization is
currently limited by the complexity of quantum circuits. Here we present a
novel approach to reduce quantum circuit complexity in VQE for electronic
structure calculations. Our algorithm, called ClusterVQE, splits the initial
qubit space into subspaces (qubit clusters) which are further distributed on
individual (shallower) quantum circuits. The clusters are obtained based on
quantum mutual information reflecting maximal entanglement between qubits,
whereas entanglement between different clusters is taken into account via a new
"dressed" Hamiltonian. ClusterVQE therefore allows exact simulation of the
problem by using fewer qubits and shallower circuit depth compared to standard
VQE at the cost of additional classical resources. In addition, a new gradient
measurement method without using an ancillary qubit is also developed in this
work. Proof-of-principle demonstrations are presented for several molecular
systems based on quantum simulators as well as an IBM quantum device with
accompanying error mitigation. The efficiency of the new algorithm is
comparable to or even improved over qubit-ADAPT-VQE and iterative Qubit Coupled
Cluster (iQCC), state-of-the-art circuit-efficient VQE methods to obtain
variational ground state energies of molecules on NISQ hardware. Above all, the
new ClusterVQE algorithm simultaneously reduces the number of qubits and
circuit depth, making it a potential leader for quantum chemistry simulations
on NISQ devices. | [
"Yu Zhang",
"Lukasz Cincio",
"Christian F. A. Negre",
"Piotr Czarnik",
"Patrick Coles",
"Petr M. Anisimov",
"Susan M. Mniszewski",
"Sergei Tretiak",
"Pavel A. Dub"
] | [
"IBM"
] | "2021-06-14T17:23:46Z" | 2106.07619v1 |
The role of quantum coherence in energy fluctuations | We discuss the role of quantum coherence in the energy fluctuations of open
quantum systems. To this aim, we introduce a protocol, to which we refer to as
the end-point-measurement scheme, allowing to define the statistics of energy
changes as a function of energy measurements performed only after the evolution
of the initial state. At the price of an additional uncertainty on the initial
energies, this approach prevents the loss of initial quantum coherences and
enables the estimation of their effects on energy fluctuations. We demonstrate
our findings by running an experiment on the IBM Quantum Experience
superconducting qubit platform. | [
"S. Gherardini",
"A. Belenchia",
"M. Paternostro",
"A. Trombettoni"
] | [
"IBM"
] | "2021-06-11T15:32:24Z" | 2106.06461v1 |
Perturbative quantum simulation | Approximation based on perturbation theory is the foundation for most of the
quantitative predictions of quantum mechanics, whether in quantum many-body
physics, chemistry, quantum field theory or other domains. Quantum computing
provides an alternative to the perturbation paradigm, yet state-of-the-art
quantum processors with tens of noisy qubits are of limited practical utility.
Here, we introduce perturbative quantum simulation, which combines the
complementary strengths of the two approaches, enabling the solution of large
practical quantum problems using limited noisy intermediate-scale quantum
hardware. The use of a quantum processor eliminates the need to identify a
solvable unperturbed Hamiltonian, while the introduction of perturbative
coupling permits the quantum processor to simulate systems larger than the
available number of physical qubits. We present an explicit perturbative
expansion that mimics the Dyson series expansion and involves only local
unitary operations, and show its optimality over other expansions under certain
conditions. We numerically benchmark the method for interacting bosons,
fermions, and quantum spins in different topologies, and study different
physical phenomena, such as information propagation, charge-spin separation,
and magnetism, on systems of up to $48$ qubits only using an $8+1$ qubit
quantum hardware. We experimentally demonstrate our scheme on the IBM quantum
cloud, verifying its noise robustness and illustrating its potential for
benchmarking large quantum processors with smaller ones. | [
"Jinzhao Sun",
"Suguru Endo",
"Huiping Lin",
"Patrick Hayden",
"Vlatko Vedral",
"Xiao Yuan"
] | [
"IBM"
] | "2021-06-10T17:38:25Z" | 2106.05938v2 |
Error Mitigation for Deep Quantum Optimization Circuits by Leveraging
Problem Symmetries | High error rates and limited fidelity of quantum gates in near-term quantum
devices are the central obstacles to successful execution of the Quantum
Approximate Optimization Algorithm (QAOA). In this paper we introduce an
application-specific approach for mitigating the errors in QAOA evolution by
leveraging the symmetries present in the classical objective function to be
optimized. Specifically, the QAOA state is projected into the
symmetry-restricted subspace, with projection being performed either at the end
of the circuit or throughout the evolution. Our approach improves the fidelity
of the QAOA state, thereby increasing both the accuracy of the sample estimate
of the QAOA objective and the probability of sampling the binary string
corresponding to that objective value. We demonstrate the efficacy of the
proposed methods on QAOA applied to the MaxCut problem, although our methods
are general and apply to any objective function with symmetries, as well as to
the generalization of QAOA with alternative mixers. We experimentally verify
the proposed methods on an IBM Quantum processor, utilizing up to 5 qubits.
When leveraging a global bit-flip symmetry, our approach leads to a 23% average
improvement in quantum state fidelity. | [
"Ruslan Shaydulin",
"Alexey Galda"
] | [
"IBM"
] | "2021-06-08T14:40:48Z" | 2106.04410v2 |
A Universal Quantum Circuit Design for Periodical Functions | We propose a universal quantum circuit design that can estimate any arbitrary
one-dimensional periodic functions based on the corresponding Fourier
expansion. The quantum circuit contains N-qubits to store the information on
the different N-Fourier components and $M+2$ auxiliary qubits with $M =
\lceil{\log_2{N}}\rceil$ for control operations. The desired output will be
measured in the last qubit $q_N$ with a time complexity of the computation of
$O(N^2\lceil \log_2N\rceil^2)$. We illustrate the approach by constructing the
quantum circuit for the square wave function with accurate results obtained by
direct simulations using the IBM-QASM simulator. The approach is general and
can be applied to any arbitrary periodic function. | [
"Junxu Li",
"Sabre Kais"
] | [
"IBM"
] | "2021-06-04T19:18:02Z" | 2106.02678v4 |
Experimental error mitigation using linear rescaling for variational
quantum eigensolving with up to 20 qubits | Quantum computers have the potential to help solve a range of physics and
chemistry problems, but noise in quantum hardware currently limits our ability
to obtain accurate results from the execution of quantum-simulation algorithms.
Various methods have been proposed to mitigate the impact of noise on
variational algorithms, including several that model the noise as damping
expectation values of observables. In this work, we benchmark various methods,
including a new method proposed here. We compare their performance in
estimating the ground-state energies of several instances of the 1D mixed-field
Ising model using the variational-quantum-eigensolver algorithm with up to 20
qubits on two of IBM's quantum computers. We find that several error-mitigation
techniques allow us to recover energies to within 10% of the true values for
circuits containing up to about 25 ansatz layers, where each layer consists of
CNOT gates between all neighboring qubits and Y-rotations on all qubits. | [
"Eliott Rosenberg",
"Paul Ginsparg",
"Peter L. McMahon"
] | [
"IBM"
] | "2021-06-02T16:18:31Z" | 2106.01264v3 |
Z3 gauge theory coupled to fermions and quantum computing | We study the Z3 gauge theory with fermions on the quantum computer using the
Variational Quantum Eigensolver (VQE) algorithm with IBM QISKit software. Using
up to 9 qubits we are able to obtain accurate results for the ground state
energy. Introducing nonzero chemical potential we are able to determine the
Equation of State (EOS) for finite density on the quantum computer. We discuss
possible realizations of quantum advantage for this system over classical
computers with regards to finite density simulations and the fermion sign
problem. | [
"Ronak Desai",
"Yuan Feng",
"Mohammad Hassan",
"Abhishek Kodumagulla",
"Michael McGuigan"
] | [
"IBM"
] | "2021-06-01T14:59:51Z" | 2106.00549v1 |
Simulating of X-states and the two-qubit XYZ Heisenberg system on IBM
quantum computer | Two qubit density matrices, which are of X-shape, are a natural
generalization of Bell Diagonal States (BDSs) recently simulated on the IBM
quantum device. We generalize the previous results and propose a quantum
circuit for simulation of a general two qubit X-state, implement it on the same
quantum device, and study its entanglement for several values of the extended
parameter space. We also show that their X-shape is approximately robust
against noisy quantum gates. To further physically motivate this study, we
invoke the two-spin Heisenberg XYZ system and show that for a wide class of
initial states, it leads to dynamical density matrices which are X-states. Due
to the symmetries of this Hamiltonian, we show that by only two qubits, one can
simulate the dynamics of this system on the IBM quantum computer. | [
"Fereshte Shahbeigi",
"Mahsa Karimi",
"Vahid Karimipour"
] | [
"IBM"
] | "2021-05-30T16:55:53Z" | 2105.14581v3 |
A Quantum Hopfield Associative Memory Implemented on an Actual Quantum
Processor | In this work, we present a Quantum Hopfield Associative Memory (QHAM) and
demonstrate its capabilities in simulation and hardware using IBM Quantum
Experience. The QHAM is based on a quantum neuron design which can be utilized
for many different machine learning applications and can be implemented on real
quantum hardware without requiring mid-circuit measurement or reset operations.
We analyze the accuracy of the neuron and the full QHAM considering hardware
errors via simulation with hardware noise models as well as with implementation
on the 15-qubit ibmq_16_melbourne device. The quantum neuron and the QHAM are
shown to be resilient to noise and require low qubit overhead and gate
complexity. We benchmark the QHAM by testing its effective memory capacity and
demonstrate its capabilities in the NISQ-era of quantum hardware. This
demonstration of the first functional QHAM to be implemented in NISQ-era
quantum hardware is a significant step in machine learning at the leading edge
of quantum computing. | [
"Nathan Eli Miller",
"Saibal Mukhopadhyay"
] | [
"IBM"
] | "2021-05-25T00:45:57Z" | 2105.11590v3 |
Digitized Adiabatic Quantum Factorization | Quantum integer factorization is a potential quantum computing solution that
may revolutionize cryptography. Nevertheless, a scalable and efficient quantum
algorithm for noisy intermediate-scale quantum computers looks far-fetched. We
propose an alternative factorization method, within the digitized-adiabatic
quantum computing paradigm, by digitizing an adiabatic quantum factorization
algorithm enhanced by shortcuts to adiabaticity techniques. We find that this
fast factorization algorithm is suitable for available gate-based quantum
computers. We test our quantum algorithm in an IBM quantum computer with up to
six qubits, surpassing the performance of the more commonly used factorization
algorithms on the long way towards quantum advantage. | [
"Narendra N. Hegade",
"Koushik Paul",
"Francisco Albarrán-Arriagada",
"Xi Chen",
"Enrique Solano"
] | [
"IBM"
] | "2021-05-19T13:26:23Z" | 2105.09480v2 |
Testing complementarity on a transmon quantum processor | We propose quantum circuits to test interferometric complementarity using
symmetric two-way interferometers coupled to a which-path detector. First, we
consider the two-qubit setup in which the controlled transfer of path
information to the detector subsystem depletes interference on the probed
subspace, testing the visibility-distinguishability trade-off via minimum-error
state discrimination measurements. Next, we consider the quantum eraser setup,
in which reading out path information in the right basis recovers an
interference pattern. These experiments are then carried out in an IBM
superconducting transmon processor. A detailed analysis of the results is
provided. Despite finding good agreement with theory at a coarse level, we also
identify small but persistent systematic deviations preventing the observation
of full particle-like and wave-like statistics. We understand them by carefully
modeling two-qubit gates, showing that even small coherent errors in their
implementation preclude the observation of Bohr's strong formulation of
complementarity. | [
"Pedro M. Q. Cruz",
"J. Fernández-Rossier"
] | [
"IBM"
] | "2021-05-17T13:46:14Z" | 2105.07832v2 |
Quantum error reduction with deep neural network applied at the
post-processing stage | Deep neural networks (DNN) can be applied at the post-processing stage for
the improvement of the results of quantum computations on noisy
intermediate-scale quantum (NISQ) processors. Here, we propose a method based
on this idea, which is most suitable for digital quantum simulation
characterized by the periodic structure of quantum circuits consisting of
Trotter steps. A key ingredient of our approach is that it does not require any
data from a classical simulator at the training stage. The network is trained
to transform data obtained from quantum hardware with artificially increased
Trotter steps number (noise level) towards the data obtained without such an
increase. The additional Trotter steps are fictitious, i.e., they contain
negligibly small rotations and, in the absence of hardware imperfections,
reduce essentially to the identity gates. This preserves, at the training
stage, information about relevant quantum circuit features. Two particular
examples are considered that are the dynamics of the transverse-field Ising
chain and XY spin chain, which were implemented on two real five-qubit IBM Q
processors. A significant error reduction is demonstrated as a result of the
DNN application that allows us to effectively increase quantum circuit depth in
terms of Trotter steps. | [
"A. A. Zhukov",
"W. V. Pogosov"
] | [
"IBM"
] | "2021-05-17T13:04:26Z" | 2105.07793v4 |
Conditional entropy production and quantum fluctuation theorem of
dissipative information: Theory and experiments | We study quantum conditional entropy production, which quantifies the
irreversibility of system-environment evolution from the perspective of a third
system, called the reference. The reference is initially correlated with the
system. We show that the quantum unconditional entropy production with respect
to the system is less than the conditional entropy production with respect to
the reference, where the latter includes a reference-induced dissipative
information. The dissipative information pinpoints the distributive correlation
established between the environment and the reference, even though they do not
interact directly. When reaching the thermal equilibrium, the
system-environment evolution has a zero unconditional entropy production.
However, one can still have a nonzero conditional entropy production with
respect to the reference, which characterizes the informational nonequilibrium
of the system-environment evolution in the view point of the reference. The
additional contribution to the conditional entropy production, the dissipative
information, characterizes a minimal thermodynamic cost that the system pays
for maintaining the correlation with the reference. Positive dissipative
information also characterizes potential work waste. We prove that both types
of entropy production and the dissipative information follow quantum
fluctuation theorems when a two-point measurement is applied. We verify the
quantum fluctuation theorem for the dissipative information experimentally on
IBM quantum computers. We also present examples based on the qubit collisional
model and demonstrate universal nonzero dissipative information in the qubit
Maxwell's demon protocol. | [
"Kun Zhang",
"Xuanhua Wang",
"Qian Zeng",
"Jin Wang"
] | [
"IBM"
] | "2021-05-13T16:53:57Z" | 2105.06419v3 |
Experimental QND measurements of complementarity on two-qubit states
with IonQ and IBM Q quantum computers | We report the experimental nondemolition measurement of coherence,
predictability and concurrence on a system of two qubits. The quantum circuits
proposed by De Melo et al. are implemented on IBM Q (superconducting circuit)
and IonQ (trapped ion) quantum computers. Three criteria are used to compare
the performance of the different machines on this task: measurement accuracy,
nondemolition of the observable, and quantum state preparation. We find that
the IonQ quantum computer provides constant state fidelity through the
nondemolition process, outperforming IBM Q systems on which the fidelity
consequently drops after the measurement. Our study compares the current
performance of these two technologies at different stages of the nondemolition
measurement of bipartite complementarity. | [
"Nicolas Schwaller",
"Valeria Vento",
"Christophe Galland"
] | [
"IBM"
] | "2021-05-13T15:54:30Z" | 2105.06368v2 |
Fast Black-Box Quantum State Preparation Based on Linear Combination of
Unitaries | Black-box quantum state preparation is a fundamental primitive in quantum
algorithms. Starting from Grover, a series of techniques have been devised to
reduce the complexity. In this work, we propose to perform black-box state
preparation using the technique of linear combination of unitaries (LCU). We
provide two algorithms based on a different structure of LCU. Our algorithms
improve upon the existed best results by reducing the required additional
qubits and Toffoli gates to 2log(n) and n, respectively, in the bit precision
n. We demonstrate the algorithms using the IBM Quantum Experience cloud
services. The further reduced complexity of the present algorithms brings the
black-box quantum state preparation closer to reality. | [
"Shengbin Wang",
"Zhimin Wang",
"Guolong Cui",
"Shangshang Shi",
"Ruimin Shang",
"Lixin Fan",
"Wendong Li",
"Zhiqiang Wei",
"Yongjian Gu"
] | [
"IBM"
] | "2021-05-13T12:29:06Z" | 2105.06230v1 |
Implementing Quantum Finite Automata Algorithms on Noisy Devices | Quantum finite automata (QFAs) literature offers an alternative mathematical
model for studying quantum systems with finite memory. As a superiority of
quantum computing, QFAs have been shown exponentially more succinct on certain
problems such as recognizing the language $ MOD_p = \{a^j \mid j \equiv 0 \mod
p\} $ with bounded error, where $p$ is a prime number. In this paper we present
improved circuit based implementations for QFA algorithms recognizing the $
MOD_p $ problem using the Qiskit framework. We focus on the case $p=11$ and
provide a 3 qubit implementation for the $MOD_{11}$ problem reducing the total
number of required gates using alternative approaches. We run the circuits on
real IBM quantum devices but due to the limitation of the real quantum devices
in the NISQ era, the results are heavily affected by the noise. This limitation
reveals once again the need for algorithms using less amount of resources.
Consequently, we consider an alternative 3 qubit implementation which works
better in practice and obtain promising results even for the problem $ MOD_{31}
$. | [
"Utku Birkan",
"Özlem Salehi",
"Viktor Olejar",
"Cem Nurlu",
"Abuzer Yakaryılmaz"
] | [
"IBM"
] | "2021-05-13T10:51:28Z" | 2105.06184v1 |
Playing quantum nonlocal games with six noisy qubits on the cloud | Nonlocal games are extensions of Bell inequalities, aimed at demonstrating
quantum advantage. These games are well suited for noisy quantum computers
because they only require the preparation of a shallow circuit, followed by the
measurement of non-commuting observable. Here, we consider the minimal
implementation of the nonlocal game proposed in Science 362, 308 (2018). We
test this game by preparing a 6-qubit cluster state using quantum computers on
the cloud by IBM, Ionq, and Honeywell. Our approach includes several levels of
optimization, such as circuit identities and error mitigation and allows us to
cross the classical threshold and demonstrate quantum advantage in one quantum
computer. We conclude by introducing a different inequality that allows us to
observe quantum advantage in less accurate quantum computers, at the expense of
probing a larger number of circuits. | [
"Meron Sheffer",
"Daniel Azses",
"Emanuele G. Dalla Torre"
] | [
"IBM"
] | "2021-05-11T18:00:08Z" | 2105.05266v3 |
Benchmarking near-term quantum computers via random circuit sampling | The increasing scale of near-term quantum hardware motivates the need for
efficient noise characterization methods, since qubit and gate level techniques
cannot capture crosstalk and correlated noise in many qubit systems. While
scalable approaches, such as cycle benchmarking, are known for special classes
of quantum circuits, the characterization of noise in general circuits with
non-Clifford gates has been an unreachable task. We develop an algorithm that
can sample-efficiently estimate the total amount of noise induced by a layer of
arbitrary non-Clifford gates, including all crosstalks, and experimentally
demonstrate the method on IBM Quantum hardware. Our algorithm is inspired by
Google's quantum supremacy experiment and is based on random circuit sampling.
In their paper, Google observed that their experimental linear cross entropy
was consistent with a simple uncorrelated noise model, and claimed this
coincidence indicated that the noise in their device was uncorrelated -- a key
step in hardware development towards fault tolerance. As an application, we
show that our result provides formal evidence to support such a conclusion. | [
"Yunchao Liu",
"Matthew Otten",
"Roozbeh Bassirianjahromi",
"Liang Jiang",
"Bill Fefferman"
] | [
"IBM"
] | "2021-05-11T17:49:16Z" | 2105.05232v2 |
Quantum Simulations of the Non-Unitary Time Evolution and Applications
to Neutral-Kaon Oscillations | In light of recent exciting progress in building up quantum computing
facilities based on both optical and cold-atom techniques, the algorithms for
quantum simulations of particle-physics systems are in rapid progress. In this
paper, we propose an efficient algorithm for simulating the non-unitary time
evolution of neutral-kaon oscillations $K^0 \leftrightarrow \overline{K}^0$,
with or without CP conservation, on the quantum computers provided by the IBM
company. The essential strategy is to realize the time-evolution operator with
basic quantum gates and an extra qubit corresponding to some external
environment. The final results are well consistent with theoretical
expectations, and the algorithm can also be applied to open systems beyond
elementary particles. | [
"Ying Chen",
"Yunheng Ma",
"Shun Zhou"
] | [
"IBM"
] | "2021-05-11T03:16:20Z" | 2105.04765v1 |
Casimir energy with chiral fermions on a quantum computer | In this paper we discuss the computation of Casimir energy on a quantum
computer. The Casimir energy is an ideal quantity to calculate on a quantum
computer as near term hybrid classical quantum algorithms exist to calculate
the ground state energy and the Casimir energy gives physical implications for
this quantity in a variety of settings. Depending on boundary conditions and
whether the field is bosonic or fermionic we illustrate how the Casimir energy
calculation can be set up on a quantum computer and calculated using the
Variational Quantum Eigensolver algorithm with IBM QISKit. We compare the
results based on a lattice regularization with a finite number of qubits with
the continuum calculation for free boson fields, free fermion fields and chiral
fermion fields. We use a regularization method introduced by Bergman and Thorn
to compute the Casimir energy of a chiral fermion. We show how the accuracy of
the calculation varies with the number of qubits. We show how the number of
Pauli terms which are used to represent the Hamiltonian on a quantum computer
scales with the number of qubits. We discuss the application of the Casimir
calculations on quantum computers to cosmology, nanomaterials, string models,
Kaluza Klein models and dark energy. | [
"Juliette K. Stecenko",
"Yuan Feng",
"Michael McGuigan"
] | [
"IBM"
] | "2021-05-05T13:04:34Z" | 2105.02032v1 |
Pulse-efficient circuit transpilation for quantum applications on
cross-resonance-based hardware | We show a pulse-efficient circuit transpilation framework for noisy quantum
hardware. This is achieved by scaling cross-resonance pulses and exposing each
pulse as a gate to remove redundant single-qubit operations with the
transpiler.Crucially, no additional calibration is needed to yield better
results than a CNOT-based transpilation. This pulse-efficient circuit
transpilation therefore enables a better usage of the finite coherence time
without requiring knowledge of pulse-level details from the user. As
demonstration, we realize a continuous family of cross-resonance-based gates
for SU(4) by leveraging Cartan's decomposition. We measure the benefits of a
pulse-efficient circuit transpilation with process tomography and observe up to
a 50% error reduction in the fidelity of RZZ({\theta}) and arbitrary SU(4)
gates on IBM Quantum devices.We apply this framework for quantum applications
by running circuits of the Quantum Approximate Optimization Algorithm applied
to MAXCUT. For an 11 qubit non-hardware native graph, our methodology reduces
the overall schedule duration by up to 52% and errors by up to 38% | [
"Nathan Earnest",
"Caroline Tornow",
"Daniel J. Egger"
] | [
"IBM"
] | "2021-05-03T17:59:55Z" | 2105.01063v1 |
Optimizing Parameterized Quantum Circuits with Free-Axis Selection | Variational quantum algorithms, which utilize Parametrized Quantum Circuits
(PQCs), are promising tools to achieve quantum advantage for optimization
problems on near-term quantum devices. Their PQCs have been conventionally
constructed from parametrized rotational angles of single-qubit gates around
predetermined set of axes, and two-qubit entangling gates, such as CNOT gates.
We propose a method to construct a PQC by continuous parametrization of both
the angles and the axes of its single-qubit rotation gates. The method is based
on the observation that when rotational angles are fixed, optimal axes of
rotations can be computed by solving a system of linear equations whose
coefficients can be determined from the PQC with small computational overhead.
The method can be further simplified to select axes freely from continuous
parameters with rotational angles fixed to half rotation or $\pi$. We show the
simplified free-axis selection method has better expressibility against other
structural optimization methods when measured with Kullback-Leibler (KL)
divergence. We also demonstrate PQCs with free-axis selection are more
effective to search the ground states of Hamiltonians for quantum chemistry and
combinatorial optimization. Because free-axis selection allows designing PQCs
without specifying their single-qubit rotational axes, it may significantly
improve the handiness of PQCs. | [
"Hiroshi C. Watanabe",
"Rudy Raymond",
"Yu-ya Ohnishi",
"Eriko Kaminishi",
"Michihiko Sugawara"
] | [] | "2021-04-30T10:03:17Z" | 2104.14875v2 |
Simulation of three-spin evolution under XX Hamiltonian on quantum
processor of IBM-Quantum Experience | We simulate the evolution of three-node spin chain on the quantum processor
of IBM Quantum Experience using the diagonalization of $XX$-Hamiltonian and
representing the evolution operator in terms of CNOT operations and one-qubit
rotations. We study the single excitation transfer from the first to the third
node and show the significant difference between calculated and theoretical
values of state transfer probability. Then we propose a method reducing this
difference by applying the two-parameter transformation including the shift and
scale of the calculated probabilities. { We demonstrate the universality of
this transformation inside of the class of three-node evolutionary systems
governed by the $XX$-Hamiltonian. | [
"S. I. Doronin",
"E. B. Fel'dman",
"A. I. Zenchuk"
] | [
"IBM"
] | "2021-04-28T14:00:17Z" | 2104.13769v2 |
Quantum circuit synthesis of Bell and GHZ states using projective
simulation in the NISQ era | Quantum Computing has been evolving in the last years. Although nowadays
quantum algorithms performance has shown superior to their classical
counterparts, quantum decoherence and additional auxiliary qubits needed for
error tolerance routines have been huge barriers for quantum algorithms
efficient use. These restrictions lead us to search for ways to minimize
algorithms costs, i.e the number of quantum logical gates and the depth of the
circuit. For this, quantum circuit synthesis and quantum circuit optimization
techniques are explored. We studied the viability of using Projective
Simulation, a reinforcement learning technique, to tackle the problem of
quantum circuit synthesis for noise quantum computers with limited number of
qubits. The agent had the task of creating quantum circuits up to 5 qubits to
generate GHZ states in the IBM Tenerife (IBM QX4) quantum processor. Our
simulations demonstrated that the agent had a good performance but its capacity
for learning new circuits decreased as the number of qubits increased. | [
"O. M. Pires",
"E. I. Duzzioni",
"J. Marchi",
"R. Santiago"
] | [
"IBM"
] | "2021-04-27T16:11:27Z" | 2104.13297v1 |
Scalable Benchmarks for Gate-Based Quantum Computers | In the near-term "NISQ"-era of noisy, intermediate-scale, quantum hardware
and beyond, reliably determining the quality of quantum devices becomes
increasingly important: users need to be able to compare them with one another,
and make an estimate whether they are capable of performing a given task ahead
of time. In this work, we develop and release an advanced quantum benchmarking
framework in order to help assess the state of the art of current quantum
devices. Our testing framework measures the performance of universal quantum
devices in a hardware-agnostic way, with metrics that are aimed to facilitate
an intuitive understanding of which device is likely to outperform others on a
given task. This is achieved through six structured tests that allow for an
immediate, visual assessment of how devices compare. Each test is designed with
scalability in mind, making this framework not only suitable for testing the
performance of present-day quantum devices, but also of those released in the
foreseeable future. The series of tests are motivated by real-life scenarios,
and therefore emphasise the interplay between various relevant characteristics
of quantum devices, such as qubit count, connectivity, and gate and measurement
fidelity. We present the benchmark results of twenty-one different quantum
devices from IBM, Rigetti and IonQ. | [
"Arjan Cornelissen",
"Johannes Bausch",
"András Gilyén"
] | [
"IBM",
"Rigetti"
] | "2021-04-21T18:00:12Z" | 2104.10698v1 |
Doubling the size of quantum simulators by entanglement forging | Quantum computers are promising for simulations of chemical and physical
systems, but the limited capabilities of today's quantum processors permit only
small, and often approximate, simulations. Here we present a method, classical
entanglement forging, that harnesses classical resources to capture quantum
correlations and double the size of the system that can be simulated on quantum
hardware. Shifting some of the computation to classical post-processing allows
us to represent ten spin-orbitals on five qubits of an IBM Quantum processor to
compute the ground state energy of the water molecule in the most accurate
simulation to date. We discuss conditions for applicability of classical
entanglement forging and present a roadmap for scaling to larger problems. | [
"Andrew Eddins",
"Mario Motta",
"Tanvi P. Gujarati",
"Sergey Bravyi",
"Antonio Mezzacapo",
"Charles Hadfield",
"Sarah Sheldon"
] | [
"IBM"
] | "2021-04-20T19:32:37Z" | 2104.10220v1 |
Digital quantum simulation of beam splitters and squeezing with IBM
quantum computers | We present results on the digital quantum simulations of beam-splitter and
squeezing interactions. The bosonic hamiltonians are mapped to qubits and then
digitalized in order to implement them in the IBM quantum devices. We use error
mitigation and post-selection to achieve high-fidelity digital quantum
simulations of single-mode and two-mode interactions, as evidenced -- where
possible -- by full tomography of the resulting states. We achieve fidelities
above 90 \% in the case of single-mode squeezing with low squeezing values and
ranging from 60 \% to 90 \% for large squeezing and in the more complex
two-mode interactions. | [
"Paula Cordero Encinar",
"Andrés Agustí",
"Carlos Sabín"
] | [
"IBM"
] | "2021-04-19T16:43:41Z" | 2104.09442v3 |
Error rate reduction of single-qubit gates via noise-aware decomposition
into native gates | In the current era of Noisy Intermediate-Scale Quantum (NISQ) technology, the
practical use of quantum computers remains inhibited by our inability to aptly
decouple qubits from their environment to mitigate computational errors. In
this work, we introduce an approach by which knowledge of a qubit's initial
quantum state and the standard parameters describing its decoherence can be
leveraged to mitigate the noise present during the execution of a single-qubit
gate. We benchmark our protocol using cloud-based access to IBM quantum
processors. On ibmq_rome, we demonstrate a reduction of the single-qubit error
rate by $38\%$, from $1.6 \times 10 ^{-3}$ to $1.0 \times 10 ^{-3}$, provided
the initial state of the input qubit is known. On ibmq_bogota, we prove that
our protocol will never decrease gate fidelity, provided the system's $T_1$ and
$T_2$ times have not drifted above $100$ times their assumed values. The
protocol can be used to reduce quantum state preparation errors, as well as to
improve the fidelity of quantum circuits for which some knowledge of the
qubits' intermediate states can be inferred. This work presents a pathway to
using information about noise levels and quantum state distributions to
significantly reduce error rates associated with quantum gates via optimized
decomposition into native gates. | [
"Thomas J. Maldonado",
"Johannes Flick",
"Stefan Krastanov",
"Alexey Galda"
] | [
"IBM"
] | "2021-04-14T18:00:01Z" | 2104.07038v2 |
Fast quantum state reconstruction via accelerated non-convex programming | We propose a new quantum state reconstruction method that combines ideas from
compressed sensing, non-convex optimization, and acceleration methods. The
algorithm, called Momentum-Inspired Factored Gradient Descent (\texttt{MiFGD}),
extends the applicability of quantum tomography for larger systems. Despite
being a non-convex method, \texttt{MiFGD} converges \emph{provably} close to
the true density matrix at an accelerated linear rate, in the absence of
experimental and statistical noise, and under common assumptions. With this
manuscript, we present the method, prove its convergence property and provide
Frobenius norm bound guarantees with respect to the true density matrix. From a
practical point of view, we benchmark the algorithm performance with respect to
other existing methods, in both synthetic and real experiments performed on an
IBM's quantum processing unit. We find that the proposed algorithm performs
orders of magnitude faster than state of the art approaches, with the same or
better accuracy. In both synthetic and real experiments, we observed accurate
and robust reconstruction, despite experimental and statistical noise in the
tomographic data. Finally, we provide a ready-to-use code for state tomography
of multi-qubit systems. | [
"Junhyung Lyle Kim",
"George Kollias",
"Amir Kalev",
"Ken X. Wei",
"Anastasios Kyrillidis"
] | [
"IBM"
] | "2021-04-14T17:38:40Z" | 2104.07006v4 |
Qubit Sensing: A New Attack Model for Multi-programming Quantum
Computing | Noisy quantum computers suffer from readout or measurement error. It is a
classical bit-flip error due to which state "1" is read out as "0" and
vice-versa. The probability of readout error shows a state dependence i.e.,
flipping probability of state "1" may differ from flipping probability of state
"0". Moreover, the probability shows correlation across qubits. These
state-dependent and correlated error probability introduces a signature of
victim outputs on adversary output when two programs are run simultaneously on
the same quantum computer. This can be exploited to sense victim output which
may contain sensitive information. In this paper, we systematically show that
such readout error-dependent signatures exist and that an adversary can use
such signature to infer a user output. We experimentally demonstrate the attack
(inference) on 3 public IBM quantum computers. Using Jensen-Shannon Distance
(JSD) a measure for statistical inference, we show that our approach identifies
victim output with an accuracy of 96% on real hardware. We also present
randomized output flipping as a lightweight yet effective countermeasure to
thwart such information leakage attacks. Our analysis shows the countermeasure
incurs a minor penalty of 0.05% in terms of fidelity. | [
"Abdullah Ash Saki",
"Swaroop Ghosh"
] | [
"IBM"
] | "2021-04-13T02:15:50Z" | 2104.05899v1 |
Application of Quantum Machine Learning using the Quantum Kernel
Algorithm on High Energy Physics Analysis at the LHC | Quantum machine learning could possibly become a valuable alternative to
classical machine learning for applications in High Energy Physics by offering
computational speed-ups. In this study, we employ a support vector machine with
a quantum kernel estimator (QSVM-Kernel method) to a recent LHC flagship
physics analysis: $t\bar{t}H$ (Higgs boson production in association with a top
quark pair). In our quantum simulation study using up to 20 qubits and up to
50000 events, the QSVM-Kernel method performs as well as its classical
counterparts in three different platforms from Google Tensorflow Quantum, IBM
Quantum and Amazon Braket. Additionally, using 15 qubits and 100 events, the
application of the QSVM-Kernel method on the IBM superconducting quantum
hardware approaches the performance of a noiseless quantum simulator. Our study
confirms that the QSVM-Kernel method can use the large dimensionality of the
quantum Hilbert space to replace the classical feature space in realistic
physics datasets. | [
"Sau Lan Wu",
"Shaojun Sun",
"Wen Guan",
"Chen Zhou",
"Jay Chan",
"Chi Lung Cheng",
"Tuan Pham",
"Yan Qian",
"Alex Zeng Wang",
"Rui Zhang",
"Miron Livny",
"Jennifer Glick",
"Panagiotis Kl. Barkoutsos",
"Stefan Woerner",
"Ivano Tavernelli",
"Federico Carminati",
"Alberto Di Meglio",
"Andy C. Y. Li",
"Joseph Lykken",
"Panagiotis Spentzouris",
"Samuel Yen-Chi Chen",
"Shinjae Yoo",
"Tzu-Chieh Wei"
] | [
"IBM"
] | "2021-04-11T17:29:49Z" | 2104.05059v2 |
A systematic variational approach to band theory in a quantum computer | Quantum computers promise to revolutionize our ability to simulate molecules,
and cloud-based hardware is becoming increasingly accessible to a wide body of
researchers. Algorithms such as Quantum Phase Estimation and the Variational
Quantum Eigensolver are being actively developed and demonstrated in small
systems. However, extremely limited qubit count and low fidelity seriously
limit useful applications, especially in the crystalline phase, where compact
orbital bases are difficult to develop. To address this difficulty, we present
a hybrid quantum-classical algorithm to solve the band structure of any
periodic system described by an adequate tight-binding model. We showcase our
algorithm by computing the band structure of a simple-cubic crystal with one
$s$ and three $p$ orbitals per site (a simple model for Polonium) using
simulators with increasingly realistic levels of noise and culminating with
calculations on IBM quantum computers. Our results show that the algorithm is
reliable in a low-noise device, functional with low precision on present-day
noisy quantum computers, and displays a complexity that scales as $\Omega(M^3)$
with the number $M$ of tight-binding orbitals per unit-cell, similarly to its
classical counterparts. Our simulations offer a new insight into the
``quantum'' mindset and demonstrate how the algorithms under active development
today can be optimized in special cases, such as band structure calculations. | [
"Kyle Sherbert",
"Frank Cerasoli",
"Marco Buongiorno Nardelli"
] | [
"IBM"
] | "2021-04-07T21:50:19Z" | 2104.03409v2 |
Collective Neutrino Oscillations on a Quantum Computer | We calculate the energy levels of a system of neutrinos undergoing collective
oscillations as functions of an effective coupling strength and radial distance
from the neutrino source using the quantum Lanczos (QLanczos) algorithm
implemented on IBM Q quantum computer hardware. Our calculations are based on
the many-body neutrino interaction Hamiltonian introduced in Ref.\
\cite{Patwardhan2019}. We show that the system Hamiltonian can be separated
into smaller blocks, which can be represented using fewer qubits than those
needed to represent the entire system as one unit, thus reducing the noise in
the implementation on quantum hardware. We also calculate transition
probabilities of collective neutrino oscillations using a Trotterization method
which is simplified before subsequent implementation on hardware. These
calculations demonstrate that energy eigenvalues of a collective neutrino
system and collective neutrino oscillations can both be computed on quantum
hardware with certain simplification to within good agreement with exact
results. | [
"Kübra Yeter-Aydeniz",
"Shikha Bangar",
"George Siopsis",
"Raphael C. Pooser"
] | [
"IBM"
] | "2021-04-07T17:27:04Z" | 2104.03273v1 |
A quantum binary classifier based on cosine similarity | We introduce the quantum implementation of a binary classifier based on
cosine similarity between data vectors. The proposed quantum algorithm
evaluates the classifier on a set of data vectors with time complexity that is
logarithmic in the product of the set cardinality and the dimension of the
vectors. It is based just on a suitable state preparation like the retrieval
from a QRAM, a SWAP test circuit (two Hadamard gates and one Fredkin gate), and
a measurement process on a single qubit. Furthermore we present a simple
implementation of the considered classifier on the IBM quantum processor
ibmq_16_melbourne. Finally we describe the combination of the classifier with
the quantum version of a K-nearest neighbors algorithm within a hybrid
quantum-classical structure. | [
"Davide Pastorello",
"Enrico Blanzieri"
] | [
"IBM"
] | "2021-04-07T07:55:49Z" | 2104.02975v1 |
Demonstration of Shor's factoring algorithm for N=21 on IBM quantum
processors | We report a proof-of-concept demonstration of a quantum order-finding
algorithm for factoring the integer 21. Our demonstration involves the use of a
compiled version of the quantum phase estimation routine, and builds upon a
previous demonstration by Mart\'in-L\'{o}pez et al. in Nature Photonics 6, 773
(2012). We go beyond this work by using a configuration of approximate Toffoli
gates with residual phase shifts, which preserves the functional correctness
and allows us to achieve a complete factoring of N=21. We implemented the
algorithm on IBM quantum processors using only 5 qubits and successfully
verified the presence of entanglement between the control and work register
qubits, which is a necessary condition for the algorithm's speedup in general.
The techniques we employ may be useful in carrying out Shor's algorithm for
larger integers, or other algorithms in systems with a limited number of noisy
qubits. | [
"Unathi Skosana",
"Mark Tame"
] | [
"IBM"
] | "2021-03-25T14:11:18Z" | 2103.13855v3 |
Real-time quantum calculations of phase shifts using wave packet time
delays | We present a method to extract the phase shift of a scattering process using
the real-time evolution in the early and intermediate stages of the collision
in order to estimate the time delay of a wave packet. This procedure is
convenient when using noisy quantum computers for which the asymptotic
out-state behavior is unreachable. We demonstrate that the challenging Fourier
transforms involved in the state preparation and measurements can be
implemented in $1+1$ dimensions with current trapped ion devices and IBM
quantum computers. We compare quantum computation of the time delays obtained
in the one-particle quantum mechanics limit and the scalable quantum field
theory formulation with accurate numerical results. We discuss the finite
volume effects in the Wigner formula connecting time delays to phase shifts.
The results reported involve two- and four-qubit calculations, and we discuss
the possibility of larger scale computations in the near future. | [
"Erik Gustafson",
"Yingyue Zhu",
"Patrick Dreher",
"Norbert M. Linke",
"Yannick Meurice"
] | [
"IBM"
] | "2021-03-11T18:22:26Z" | 2103.06848v1 |
Quantum Algorithms in Cybernetics | A new method for simulation of a binary homogeneous Markov process using a
quantum computer was proposed. This new method allows using the distinguished
properties of the quantum mechanical systems -- superposition, entanglement and
probability calculations. Implementation of an algorithm based on this method
requires the creation of a new quantum logic gate, which creates entangled
state between two qubits. This is a two-qubit logic gate and it must perform a
predefined rotation over the X-axis for the qubit that acts as a target, where
the rotation accurately represents the transient probabilities for a given
Markov process. This gate fires only when the control qubit is in state |1>. It
is necessary to develop an algorithm, which uses the distribution for the
transient probabilities of the process in a simple and intuitive way and then
transform those into X-axis offsets. The creation of a quantum controlled n-th
root of X gate using only the existing basic quantum logic gates at the
available cloud platforms is possible, although the hardware devices are still
too noisy, which results in a significant measurement error increase. The IBM's
Yorktown 'bow-tie' back-end performs quite better than the 5-qubit T-shaped and
the 14-qubit Melbourne quantum processors in terms of quantum fidelity. The
simulation of the binary homogeneous Markov process on a real quantum processor
gives best results on the Vigo and Yorktown (both 5-qubit) back-ends with
Hellinger fidelity of near 0.82. The choice of the right quantum circuit, based
on the available hardware (topology, size, timing properties), would be the
approach for maximizing the fidelity. | [
"Petar Nikolov"
] | [
"IBM"
] | "2021-03-10T09:19:12Z" | 2103.05952v2 |
Investigating the Exchange of Ising Chains on a Digital Quantum Computer | The ferromagnetic state of an Ising chain can represent a two-fold degenerate
subspace or equivalently a logical qubit which is protected from excitations by
an energy gap. We study a a braiding-like exchange operation through the
movement of the state in the qubit subspace which resembles that of the
localized edge modes in a Kitaev chain. The system consists of two Ising chains
in a 1D geometry where the operation is simulated through the adiabatic time
evolution of the ground state. The time evolution is implemented via the
Suzuki-Trotter expansion on basic single- and two-qubit quantum gates using
IBM's Aer QASM simulator. The fidelity of the system is investigated as a
function of the evolution and system parameters to obtain optimum efficiency
and accuracy for different system sizes. Various aspects of the implementation
including the circuit depth, Trotterization error, and quantum gate errors
pertaining to the Noisy Intermediate-Scale Quantum (NISQ) hardware are
discussed as well. We show that the quantum gate errors, i.e. bit-flip, phase
errors, are the dominating factor in determining the fidelity of the system as
the Trotter error and the adiabatic condition are less restrictive even for
modest values of Trotter time steps. We reach an optimum fidelity $>99\%$ on
systems of up to $11$ sites per Ising chain and find that the most efficient
implementation of a single braiding-like operation for a fidelity above $90\%$
requires a circuit depth of the order of $\sim 10^{3}$ restricting the
individual gate errors to be less than $\sim 10^{-6}$ which is prohibited in
current NISQ hardware. | [
"Bassel Heiba Elfeky",
"Matthieu C. Dartiailh",
"S. M. Farzaneh",
"Javad Shabani"
] | [
"IBM"
] | "2021-03-09T15:50:41Z" | 2103.05502v1 |
Perfect quantum-state synchronization | We investigate the most general mechanisms that lead to perfect
synchronization of the quantum states of all subsystems of an open quantum
system starting from an arbitrary initial state. We provide a necessary and
sufficient condition for such "quantum-state synchronization", prove tight
lower bounds on the dimension of the environment's Hilbert space in two main
classes of quantum-state synchronizers, and give an analytical solution for
their construction. The functioning of the found quantum-state synchronizer of
two qubits is demonstrated experimentally on an IBM quantum computer and we
show that the remaining asynchronicity is a sensitive measure of the quantum
computer's imperfection. | [
"Jakub Czartowski",
"Ronny Müller",
"Karol Zyczkowski",
"Daniel Braun"
] | [
"IBM"
] | "2021-03-02T21:23:34Z" | 2103.02031v2 |
Whole-device entanglement in a 65-qubit superconducting quantum computer | The ability to generate large-scale entanglement is an important progenitor
of quantum information processing capability in noisy intermediate-scale
quantum (NISQ) devices. In this paper, we investigate the extent to which
entangled quantum states over large numbers of qubits can be prepared on
current superconducting quantum devices. We prepared native-graph states on the
IBM Quantum 65-qubit $\textit{ibmq_manhattan}$ device and the 53-qubit
$\textit{ibmq_rochester}$ device and applied quantum readout-error mitigation
(QREM). Connected entanglement graphs spanning each of the full devices were
detected, indicating bipartite entanglement over the whole of each device. The
application of QREM was shown to increase the observed entanglement within all
measurements, in particular, the detected number of entangled pairs of qubits
found within $\textit{ibmq_rochester}$ increased from 31 to 56 of the total 58
connected pairs. The results of this work indicate full bipartite entanglement
in two of the largest superconducting devices to date. | [
"Gary J. Mooney",
"Gregory A. L. White",
"Charles D. Hill",
"Lloyd C. L. Hollenberg"
] | [
"IBM"
] | "2021-02-23T07:07:22Z" | 2102.11521v2 |
Orchestrated Trios: Compiling for Efficient Communication in Quantum
Programs with 3-Qubit Gates | Current quantum computers are especially error prone and require high levels
of optimization to reduce operation counts and maximize the probability the
compiled program will succeed. These computers only support operations
decomposed into one- and two-qubit gates and only two-qubit gates between
physically connected pairs of qubits. Typical compilers first decompose
operations, then route data to connected qubits. We propose a new compiler
structure, Orchestrated Trios, that first decomposes to the three-qubit
Toffoli, routes the inputs of the higher-level Toffoli operations to groups of
nearby qubits, then finishes decomposition to hardware-supported gates.
This significantly reduces communication overhead by giving the routing pass
access to the higher-level structure of the circuit instead of discarding it. A
second benefit is the ability to now select an architecture-tuned Toffoli
decomposition such as the 8-CNOT Toffoli for the specific hardware qubits now
known after the routing pass. We perform real experiments on IBM Johannesburg
showing an average 35% decrease in two-qubit gate count and 23% increase in
success rate of a single Toffoli over Qiskit. We additionally compile many
near-term benchmark algorithms showing an average 344% increase in (or 4.44x)
simulated success rate on the Johannesburg architecture and compare with other
architecture types. | [
"Casey Duckering",
"Jonathan M. Baker",
"Andrew Litteken",
"Frederic T. Chong"
] | [
"IBM"
] | "2021-02-16T21:06:58Z" | 2102.08451v1 |
Pulse-engineered Controlled-V gate and its applications on
superconducting quantum device | In this paper, we demonstrate that, by employing OpenPulse design kit for IBM
superconducting quantum devices, the controlled-V gate (CV gate) can be
implemented in about half the gate time to the controlled-X (CX or CNOT gate)
and consequently 65.5\% reduced gate time compared to the CX-based
implementation of CV. Then, based on the theory of Cartan decomposition, we
characterize the set of all two-qubit gates implemented with only two or three
CV gates; using pulse-engineered CV gates enables us to implement these gates
with shorter gate time and possibly better gate fidelity than the CX-based one,
as actually demonstrated in two examples. Moreover, we showcase the improvement
of linearly-coupled three-qubit Toffoli gate, by implementing it with the
pulse-engineered CV gate, both in gate time and the averaged output-state
fidelity. These results imply the importance of our CV gate implementation
technique, which, as an additional option for the basis gate set design, may
shorten the overall computation time and consequently improve the precision of
several quantum algorithms executed on a real device. | [
"Takahiko Satoh",
"Shun Oomura",
"Michihiko Sugawara",
"Naoki Yamamoto"
] | [
"IBM"
] | "2021-02-11T16:56:56Z" | 2102.06117v3 |
Enabling Multi-programming Mechanism for Quantum Computing in the NISQ
Era | NISQ devices have several physical limitations and unavoidable noisy quantum
operations, and only small circuits can be executed on a quantum machine to get
reliable results. This leads to the quantum hardware under-utilization issue.
Here, we address this problem and improve the quantum hardware throughput by
proposing a Quantum Multi-programming Compiler (QuMC) to execute multiple
quantum circuits on quantum hardware simultaneously. This approach can also
reduce the total runtime of circuits. We first introduce a parallelism manager
to select an appropriate number of circuits to be executed at the same time.
Second, we present two different qubit partitioning algorithms to allocate
reliable partitions to multiple circuits - a greedy and a heuristic. Third, we
use the Simultaneous Randomized Benchmarking protocol to characterize the
crosstalk properties and consider them in the qubit partition process to avoid
the crosstalk effect during simultaneous executions. Finally, we enhance the
mapping transition algorithm to make circuits executable on hardware using a
decreased number of inserted gates. We demonstrate the performance of our QuMC
approach by executing circuits of different sizes on IBM quantum hardware
simultaneously. We also investigate this method on VQE algorithm to reduce its
overhead. | [
"Siyuan Niu",
"Aida Todri-Sanial"
] | [
"IBM"
] | "2021-02-10T08:46:16Z" | 2102.05321v3 |
Quantum Divide and Compute: Exploring The Effect of Different Noise
Sources | Our recent work (Ayral et al., 2020 IEEE Computer Society Annual Symposium on
VLSI (ISVLSI)) showed the first implementation of the Quantum Divide and
Compute (QDC) method, which allows to break quantum circuits into smaller
fragments with fewer qubits and shallower depth. QDC can thus deal with the
limited number of qubits and short coherence times of noisy, intermediate-scale
quantum processors. This article investigates the impact of different noise
sources -- readout error, gate error and decoherence -- on the success
probability of the QDC procedure. We perform detailed noise modeling on the
Atos Quantum Learning Machine, allowing us to understand tradeoffs and
formulate recommendations about which hardware noise sources should be
preferentially optimized. We describe in detail the noise models we used to
reproduce experimental runs on IBM's Johannesburg processor. This work also
includes a detailed derivation of the equations used in the QDC procedure to
compute the output distribution of the original quantum circuit from the output
distribution of its fragments. Finally, we analyze the computational complexity
of the QDC method for the circuit under study via tensor-network
considerations, and elaborate on the relation the QDC method with
tensor-network simulation methods. | [
"Thomas Ayral",
"François-Marie Le Régent",
"Zain Saleem",
"Yuri Alexeev",
"Martin Suchara"
] | [
"IBM"
] | "2021-02-07T12:18:04Z" | 2102.03788v1 |
Implementation of efficient quantum search algorithms on NISQ computers | Despite the advent of Grover's algorithm for the unstructured search, its
successful implementation on near-term quantum devices is still limited. We
apply three strategies to reduce the errors associated with implementing
quantum search algorithms. Our improved search algorithms have been implemented
on the IBM quantum processors. Using them, we demonstrate three- and four-qubit
search algorithm with higher average success probabilities compared to previous
works. We present the successful execution of the five-qubit search on the IBM
quantum processor for the first time. The results have been benchmarked using
degraded ratio, which is the ratio between the experimental and the theoretical
success probabilities. The fast decay of the degraded ratio supports our
divide-and-conquer strategy. Our proposed strategies are also useful for
implementation of quantum search algorithms in the post-NISQ era. | [
"Kun Zhang",
"Pooja Rao",
"Kwangmin Yu",
"Hyunkyung Lim",
"Vladimir Korepin"
] | [
"IBM"
] | "2021-02-02T22:30:30Z" | 2102.01783v2 |
Testing Scalable Bell Inequalities for Quantum Graph States on IBM
Quantum Devices | Testing and verifying imperfect multi-qubit quantum devices are important as
such noisy quantum devices are widely available today. Bell inequalities are
known useful for testing and verifying the quality of the quantum devices from
their nonlocal quantum states and local measurements. There have been many
experiments demonstrating the violations of Bell inequalities but they are
limited in the number of qubits and the types of quantum states. We report
violations of Bell inequalities on IBM Quantum devices based on the scalable
and robust inequalities maximally violated by graph states as proposed by
Baccari et al. (Ref.[1]). The violations are obtained from the quantum states
of path graphs up to 57 and 21 qubits on the 65-qubit and 27-qubit IBM Quantum
devices, respectively, and from those of star graphs up to 8 and 7 qubits with
error mitigation on the same devices. We are able to show violations of the
inequalities on various graph states by constructing low-depth quantum circuits
producing them, and by applying the readout error mitigation technique. We also
point out that quantum circuits for star graph states of size N can be realized
with circuits of depth $O(\sqrt n)$ on subdivided honeycomb lattices which are
the topology of the 65-qubit IBM Quantum device. Our experiments show
encouraging results on the ability of existing quantum devices to prepare
entangled quantum states, and provide experimental evidences on the benefit of
scalable Bell inequalities for testing them. | [
"Bo Yang",
"Rudy Raymond",
"Hiroshi Imai",
"Hyungseok Chang",
"Hidefumi Hiraishi"
] | [
"IBM"
] | "2021-01-25T18:46:19Z" | 2101.10307v1 |
A Trailhead for Quantum Simulation of SU(3) Yang-Mills Lattice Gauge
Theory in the Local Multiplet Basis | Maintaining local interactions in the quantum simulation of gauge field
theories relegates most states in the Hilbert space to be unphysical --
theoretically benign, but experimentally difficult to avoid. Reformulations of
the gauge fields can modify the ratio of physical to gauge-variant states often
through classically preprocessing the Hilbert space and modifying the
representation of the field on qubit degrees of freedom. This paper considers
the implications of representing SU(3) Yang-Mills gauge theory on a lattice of
irreducible representations in both a global basis of projected global quantum
numbers and a local basis in which controlled-plaquette operators support
efficient time evolution. Classically integrating over the internal gauge space
at each vertex (e.g., color isospin and color hypercharge) significantly
reduces both the qubit requirements and the dimensionality of the unphysical
Hilbert space. Initiating tuning procedures that may inform future calculations
at scale, the time evolution of one- and two-plaquettes are implemented on one
of IBM's superconducting quantum devices, and early benchmark quantities are
identified. The potential advantages of qudit environments, with either
constrained 2D hexagonal or 1D nearest-neighbor internal state connectivity,
are discussed for future large-scale calculations. | [
"Anthony Ciavarella",
"Natalie Klco",
"Martin J. Savage"
] | [
"IBM"
] | "2021-01-25T16:41:56Z" | 2101.10227v2 |
Generation and verification of 27-qubit Greenberger-Horne-Zeilinger
states in a superconducting quantum computer | Generating and detecting genuine multipartite entanglement (GME) of sizeable
quantum states prepared on physical devices is an important benchmark for
highlighting the progress of near-term quantum computers. A common approach to
certify GME is to prepare a Greenberger-Horne-Zeilinger (GHZ) state and measure
a GHZ fidelity of at least 0.5. We measure the fidelities using multiple
quantum coherences of GHZ states on 11 to 27 qubits prepared on the IBM Quantum
ibmq_montreal device. Combinations of quantum readout error mitigation (QREM)
and parity verification error detection are applied to the states. A fidelity
of $0.546 \pm 0.017$ was recorded for a 27-qubit GHZ state when QREM was used,
demonstrating GME across the full device with a confidence level of 98.6%. We
benchmarked the effect of parity verification on GHZ fidelity for two GHZ state
preparation embeddings on the heavy-hexagon architecture. The results show that
the effect of parity verification, while relatively modest, led to a detectable
improvement of GHZ fidelity. | [
"Gary J. Mooney",
"Gregory A. L. White",
"Charles D. Hill",
"Lloyd C. L. Hollenberg"
] | [
"IBM"
] | "2021-01-22T04:36:33Z" | 2101.08946v3 |
Noisy intermediate scale quantum simulation of time dependent
Hamiltonians | Quantum computers are expected to help us to achieve accurate simulation of
the dynamics of many-body quantum systems. However, the limitations of current
NISQ devices prevents us from realising this goal today. Recently an algorithm
for performing quantum simulations called quantum assisted simulator has been
proposed that promises realization on current experimental devices. In this
work, we extend the quantum assisted simulator to simulate the dynamics of a
class of time-dependent Hamiltonians. We show that the quantum assisted
simulator is easier to implement as well as can realize multi-qubit
interactions and challenging driving protocols that are difficult with other
existing methods. We demonstrate this for a time-dependent Hamiltonian on the
IBM Quantum Experience cloud quantum computer by showing superior performance
of the quantum assisted simulator compared to Trotterization and variational
quantum simulation. Further, we demonstrate the capability to simulate the
dynamics of Hamiltonians consisting of 10000 qubits. Our results indicate that
quantum assisted simulator is a promising algorithm for current term quantum
hardware. | [
"Jonathan Wei Zhong Lau",
"Kishor Bharti",
"Tobias Haug",
"Leong Chuan Kwek"
] | [
"IBM"
] | "2021-01-19T15:20:03Z" | 2101.07677v2 |
Assessing the Precision of Quantum Simulation of Many-Body Effects in
Atomic Systems using the Variational Quantum Eigensolver Algorithm | The emerging field of quantum simulation of many-body systems is widely
recognized as a very important application of quantum computing. A crucial step
towards its realization in the context of many-electron systems requires a
rigorous quantum mechanical treatment of the different interactions. In this
pilot study, we investigate the physical effects beyond the mean-field
approximation, known as electron correlation, in the ground state energies of
atomic systems using the classical-quantum hybrid variational quantum
eigensolver (VQE) algorithm. To this end, we consider three isoelectronic
species, namely Be, Li-, and B+. This unique choice spans three classes, a
neutral atom, an anion, and a cation. We have employed the unitary
coupled-cluster (UCC) ansatz to perform a rigorous analysis of two very
important factors that could affect the precision of the simulations of
electron correlation effects within a basis, namely mapping and backend
simulator. We carry out our all-electron calculations with four such basis
sets. The results obtained are compared with those calculated by using the full
configuration interaction, traditional coupled-cluster and the UCC methods, on
a classical computer, to assess the precision of our results. A salient feature
of the study involves a detailed analysis to find the number of shots (the
number of times a VQE algorithm is repeated to build statistics) required for
calculations with IBM Qiskit's QASM simulator backend, which mimics an ideal
quantum computer. When more qubits become available, our study will serve as
among the first steps taken towards computing other properties of interest to
various applications such as new physics beyond the Standard Model of
elementary particles and atomic clocks using the VQE algorithm. | [
" Sumeet",
"V. S. Prasannaa",
"B. P. Das",
"B. K. Sahoo"
] | [
"IBM"
] | "2021-01-14T11:26:32Z" | 2101.05553v2 |
Fair Sampling Error Analysis on NISQ Devices | We study the status of fair sampling on Noisy Intermediate Scale Quantum
(NISQ) devices, in particular the IBM Q family of backends. Using the recently
introduced Grover Mixer-QAOA algorithm for discrete optimization, we generate
fair sampling circuits to solve six problems of varying difficulty, each with
several optimal solutions, which we then run on twenty backends across the IBM
Q system. For a given circuit evaluated on a specific set of qubits, we
evaluate: how frequently the qubits return an optimal solution to the problem,
the fairness with which the qubits sample from all optimal solutions, and the
reported hardware error rate of the qubits. To quantify fairness, we define a
novel metric based on Pearson's $\chi^2$ test. We find that fairness is
relatively high for circuits with small and large error rates, but drops for
circuits with medium error rates. This indicates that structured errors
dominate in this regime, while unstructured errors, which are random and thus
inherently fair, dominate in noisier qubits and longer circuits. Our results
show that fairness can be a powerful tool for understanding the intricate web
of errors affecting current NISQ hardware. | [
"John Golden",
"Andreas Bärtschi",
"Daniel O'Malley",
"Stephan Eidenbenz"
] | [
"IBM"
] | "2021-01-08T23:48:53Z" | 2101.03258v2 |
Modeling and mitigation of cross-talk effects in readout noise with
applications to the Quantum Approximate Optimization Algorithm | We introduce a correlated measurement noise model that can be efficiently
described and characterized, and which admits effective noise-mitigation on the
level of marginal probability distributions. Noise mitigation can be performed
up to some error for which we derive upper bounds. Characterization of the
model is done efficiently using Diagonal Detector Overlapping Tomography -- a
generalization of the recently introduced Quantum Overlapping Tomography to the
problem of reconstruction of readout noise with restricted locality. The
procedure allows to characterize $k$-local measurement cross-talk on $N$-qubit
device using $O(k2^klog(N))$ circuits containing random combinations of X and
identity gates. We perform experiments on 15 (23) qubits using IBM's
(Rigetti's) devices to test both the noise model and the error-mitigation
scheme, and obtain an average reduction of errors by a factor $>22$ ($>5.5$)
compared to no mitigation. Interestingly, we find that correlations in the
measurement noise do not correspond to the physical layout of the device.
Furthermore, we study numerically the effects of readout noise on the
performance of the Quantum Approximate Optimization Algorithm (QAOA). We
observe in simulations that for numerous objective Hamiltonians, including
random MAX-2-SAT instances and the Sherrington-Kirkpatrick model, the
noise-mitigation improves the quality of the optimization. Finally, we provide
arguments why in the course of QAOA optimization the estimates of the local
energy (or cost) terms often behave like uncorrelated variables, which greatly
reduces sampling complexity of the energy estimation compared to the
pessimistic error analysis. We also show that similar effects are expected for
Haar-random quantum states and states generated by shallow-depth random
circuits. | [
"Filip B. Maciejewski",
"Flavio Baccari",
"Zoltán Zimborás",
"Michał Oszmaniec"
] | [
"IBM",
"Rigetti"
] | "2021-01-07T02:19:58Z" | 2101.02331v3 |
Simulating the dynamics of braiding of Majorana zero modes using an IBM
quantum computer | We simulate the dynamics of braiding Majorana zero modes on an IBM Quantum
computer. We find the native quantum gates introduce too much noise to observe
braiding. Instead, we use Qiskit Pulse to develop scaled two-qubit quantum
gates that better match the unitary time evolution operator and enable us to
observe braiding. This work demonstrates that quantum computers can be used for
simulation, and highlights the use of pulse-level control for programming
quantum computers and constitutes the first experimental evidence of braiding
via dynamical Hamiltonian evolution. | [
"John P. T. Stenger",
"Nicholas T. Bronn",
"Daniel J. Egger",
"David Pekker"
] | [
"IBM"
] | "2020-12-21T19:59:50Z" | 2012.11660v2 |
Application of Quantum Machine Learning using the Quantum Variational
Classifier Method to High Energy Physics Analysis at the LHC on IBM Quantum
Computer Simulator and Hardware with 10 qubits | One of the major objectives of the experimental programs at the LHC is the
discovery of new physics. This requires the identification of rare signals in
immense backgrounds. Using machine learning algorithms greatly enhances our
ability to achieve this objective. With the progress of quantum technologies,
quantum machine learning could become a powerful tool for data analysis in high
energy physics. In this study, using IBM gate-model quantum computing systems,
we employ the quantum variational classifier method in two recent LHC flagship
physics analyses: $t\bar{t}H$ (Higgs boson production in association with a top
quark pair) and $H\rightarrow\mu^{+}\mu^{-}$ (Higgs boson decays to two muons,
probing the Higgs boson couplings to second-generation fermions). We have
obtained early results with 10 qubits on the IBM quantum simulator and the IBM
quantum hardware. With small training samples of 100 events on the quantum
simulator, the quantum variational classifier method performs similarly to
classical algorithms such as SVM (support vector machine) and BDT (boosted
decision tree), which are often employed in LHC physics analyses. On the
quantum hardware, the quantum variational classifier method has shown promising
discrimination power, comparable to that on the quantum simulator. This study
demonstrates that quantum machine learning has the ability to differentiate
between signal and background in realistic physics datasets. We foresee the
usage of quantum machine learning in future high-luminosity LHC physics
analyses, including measurements of the Higgs boson self-couplings and searches
for dark matter. | [
"Sau Lan Wu",
"Jay Chan",
"Wen Guan",
"Shaojun Sun",
"Alex Wang",
"Chen Zhou",
"Miron Livny",
"Federico Carminati",
"Alberto Di Meglio",
"Andy C. Y. Li",
"Joseph Lykken",
"Panagiotis Spentzouris",
"Samuel Yen-Chi Chen",
"Shinjae Yoo",
"Tzu-Chieh Wei"
] | [
"IBM"
] | "2020-12-21T18:39:36Z" | 2012.11560v2 |
When Machine Learning Meets Quantum Computers: A Case Study | Along with the development of AI democratization, the machine learning
approach, in particular neural networks, has been applied to wide-range
applications. In different application scenarios, the neural network will be
accelerated on the tailored computing platform. The acceleration of neural
networks on classical computing platforms, such as CPU, GPU, FPGA, ASIC, has
been widely studied; however, when the scale of the application consistently
grows up, the memory bottleneck becomes obvious, widely known as memory-wall.
In response to such a challenge, advanced quantum computing, which can
represent 2^N states with N quantum bits (qubits), is regarded as a promising
solution. It is imminent to know how to design the quantum circuit for
accelerating neural networks. Most recently, there are initial works studying
how to map neural networks to actual quantum processors. To better understand
the state-of-the-art design and inspire new design methodology, this paper
carries out a case study to demonstrate an end-to-end implementation. On the
neural network side, we employ the multilayer perceptron to complete image
classification tasks using the standard and widely used MNIST dataset. On the
quantum computing side, we target IBM Quantum processors, which can be
programmed and simulated by using IBM Qiskit. This work targets the
acceleration of the inference phase of a trained neural network on the quantum
processor. Along with the case study, we will demonstrate the typical procedure
for mapping neural networks to quantum circuits. | [
"Weiwen Jiang",
"Jinjun Xiong",
"Yiyu Shi"
] | [
"IBM"
] | "2020-12-18T17:06:11Z" | 2012.10360v1 |
Gate-Based Circuit Designs For Quantum Adder Inspired Quantum Random
Walks on Superconducting Qubits | Quantum Random Walks, which have drawn much attention over the past few
decades for their distinctly non-classical behavior, is a promising subfield
within Quantum Computing. Theoretical framework and applications for these
walks have seen many great mathematical advances, with experimental
demonstrations now catching up. In this study, we examine the viability of
implementing Coin Quantum Random Walks using a Quantum Adder based Shift
Operator, with quantum circuit designs specifically for superconducting qubits.
We focus on the strengths and weaknesses of these walks, particularly circuit
depth, gate count, connectivity requirements, and scalability. We propose and
analyze a novel approach to implementing boundary conditions for these walks,
demonstrating the technique explicitly in one and two dimensions. And finally,
we present several fidelity results from running our circuits on IBM's quantum
volume 32 `Toronto' chip, showcasing the extent to which these NISQ devices can
currently handle quantum walks. | [
"Daniel Koch",
"Michael Samodurov",
"Andrew Projansky",
"Paul M. Alsing"
] | [
"IBM"
] | "2020-12-18T14:34:18Z" | 2012.10268v2 |
QGo: Scalable Quantum Circuit Optimization Using Automated Synthesis | The current phase of quantum computing is in the Noisy Intermediate-Scale
Quantum (NISQ) era. On NISQ devices, two-qubit gates such as CNOTs are much
noisier than single-qubit gates, so it is essential to minimize their count.
Quantum circuit synthesis is a process of decomposing an arbitrary unitary into
a sequence of quantum gates, and can be used as an optimization tool to produce
shorter circuits to improve overall circuit fidelity. However, the
time-to-solution of synthesis grows exponentially with the number of qubits. As
a result, synthesis is intractable for circuits on a large qubit scale.
In this paper, we propose a hierarchical, block-by-block optimization
framework, QGo, for quantum circuit optimization. Our approach allows an
exponential cost optimization to scale to large circuits. QGo uses a
combination of partitioning and synthesis: 1) partition the circuit into a
sequence of independent circuit blocks; 2) re-generate and optimize each block
using quantum synthesis; and 3) re-compose the final circuit by stitching all
the blocks together. We perform our analysis and show the fidelity improvements
in three different regimes: small-size circuits on real devices, medium-size
circuits on noise simulations, and large-size circuits on analytical models.
Using a set of NISQ benchmarks, we show that QGo can reduce the number of CNOT
gates by 29.9% on average and up to 50% when compared with industrial compilers
such as t|ket>. When executed on the IBM Athens system, shorter depth leads to
higher circuit fidelity. We also demonstrate the scalability of our QGo
technique to optimize circuits of 60+ qubits. Our technique is the first
demonstration of successfully employing and scaling synthesis in the
compilation toolchain for large circuits. Overall, our approach is robust for
direct incorporation in production compiler toolchains. | [
"Xin-Chuan Wu",
"Marc Grau Davis",
"Frederic T. Chong",
"Costin Iancu"
] | [
"IBM"
] | "2020-12-17T18:54:38Z" | 2012.09835v5 |
On the experimental feasibility of quantum state reconstruction via
machine learning | We determine the resource scaling of machine learning-based quantum state
reconstruction methods, in terms of inference and training, for systems of up
to four qubits when constrained to pure states. Further, we examine system
performance in the low-count regime, likely to be encountered in the tomography
of high-dimensional systems. Finally, we implement our quantum state
reconstruction method on an IBM Q quantum computer, and compare against both
unconstrained and constrained MLE state reconstruction. | [
"Sanjaya Lohani",
"Thomas A. Searles",
"Brian T. Kirby",
"Ryan T. Glasser"
] | [
"IBM"
] | "2020-12-17T07:51:47Z" | 2012.09432v3 |
Relaxed Peephole Optimization: A Novel Compiler Optimization for Quantum
Circuits | In this paper, we propose a novel quantum compiler optimization, named
relaxed peephole optimization (RPO) for quantum computers. RPO leverages the
single-qubit state information that can be determined statically by the
compiler. We define that a qubit is in a basis state when, at a given point in
time, its state is either in the X-, Y-, or Z-basis. When basis qubits are used
as inputs to quantum gates, there exist opportunities for strength reduction,
which replaces quantum operations with equivalent but less expensive ones.
Compared to the existing peephole optimization for quantum programs, the
difference is that our proposed optimization does not require an identical
unitary matrix, thereby named `relaxed' peephole optimization. We also extend
our approach to optimize the quantum gates when some input qubits are in known
pure states. Both optimizations, namely the Quantum Basis-state Optimization
(QBO) and the Quantum Pure-state Optimization (QPO), are implemented in the
IBM's Qiskit transpiler. Our experimental results show that our proposed
optimization pass is fast and effective. The circuits optimized with our
compiler optimizations obtain up to 18.0% (11.7% on average) fewer CNOT gates
and up to 8.2% (7.1% on average) lower transpilation time than that of the most
aggressive optimization level in the Qiskit compiler. When running on real
quantum computers, the success rates of 3-qubit quantum phase estimation
algorithm improve by 2.30X due to the reduced gate counts. | [
"Ji Liu",
"Luciano Bello",
"Huiyang Zhou"
] | [
"IBM"
] | "2020-12-14T17:03:06Z" | 2012.07711v1 |
Embedding classical dynamics in a quantum computer | We develop a framework for simulating measure-preserving, ergodic dynamical
systems on a quantum computer. Our approach provides a new operator-theoretic
representation of classical dynamics by combining ergodic theory with quantum
information science. The resulting quantum embedding of classical dynamics
(QECD) enables efficient simulation of spaces of classical observables with
exponentially large dimension using a quadratic number of quantum gates. The
QECD framework is based on a quantum feature map for representing classical
states by density operators on a reproducing kernel Hilbert space, $\mathcal H
$, and an embedding of classical observables into self-adjoint operators on
$\mathcal H$. In this scheme, quantum states and observables evolve unitarily
under the lifted action of Koopman evolution operators of the classical system.
Moreover, by virtue of the reproducing property of $\mathcal H$, the quantum
system is pointwise-consistent with the underlying classical dynamics. To
achieve an exponential quantum computational advantage, we project the state of
the quantum system to a density matrix on a $2^n$-dimensional tensor product
Hilbert space associated with $n$ qubits. By employing discrete Fourier-Walsh
transforms, the evolution operator of the finite-dimensional quantum system is
factorized into tensor product form, enabling implementation through a quantum
circuit of size $O(n)$. Furthermore, the circuit features a state preparation
stage, also of size $O(n)$, and a quantum Fourier transform stage of size
$O(n^2)$, which makes predictions of observables possible by measurement in the
standard computational basis. We prove theoretical convergence results for
these predictions as $n\to\infty$. We present simulated quantum circuit
experiments in Qiskit Aer, as well as actual experiments on the IBM Quantum
System One. | [
"Dimitrios Giannakis",
"Abbas Ourmazd",
"Philipp Pfeffer",
"Joerg Schumacher",
"Joanna Slawinska"
] | [
"IBM"
] | "2020-12-11T03:25:48Z" | 2012.06097v3 |
Transmon platform for quantum computing challenged by chaotic
fluctuations | From the perspective of many body physics, the transmon qubit architectures
currently developed for quantum computing are systems of coupled nonlinear
quantum resonators. A significant amount of intentional frequency detuning
(disorder) is required to protect individual qubit states against the
destabilizing effects of nonlinear resonator coupling. Here we investigate the
stability of this variant of a many-body localized (MBL) phase for system
parameters relevant to current quantum processors of two different types, those
using untunable qubits (IBM type) and those using tunable qubits (Delft/Google
type). Applying three independent diagnostics of localization theory -- a
Kullback-Leibler analysis of spectral statistics, statistics of many-body wave
functions (inverse participation ratios), and a Walsh transform of the
many-body spectrum -- we find that these computing platforms are dangerously
close to a phase of uncontrollable chaotic fluctuations. | [
"Christoph Berke",
"Evangelos Varvelis",
"Simon Trebst",
"Alexander Altland",
"David P. DiVincenzo"
] | [
"IBM"
] | "2020-12-10T19:00:03Z" | 2012.05923v2 |
Quantum-Enhanced Machine Learning for Covid-19 and Anderson Insulator
Predictions | Quantum Machine Learning (QML) algorithms to solve classifications problems
have been made available thanks to recent advancements in quantum computation.
While the number of qubits are still relatively small, they have been used for
"quantum enhancement" of machine learning. An important question is related to
the efficacy of such protocols. We evaluate this efficacy using common baseline
data sets, in addition to recent coronavirus spread data as well as the quantum
metal-insulator transition in three dimensions. For the computation, we used
the 16 qubit IBM quantum computer. We find that the "quantum enhancement" is
not generic and fails for more complex machine learning tasks. | [
"Paul-Aymeric McRae",
"Michael Hilke"
] | [
"IBM"
] | "2020-12-07T06:33:20Z" | 2012.03472v1 |
Topological two-dimensional Floquet lattice on a single superconducting
qubit | Previous theoretical and experimental research has shown that current NISQ
devices constitute powerful platforms for analogue quantum simulation. With the
exquisite level of control offered by state-of-the-art quantum computers, we
show that one can go further and implement a wide class of Floquet
Hamiltonians, or timedependent Hamiltonians in general. We then implement a
single-qubit version of these models in the IBM Quantum Experience and
experimentally realize a temporal version of the Bernevig-Hughes-Zhang Chern
insulator. From our data we can infer the presence of a topological transition,
thus realizing an earlier proposal of topological frequency conversion by
Martin, Refael, and Halperin. Our study highlights promises and limitations
when studying many-body systems through multi-frequency driving of quantum
computers. | [
"Daniel Malz",
"Adam Smith"
] | [
"IBM"
] | "2020-12-02T19:03:18Z" | 2012.01459v2 |
Quantum Computing for Atomic and Molecular Resonances | The complex-scaling method can be used to calculate molecular resonances
within the Born-Oppenheimer approximation, assuming the electronic coordinates
are dilated independently of the nuclear coordinates. With this method, one
will calculate the complex energy of a non-Hermitian Hamiltonian, whose real
part is associated with the resonance position and the imaginary part is the
inverse of the lifetime. In this study, we propose techniques to simulate
resonances on a quantum computer. First, we transformed the scaled molecular
Hamiltonian to second-quantization and then used the Jordan-Wigner
transformation to transform the scaled Hamiltonian to the qubit space. To
obtain the complex eigenvalues, we introduce the Direct Measurement method,
which is applied to obtain the resonances of a simple one-dimensional model
potential that exhibits pre-dissociating resonances analogous to those found in
diatomic molecules. Finally, we applied the method to simulate the resonances
of the H$_2^-$ molecule. Numerical results from the IBM Qiskit simulators and
IBM quantum computers verify our techniques. | [
"Teng Bian",
"Sabre Kais"
] | [
"IBM"
] | "2020-11-27T21:39:23Z" | 2011.13999v3 |
Reducing the CNOT count for Clifford+T circuits on NISQ architectures | While mapping a quantum circuit to the physical layer one has to consider the
numerous constraints imposed by the underlying hardware architecture.
Connectivity of the physical qubits is one such constraint that restricts
two-qubit operations, such as CNOT, to "connected" qubits. SWAP gates can be
used to place the logical qubits on admissible physical qubits, but they entail
a significant increase in CNOT-count. In this paper we consider the problem of
reducing the CNOT-count in Clifford+T circuits on connectivity constrained
architectures, like noisy intermediate-scale quantum (NISQ) computing devices.
We "slice" the circuit at the position of Hadamard gates and "build" the
intermediate {CNOT,T} sub-circuits using Steiner trees, significantly improving
on previous methods. We compared the performance of our algorithms while
mapping different benchmark and random circuits to some well-known
architectures such as 9-qubit square grid, 16-qubit square grid, Rigetti
16-qubit Aspen, 16-qubit IBM QX5 and 20-qubit IBM Tokyo. Our methods give less
CNOT-count compared to Qiskit and TKET transpiler as well as using SWAP gates.
Assuming most of the errors in a NISQ circuit implementation are due to CNOT
errors, then our method would allow circuits with few times more CNOT gates be
reliably implemented than the previous methods would permit. | [
"Vlad Gheorghiu",
"Jiaxin Huang",
"Sarah Meng Li",
"Michele Mosca",
"Priyanka Mukhopadhyay"
] | [
"IBM",
"Rigetti"
] | "2020-11-24T16:35:05Z" | 2011.12191v4 |
Non-Equilibrium Dynamics of a Dissipative Two-Site Hubbard Model
Simulated on IBM Quantum Computers | Many-body physics is one very well suited field for testing quantum
algorithms and for finding working heuristics on present quantum computers. We
have investigated the non-equilibrium dynamics of one- and two-electron
systems, which are coupled to an environment that introduces decoherence and
dissipation. In our approach, the electronic system is represented in the
framework of a two-site Hubbard model while the environment is modelled by a
spin bath. To simulate the non-equilibrium population probabilities of the
different states on a quantum computer we have encoded the electronic states
and environmental degrees of freedom into qubits and ancilla qubits (bath),
respectively. The total evolution time was divided into short time intervals,
during which the system evolves. After each of these time steps, the system
interacts with ancilla qubits representing the bath in thermal equilibrium. We
have specifically studied spin baths leading to both, unital and non-unital
dynamics of the electronic system and have found that electron correlations
clearly enhance the electron transfer rates in the latter case. For short time
periods, the simulation on the quantum computer is found to be in very good
agreement with the exact results if error mitigation methods are applied. Our
method to simulate also non-unitary time-evolution on a quantum computer can be
well extended to simulate electronic systems in correlated spin baths as well
as in bosonic and fermionic baths. | [
"Sabine Tornow",
"Wolfgang Gehrke",
"Udo Helmbrecht"
] | [] | "2020-11-22T16:49:50Z" | 2011.11059v3 |
General error mitigation for quantum circuits | A general method to mitigate the effect of errors in quantum circuits is
outlined. The method is developed in sight of characteristics that an ideal
method should possess and to ameliorate an existing method which only mitigates
state preparation and measurement errors. The method is tested on different IBM
Q quantum devices, using randomly generated circuits with up to four qubits. A
large majority of results show significant error mitigation. | [
"Manpreet Singh Jattana",
"Fengping Jin",
"Hans De Raedt",
"Kristel Michielsen"
] | [
"IBM"
] | "2020-11-21T20:21:14Z" | 2011.10860v1 |
Many-body Hierarchy of Dissipative Timescales in a Quantum Computer | We show that current noisy quantum computers are ideal platforms for the
simulation of quantum many-body dynamics in generic open systems. We
demonstrate this using the IBM Quantum Computer as an experimental platform for
confirming the theoretical prediction from [Phys. Rev. Lett.124, 100604 (2020)]
of an emergent hierarchy of relaxation timescales of many-body observables
involving different numbers of qubits. Using different protocols, we leverage
the intrinsic dissipation of the machine responsible for gate errors, to
implement a quantum simulation of generic (i.e. structureless) local
dissipative interactions. | [
"Oscar Emil Sommer",
"Francesco Piazza",
"David J. Luitz"
] | [
"IBM"
] | "2020-11-17T19:00:00Z" | 2011.08853v1 |
Quantum simulations of molecular systems with intrinsic atomic orbitals | Quantum simulations of molecular systems on quantum computers often employ
minimal basis sets of Gaussian orbitals. In comparison with more realistic
basis sets, quantum simulations employing minimal basis sets require fewer
qubits and quantum gates, but yield results of lower accuracy. A natural
strategy to achieve more accurate results is to increase the basis set size,
which in turn requires increasing the number of qubits and quantum gates. Here
we explore the use of intrinsic atomic orbitals (IAOs) in quantum simulations
of molecules, to improve the accuracy of energies and properties at the same
computational cost required by a minimal basis. We investigate ground-state
energies and one- and two-body density operators in the framework of the
variational quantum eigensolver, employing and comparing different Ans\"{a}tze.
We also demonstrate the use of this approach in the calculation of ground- and
excited-states energies of small molecules by a combination of quantum
algorithms, using IBM Quantum computers. | [
"Stefano Barison",
"Davide Emilio Galli",
"Mario Motta"
] | [
"IBM"
] | "2020-11-16T18:01:44Z" | 2011.08137v3 |
Exploiting Quantum Teleportation in Quantum Circuit Mapping | Quantum computers are constantly growing in their number of qubits, but
continue to suffer from restrictions such as the limited pairs of qubits that
may interact with each other. Thus far, this problem is addressed by mapping
and moving qubits to suitable positions for the interaction (known as quantum
circuit mapping). However, this movement requires additional gates to be
incorporated into the circuit, whose number should be kept as small as possible
since each gate increases the likelihood of errors and decoherence.
State-of-the-art mapping methods utilize swapping and bridging to move the
qubits along the static paths of the coupling map---solving this problem
without exploiting all means the quantum domain has to offer. In this paper, we
propose to additionally exploit quantum teleportation as a possible
complementary method. Quantum teleportation conceptually allows to move the
state of a qubit over arbitrary long distances with constant
overhead---providing the potential of determining cheaper mappings. The
potential is demonstrated by a case study on the IBM Q Tokyo architecture which
already shows promising improvements. With the emergence of larger quantum
computing architectures, quantum teleportation will become more effective in
generating cheaper mappings. | [
"Stefan Hillmich",
"Alwin Zulehner",
"Robert Wille"
] | [
"IBM"
] | "2020-11-14T15:03:24Z" | 2011.07314v1 |
Lipkin model on a quantum computer | Atomic nuclei are important laboratories for exploring and testing new
insights into the universe, such as experiments to directly detect dark matter
or explore properties of neutrinos. The targets of interest are often heavy,
complex nuclei that challenge our ability to reliably model them (as well as
quantify the uncertainty of those models) with classical computers. Hence there
is great interest in applying quantum computation to nuclear structure for
these applications. As an early step in this direction, especially with regards
to the uncertainties in the relevant quantum calculations, we develop circuits
to implement variational quantum eigensolver (VQE) algorithms for the
Lipkin-Meshkov-Glick model, which is often used in the nuclear physics
community as a testbed for many-body methods. We present quantum circuits for
VQE for two and three particles and discuss the construction of circuits for
more particles. Implementing the VQE for a two-particle system on the IBM
Quantum Experience, we identify initialization and two-qubit gates as the
largest sources of error. We find that error mitigation procedures reduce the
errors in the results significantly, but additional quantum hardware
improvements are needed for quantum calculations to be sufficiently accurate to
be competitive with the best current classical methods. | [
"Michael J. Cervia",
"A. B. Balantekin",
"S. N. Coppersmith",
"Calvin W. Johnson",
"Peter J. Love",
"C. Poole",
"K. Robbins",
"M. Saffman"
] | [
"IBM"
] | "2020-11-08T22:36:43Z" | 2011.04097v4 |
Testing of flag-based fault-tolerance on IBM quantum devices | It is hard to achieve a theoretical quantum advantage on NISQ devices.
Besides the attempts to reduce error using error mitigation and dynamical
decoupling, small quantum error correction and fault-tolerant schemes that
reduce the high overhead of traditional schemes have also been proposed.
According to the recent advancements in fault tolerance, it is possible to
minimize the number of ancillary qubits using flags. While implementing those
schemes is still impossible, it is worthwhile to bridge the gap between the
NISQ era and the FTQC era. Here, we introduce a benchmarking method to test
fault-tolerant quantum error correction with flags for the [[5,1,3]] code on
NISQ devices. Based on results obtained using IBM's qasm simulator and its
15-qubit Melbourne processor, we show that this flagged scheme is testable on
NISQ devices by checking how much the subspace of intermediate state overlaps
with the expected state in the presence of noise. | [
"Anirudh Lanka"
] | [
"IBM"
] | "2020-11-06T08:07:53Z" | 2011.03224v3 |
Entangled state generation via quantum walks with multiple coins | Generation of entangled state is of paramount importance both from quantum
theoretical foundation and technology applications. Entanglement swapping
provides an efficient method to generate entanglement in quantum communication
protocols. However, perfect Bell measurements for qudits, the key to
entanglement swapping, have been proven impossible to achieve by using only
linear elements and particle detectors. To avoid this bottleneck, we propose a
novel scheme to generate entangled state including two-qubit entangled state,
two-qudit entangled state, three-qubit GHZ state and three-qudit GHZ state
between several designate parties via the model of quantum walks with multiple
coins. Then we conduct experimental realization of Bell state and three-qubit
GHZ state between several designate parties on IBM quantum platform and the
result has high fidelity by preforming quantum tomography. In the end, we give
a practical application of our scheme in multiparty quantum secret sharing. | [
"Meng Li",
"Yun Shang"
] | [
"IBM"
] | "2020-11-03T11:39:40Z" | 2011.01643v2 |
Unified approach to data-driven quantum error mitigation | Achieving near-term quantum advantage will require effective methods for
mitigating hardware noise. Data-driven approaches to error mitigation are
promising, with popular examples including zero-noise extrapolation (ZNE) and
Clifford data regression (CDR). Here we propose a novel, scalable error
mitigation method that conceptually unifies ZNE and CDR. Our approach, called
variable-noise Clifford data regression (vnCDR), significantly outperforms
these individual methods in numerical benchmarks. vnCDR generates training data
first via near-Clifford circuits (which are classically simulable) and second
by varying the noise levels in these circuits. We employ a noise model obtained
from IBM's Ourense quantum computer to benchmark our method. For the problem of
estimating the energy of an 8-qubit Ising model system, vnCDR improves the
absolute energy error by a factor of 33 over the unmitigated results and by
factors 20 and 1.8 over ZNE and CDR, respectively. For the problem of
correcting observables from random quantum circuits with 64 qubits, vnCDR
improves the error by factors of 2.7 and 1.5 over ZNE and CDR, respectively. | [
"Angus Lowe",
"Max Hunter Gordon",
"Piotr Czarnik",
"Andrew Arrasmith",
"Patrick J. Coles",
"Lukasz Cincio"
] | [
"IBM"
] | "2020-11-02T17:56:02Z" | 2011.01157v2 |
Experimental tests of density matrix's properties-based complementarity
relations | Bohr's complementarity principle is of fundamental historic and conceptual
importance for Quantum Mechanics (QM), and states that, with a given
experimental apparatus configuration, one can observe either the wave-like or
the particle-like character of a quantum system, but not both. However, it was
eventually realized that these dual behaviors can both manifest partially in
the same experimental setup, and, using ad hoc proposed measures for the wave
and particle aspects of the quanton, complementarity relations were proposed
limiting how strong these manifestations can be. Recently, a formalism was
developed and quantifiers for the particleness and waveness of a quantum system
were derived from the mathematical structure of QM entailed in the density
matrix's basic properties ($\rho\ge 0$, $\mathrm{Tr}\rho=1$). In this article,
using IBM Quantum Experience quantum computers, we perform experimental tests
of these complementarity relations applied to a particular class of one-qubit
quantum states and also for random quantum states of one, two, and three
qubits. | [
"Mauro B. Pozzobom",
"Marcos L. W. Basso",
"Jonas Maziero"
] | [
"IBM"
] | "2020-10-29T20:27:49Z" | 2011.00723v3 |
Bipartite quantum measurements with optimal single-sided
distinguishability | We analyse orthogonal bases in a composite $N\times N$ Hilbert space
describing a bipartite quantum system and look for a basis with optimal
single-sided mutual state distinguishability. This condition implies that in
each subsystem the $N^2$ reduced states form a regular simplex of a maximal
edge length, defined with respect to the trace distance. In the case $N=2$ of a
two-qubit system our solution coincides with the elegant joint measurement
introduced by Gisin. We derive explicit expressions of an analogous
constellation for $N=3$ and provide a general construction of $N^2$ states
forming such an optimal basis in ${\cal H}_N \otimes {\cal H}_N$. Our
construction is valid for all dimensions for which a symmetric informationally
complete (SIC) generalized measurement is known. Furthermore, we show that the
one-party measurement that distinguishes the states of an optimal basis of the
composite system leads to a local quantum state tomography with a linear
reconstruction formula. Finally, we test the introduced tomographical scheme on
a complete set of three mutually unbiased bases for a single qubit using two
different IBM machines. | [
"Jakub Czartowski",
"Karol Życzkowski"
] | [
"IBM"
] | "2020-10-28T10:30:35Z" | 2010.14868v3 |
A Unified Framework for Quantum Supervised Learning | Quantum machine learning is an emerging field that combines machine learning
with advances in quantum technologies. Many works have suggested great
possibilities of using near-term quantum hardware in supervised learning.
Motivated by these developments, we present an embedding-based framework for
supervised learning with trainable quantum circuits. We introduce both explicit
and implicit approaches. The aim of these approaches is to map data from
different classes to separated locations in the Hilbert space via the quantum
feature map. We will show that the implicit approach is a generalization of a
recently introduced strategy, so-called \textit{quantum metric learning}. In
particular, with the implicit approach, the number of separated classes (or
their labels) in supervised learning problems can be arbitrarily high with
respect to the number of given qubits, which surpasses the capacity of some
current quantum machine learning models. Compared to the explicit method, this
implicit approach exhibits certain advantages over small training sizes.
Furthermore, we establish an intrinsic connection between the explicit approach
and other quantum supervised learning models. Combined with the implicit
approach, this connection provides a unified framework for quantum supervised
learning. The utility of our framework is demonstrated by performing both
noise-free and noisy numerical simulations. Moreover, we have conducted
classification testing with both implicit and explicit approaches using several
IBM Q devices. | [
"Nhat A. Nghiem",
"Samuel Yen-Chi Chen",
"Tzu-Chieh Wei"
] | [
"IBM"
] | "2020-10-25T18:43:13Z" | 2010.13186v2 |
Adaptive quantum state tomography with iterative particle filtering | Several Bayesian estimation based heuristics have been developed to perform
quantum state tomography (QST). Their ability to quantify uncertainties using
region estimators and include a priori knowledge of the experimentalists makes
this family of methods an attractive choice for QST. However, specialized
techniques for pure states do not work well for mixed states and vice versa. In
this paper, we present an adaptive particle filter (PF) based QST protocol
which improves the scaling of fidelity compared to nonadaptive Bayesian schemes
for arbitrary multi-qubit states. This is due to the protocol's unabating
perseverance to find the states's diagonal bases and more systematic handling
of enduring problems in popular PF methods relating to the subjectivity of
informative priors and the invalidity of particles produced by resamplers.
Numerical examples and implementation on IBM quantum devices demonstrate
improved performance for arbitrary quantum states and the application readiness
of our proposed scheme. | [
"Syed Muhammad Kazim",
"Ahmad Farooq",
"Junaid ur Rehman",
"Hyundong Shin"
] | [
"IBM"
] | "2020-10-24T11:00:33Z" | 2010.12867v2 |
Adaptive Circuit Learning for Quantum Metrology | Quantum sensing is an important application of emerging quantum technologies.
We explore whether a hybrid system of quantum sensors and quantum circuits can
surpass the classical limit of sensing. In particular, we use optimization
techniques to search for encoder and decoder circuits that scalably improve
sensitivity under given application and noise characteristics. Our approach
uses a variational algorithm that can learn a quantum sensing circuit based on
platform-specific control capacity, noise, and signal distribution. The quantum
circuit is composed of an encoder which prepares the optimal sensing state and
a decoder which gives an output distribution containing information of the
signal. We optimize the full circuit to maximize the Signal-to-Noise Ratio
(SNR). Furthermore, this learning algorithm can be run on real hardware
scalably by using the "parameter-shift" rule which enables gradient evaluation
on noisy quantum circuits, avoiding the exponential cost of quantum system
simulation. We demonstrate up to 13.12x SNR improvement over existing fixed
protocol (GHZ), and 3.19x Classical Fisher Information (CFI) improvement over
the classical limit on 15 qubits using IBM quantum computer. More notably, our
algorithm overcomes the decreasing performance of existing entanglement-based
protocols with increased system sizes. | [
"Ziqi Ma",
"Pranav Gokhale",
"Tian-Xing Zheng",
"Sisi Zhou",
"Xiaofei Yu",
"Liang Jiang",
"Peter Maurer",
"Frederic T. Chong"
] | [
"IBM"
] | "2020-10-17T03:21:22Z" | 2010.08702v3 |
Error-robust quantum logic optimization using a cloud quantum computer
interface | We describe an experimental effort designing and deploying error-robust
single-qubit operations using a cloud-based quantum computer and analog-layer
programming access. We design numerically-optimized pulses that implement
target operations and exhibit robustness to various error processes including
dephasing noise, instabilities in control amplitudes, and crosstalk. Pulse
optimization is performed using a flexible optimization package incorporating a
device model and physically-relevant constraints (e.g. bandwidth limits on the
transmission lines of the dilution refrigerator housing IBM Quantum hardware).
We present techniques for conversion and calibration of physical Hamiltonian
definitions to pulse waveforms programmed via Qiskit Pulse and compare
performance against hardware default DRAG pulses on a five-qubit device.
Experimental measurements reveal default DRAG pulses exhibit coherent errors an
order of magnitude larger than tabulated randomized-benchmarking measurements;
solutions designed to be robust against these errors outperform
hardware-default pulses for all qubits across multiple metrics. Experimental
measurements demonstrate performance enhancements up to: $\sim10\times$
single-qubit gate coherent-error reduction; $\sim5\times$ average
coherent-error reduction across a five qubit system; $\sim10\times$ increase in
calibration window to one week of valid pulse calibration; $\sim12\times$
reduction gate-error variability across qubits and over time; and up to
$\sim9\times$ reduction in single-qubit gate error (including crosstalk) in the
presence of fully parallelized operations. Randomized benchmarking reveals
error rates for Clifford gates constructed from optimized pulses consistent
with tabulated $T_{1}$ limits, and demonstrates a narrowing of the distribution
of outcomes over randomizations associated with suppression of coherent-errors. | [
"Andre R. R. Carvalho",
"Harrison Ball",
"Michael J. Biercuk",
"Michael R. Hush",
"Felix Thomsen"
] | [
"IBM"
] | "2020-10-15T22:47:16Z" | 2010.08057v1 |
Subsets and Splits