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Two- and three-body calculations within the dominantly orbital state
method: The dominantly orbital state method allows a semiclassical description of
quantum systems. At the origin, it was developed for two-body relativistic
systems. Here, the method is extended to treat two-body Hamiltonians and
systems with three identical particles, in $D\ge 2$ dimensions, with arbitrary
kinetic energy and potential. This method is very easy to implement and can be
used in a large variety of fields. Results are expected to be reliable for
large values of the orbital angular momentum and small radial excitations, but
information about the whole spectrum can also be obtained in some very specific
cases.
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quant-ph
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Simulating the flight gate assignment problem on a trapped ion quantum
computer: We study the flight gate assignment problem on IonQ's Aria trapped ion
quantum computer using the variational quantum eigensolver. Utilizing the
conditional value at risk as an aggregation function, we demonstrate that
current trapped ion quantum hardware is able to obtain good solutions for this
combinatorial optimization problem with high probability. In particular, we run
the full variational quantum eigensolver for small instances and we perform
inference runs for larger systems, demonstrating that current and near-future
quantum hardware is suitable for addressing combinatorial optimization
problems.
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quant-ph
|
Coherent optical and spin spectroscopy of nanoscale Pr3+:Y2O3: We investigate the potential for optical quantum technologies of Pr3+:Y2O3 in
the form of monodisperse spherical nanoparticles. We measured optical
inhomogeneous lines of 27 GHz, and optical homogeneous linewidths of 108 kHz
and 315 kHz in particles of 400 nm and 150 nm average diameters respectively
for the 1D2(0)--> 3H4(0) transition at 1.4 K. Furthermore, ground state and 1D2
excited state hyperfine structures in Y2O3 are here for the first time
determined by spectral hole burning and modeled by complete Hamiltonian
calculations. Ground-state spin transitions have energies of 5.99 MHz and 10.42
MHz for which we demonstrate spin inhomogeneous linewidths of 42 and 45 kHz
respectively. Spin T2 up to 880 microseconds was obtained for the +-3/2-->+-5/2
transition at 10.42 MHz, a value which exceeds that of bulk Pr3+ doped crystals
so far reported. These promising results confirm nanoscale Pr3+:Y2O3 as a very
appealing candidate to integrate quantum devices. In particular, we discuss
here the possibility of using this material for realizing spin photon
interfaces emitting indistinguishable single photons.
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quant-ph
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Energy transport and optimal design of noisy Platonic quantum networks: Optimal transport is one of the primary goals for designing efficient quantum
networks. In this work, the maximum transport is investigated for
three-dimensional quantum networks with Platonic geometries affected by
dephasing and dissipative Markovian noise. The network and the environmental
characteristics corresponding the optimal design are obtained and investigated
for five Platonic networks with 4, 6, 8, 12, and 20 number of sites that one of
the sites is connected to a sink site through a dissipative process. Such
optimal designs could have various applications like switching and multiplexing
in quantum circuits.
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quant-ph
|
NMR Techniques for Quantum Control and Computation: Fifty years of developments in nuclear magnetic resonance (NMR) have resulted
in an unrivaled degree of control of the dynamics of coupled two-level quantum
systems. This coherent control of nuclear spin dynamics has recently been taken
to a new level, motivated by the interest in quantum information processing.
NMR has been the workhorse for the experimental implementation of quantum
protocols, allowing exquisite control of systems up to seven qubits in size.
Here, we survey and summarize a broad variety of pulse control and tomographic
techniques which have been developed for and used in NMR quantum computation.
Many of these will be useful in other quantum systems now being considered for
implementation of quantum information processing tasks.
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quant-ph
|
Resonance Fluorescence Spectrum of a Trapped Ion Undergoing Quantum
Jumps: We experimentally investigate the resonance fluorescence spectrum of single
171Yb and 172Yb ions which are laser cooled to the Lamb-Dicke regime in a
radiofrequency trap. While the fluorescence scattering of 172Yb is continuous,
the 171Yb fluorescence is interrupted by quantum jumps because a nonvanishing
rate of spontaneous transitions leads to electron shelving in the metastable
hyperfine sublevel 2D3/2(F=2). The average duration of the resulting dark
periods can be varied by changing the intensity of a repumping laser field.
Optical heterodyne detection is employed to analyze the fluorescence spectrum
near the Rayleigh elastic scattering peak. It is found that the stochastic
modulation of the fluorescence emission by quantum jumps gives rise to a
Lorentzian component in the fluorescence spectrum, and that the linewidth of
this component varies according to the average duration of the dark
fluorescence periods. The experimental observations are in quantitative
agreement with theoretical predictions.
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quant-ph
|
Ultrafast modulation of vibrational polaritons for controlling the
quantum field statistics at mid-infrared frequencies: Controlling the quantum field statistics of confined light is a long-standing
goal in integrated photonics. We show that by coupling molecular vibrations
with a confined mid-infrared cavity vacuum, the photocount and quadrature field
statistics of the cavity field can be reversibly manipulated over
sub-picosecond timescales. The mechanism involves changing the cavity resonance
frequency through a modulation of the dielectric response of the cavity
materials using femtosecond UV pulses. For a single anharmonic molecular
vibration in an infrared cavity under ultrastrong coupling conditions, the
pulsed modulation of the cavity frequency can adiabatically produce
mid-infrared light that is simultaneously sub-Poissonian and quadrature
squeezed, depending on the dipolar behavior of the vibrational mode. For a
vibration-cavity system in strong coupling, non-adiabatic polariton excitations
can be produced after the frequency modulation pulse is over, when the system
is initially prepared in the lower polariton state. We propose design
principles for the generation of mid-infrared quantum light by analyzing the
dependence of the cavity field statistics on the shape of the electric dipole
function of the molecule, the cavity detuning at the modulation peak and the
anharmonicity of the Morse potential. Feasible experimental implementations of
the modulation scheme are suggested. This work paves the way for the
development of molecule-based mid-infrared quantum optical devices at room
temperature.
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quant-ph
|
Galoisian Approach to integrability of Schrödinger Equation: In this paper, we examine the non-relativistic stationary Schr\"odinger
equation from a differential Galois-theoretic perspective. The main algorithmic
tools are pullbacks of second order ordinary linear differential operators, so
as to achieve rational function coefficients ("algebrization"), and Kovacic's
algorithm for solving the resulting equations. In particular, we use this
Galoisian approach to analyze Darboux transformations, Crum iterations and
supersymmetric quantum mechanics. We obtain the ground states, eigenvalues,
eigenfunctions, eigenstates and differential Galois groups of a large class of
Schr\"odinger equations, e.g. those with exactly solvable and shape invariant
potentials (the terms are defined within). Finally, we introduce a method for
determining when exact solvability is possible.
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quant-ph
|
Mechanical interpretation of the Klein-Gordon equation: The substratum for physics can be seen microscopically as an ideal fluid
pierced in all directions by the straight vortex filaments. Small disturbances
of an isolated filament are considered. The Klein-Gordon equation without mass
corresponds to elastic stretching of the filament. The wave function has the
meaning of the curve's position vector. The mass part of the Klein-Gordon
equation describes the rotation of the helical curve about the screw axis due
to the hydrodynamic self-induction of the bent vortex filament.
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quant-ph
|
Probabilistic quantum teleportation in the presence of noise: We extend the research program initiated in [Phys. Rev. A 92, 012338 (2015)],
where we restricted our attention to noisy deterministic teleportation
protocols, to noisy probabilistic (conditional) protocols. Our main goal now is
to study how we can increase the fidelity of the teleported state in the
presence of noise by working with probabilistic protocols. We work with several
scenarios involving the most common types of noise in realistic implementations
of quantum communication tasks and find many cases where adding more noise to
the probabilistic protocol increases considerably the fidelity of the
teleported state, without decreasing the probability of a successful run of the
protocol. Also, there are cases where the entanglement of the channel
connecting Alice and Bob leading to the greatest fidelity is not maximal.
Moreover, there exist cases where the optimal fidelity for the probabilistic
protocols are greater than the maximal fidelity (2/3) achievable by using only
classical resources, while the optimal ones for the deterministic protocols
under the same conditions lie below this limit. This result clearly illustrates
that in some cases we can only get a truly quantum teleportation if we use
probabilistic instead of deterministic protocols.
|
quant-ph
|
Perfect quantum excitation energy transport via single edge perturbation
in a complete network: We consider quantum excitation energy transport (EET) in a network of
two-state nodes in the Markovian approximation by employing the Lindblad
formulation. We find that EET from an initial site, where the excitation is
inserted to the sink, is generally inefficient due to the inhibition of
transport by localization of the excitation wave packet in a symmetric,
fully-connected network. We demonstrate that the EET efficiency can be
significantly increased up to %100 by perturbing hopping transport between the
initial node and the one connected directly to the sink, while the rate of
energy transport is highest at a finite value of the hopping parameter. We also
show that prohibiting hopping between the other nodes which are not directly
linked to the sink does not improve the efficiency. We show that external
dephasing noise in the network plays a constructive role for EET in the
presence of localization in the network, while in the absence of localization
it reduces the efficiency of EET.
|
quant-ph
|
Levinson theorem in two dimensions: A two-dimensional analogue of Levinson's theorem for nonrelativistic quantum
mechanics is established, which relates the phase shift at threshold(zero
momentum) for the $m$th partial wave to the total number of bound states with
angular momentum $m\hbar(m=0,1,2,...)$ in an attractive central field.
|
quant-ph
|
Introduction to the theory of open quantum systems: This manuscript is an edited and refined version of the lecture script for a
one-semester graduate course given originally at the PhD school in the
Institute of Physics of Polish Academy of Sciences in the Spring/Summer
semester of 2022. The course expects from the student only a basic knowledge on
graduate-level quantum mechanics. The script itself is largely self-contained
and could be used as a textbook on the topic of open quantum systems. The
program of this course is based on a novel approach to the description of the
open system dynamics: It is showed how the environmental degrees of freedom
coupled to the system can be represented by a multi-component quasi-stochastic
process. Using this representation one constructs the super-quasi-cumulant (or
super-qumulant) expansion for the system's dynamical map -- a parametrization
that naturally lends itself for the development of a robust and practical
perturbation theory. Thus, even an experienced researcher might find this
manuscript of some interest.
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quant-ph
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The quantum moment problem and bounds on entangled multi-prover games: We study the quantum moment problem: Given a conditional probability
distribution together with some polynomial constraints, does there exist a
quantum state rho and a collection of measurement operators such that (i) the
probability of obtaining a particular outcome when a particular measurement is
performed on rho is specified by the conditional probability distribution, and
(ii) the measurement operators satisfy the constraints. For example, the
constraints might specify that some measurement operators must commute.
We show that if an instance of the quantum moment problem is unsatisfiable,
then there exists a certificate of a particular form proving this. Our proof is
based on a recent result in algebraic geometry, the noncommutative
Positivstellensatz of Helton and McCullough [Trans. Amer. Math. Soc.,
356(9):3721, 2004].
A special case of the quantum moment problem is to compute the value of
one-round multi-prover games with entangled provers. Under the conjecture that
the provers need only share states in finite-dimensional Hilbert spaces, we
prove that a hierarchy of semidefinite programs similar to the one given by
Navascues, Pironio and Acin [Phys. Rev. Lett., 98:010401, 2007] converges to
the entangled value of the game. It follows that the class of languages
recognized by a multi-prover interactive proof system where the provers share
entanglement is recursive.
|
quant-ph
|
Experimental super-Heisenberg quantum metrology with indefinite gate
order: The precision of quantum metrology is widely believed to be restricted by the
Heisenberg limit, corresponding to a root mean square error that is inversely
proportional to the number of independent processes probed in an experiment, N.
In the past, some proposals have challenged this belief, for example using
non-linear interactions among the probes. However, these proposals turned out
to still obey the Heisenberg limit with respect to other relevant resources,
such as the total energy of the probes. Here, we present a photonic
implementation of a quantum metrology protocol surpassing the Heisenberg limit
by probing two groups of independent processes in a superposition of two
alternative causal orders. Each process creates a phase space displacement, and
our setup is able to estimate a geometric phase associated to two sets of N
displacements with an error that falls quadratically with N. Our results only
require a single-photon probe with an initial energy that is independent of N.
Using a superposition of causal orders outperforms every setup where the
displacements are probed in a definite order. Our experiment features the
demonstration of indefinite causal order in a continuous-variable system, and
opens up the experimental investigation of quantum metrology setups boosted by
indefinite causal order.
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quant-ph
|
Non-Hermitian wave packet approximation for coupled two-level systems in
weak and intense fields: We introduce an accurate non-Hermitian Schr\"odinger-type approximation of
Bloch optical equations for two-level systems. This approximation provides a
complete description of the excitation, relaxation and decoherence dynamics in
both weak and strong laser fields. In this approach, it is sufficient to
propagate the wave function of the quantum system instead of the density
matrix, providing that relaxation and dephasing are taken into account via
automatically-adjusted time-dependent gain and decay rates. The developed
formalism is applied to the problem of scattering and absorption of
electromagnetic radiation by a thin layer comprised of interacting two-level
emitters.
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quant-ph
|
Testable non-linearity through entanglement measurement: A model of correlated particles described by a generalized probability theory
is suggested whose dynamics is subject to a non-linear version of Schr\"odinger
equation. Such equations arise in many different contexts, most notably in the
proposals for the gravitationally induced collapse of wave function. Here, it
is shown that the consequence of the connection demonstrates a possible
deviation of the theory from the standard formulation of quantum mechanics in
the probability prediction of experiments. The links are identified from the
fact that the analytic solution of the equation is given by Dirichlet
eigenvalues which can be expressed by generalized trigonometric function.
Consequently, modified formulation of Born's rule is obtained by relating the
event probability of the measuement to an arbitrary exponent of the modulus of
the eigenvalue solution. Such system, which is subject to the non-linear
dynamic equation, illustrates the violation of the Clauser-Hore-Shimony-Holt
inequality proportional to the degree of the non-linearity as it can be tested
by a real experiment. Depending upon the degree, it is found that the violation
can go beyond Tsirelson bound $2\sqrt{2}$ and reaches to the value of nonlocal
box.
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quant-ph
|
Entangled Markov Chains generated by Symmetric Channels: A notion of entangled Markov chain was introduced by Accardi and Fidaleo in
the context of quantum random walk. They proved that, in the finite dimensional
case, the corresponding states have vanishing entropy density, but they did not
prove that they are entangled.
In the present note this entropy result is extended to the infinite
dimensional case under the assumption of finite speed of hopping. Then the
entanglement problem is discussed for spin 1/2, entangled Markov chains
generated by a binary symmetric channel with hopping probability $1-q$. The von
Neumann entropy of these states, restricted on a sublattice is explicitly
calculated and shown to be independent of the size of the sublattice. This is a
new, purely quantum, phenomenon.
Finally the entanglement property between the sublattices ${\cal
A}(\{0,1,...,N\})$ and ${\cal A}(\{N+1\})$ is investigated using the PPT
criterium. It turns out that, for $q\neq 0,1,{1/2}$ the states are non
separable, thus truly entangled, while for $q=0,1,{1/2}$, they are separable.
|
quant-ph
|
An Algorithm for Constructing Polynomial Systems Whose Solution Space
Characterizes Quantum Circuits: An algorithm and its first implementation in C# are presented for assembling
arbitrary quantum circuits on the base of Hadamard and Toffoli gates and for
constructing multivariate polynomial systems over the finite field Z_2 arising
when applying the Feynman's sum-over-paths approach to quantum circuits. The
matrix elements determined by a circuit can be computed by counting the number
of common roots in Z_2 for the polynomial system associated with the circuit.
To determine the number of solutions in Z_2 for the output polynomial system,
one can use the Groebner bases method and the relevant algorithms for computing
Groebner bases.
|
quant-ph
|
Non-classicality thresholds for multiqubit states - numerical analysis: States that strongly violate Bell's inequalities are required in many quantum
informational protocols as, for example, in cryptography, secret sharing and
the reduction of communication complexity. We investigate families of such
states with a numerical method which allows to reveal non-classicality even
without direct knowledge of Bell's inequalities for the given problem. An
extensive set of numerical results is presented and discussed.
|
quant-ph
|
An artificial game with equilibrium state of entangled strategy: Using the representation introduced in \cite{frame}, an artificial game in
quantum strategy space is proposed and studied. Although it has well-known
classical correspondence, which has classical mixture strategy Nash Equilibrium
states, the equilibrium state of this quantum game is an entangled strategy
(operator) state of the two players. By discovering such behavior, it partially
shows the independent meaning of the new representation. The idea of
entanglement of strategies, instead of quantum states, is proposed, and in some
sense, such entangled strategy state can be regarded as a cooperative behavior
between game players.
|
quant-ph
|
Determining the validity of solutions of the meanfield Bogoliubov-de
Gennes equation: We provide a general methodology to directly determine the validity of the
meanfield Bogoliubov-de Gennes equation. In particular we apply this
methodology to the case of two component interacting ultracold Fermi gases. As
an example, we consider the case of population imbalance, between the two
components, in the strongly attractive interacting regime, where meanfield
results predict Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states. For these
states we find at finite temperatures that the assumptions used to derive the
Bogoliubov-de Gennes equation are invalid.
|
quant-ph
|
Quantum conformal symmetries for spacetimes in superposition: Without a complete theory of quantum gravity, the question of how quantum
fields and quantum particles behave in a superposition of spacetimes seems
beyond the reach of theoretical and experimental investigations. Here we use an
extension of the quantum reference frame formalism to address this question for
the Klein-Gordon field residing on a superposition of conformally equivalent
metrics. Based on the group structure of ``quantum conformal transformations'',
we construct an explicit quantum operator that can map states describing a
quantum field on a superposition of spacetimes to states representing a quantum
field with a superposition of masses on a Minkowski background. This
constitutes an extended symmetry principle, namely invariance under quantum
conformal transformations. The latter allows to build an understanding of
superpositions of diffeomorphically non-equivalent spacetimes by relating them
to a more intuitive superposition of quantum fields on curved spacetime.
Furthermore, it can be used to import the phenomenon of particle production in
curved spacetime to its conformally equivalent counterpart, thus revealing new
features in modified Minkowski spacetime.
|
quant-ph
|
Multi-particle entanglement and generalized N-particle teleportation
using quantum statistical correlations: Construction of multi-particle entangled states and direct teleportation of
N-(spin 1/2) particles are important areas of quantum information processing. A
number of different schemes which have been presented already, address the
problem through controlled teleportation. In this article, a criterion based on
standard quantum statistical correlations employed in the many body virial
expansions is used to determine maximum entanglement for a N-particle state.
These states remain entangled through proper traces to states for a smaller
number of particles and can be generalized for arbitrary number of particles.
It is shown that they are quite useful in generalized, N-particle, direct
teleportation. The corresponding quantum gates are also indicated for
teleportation schemes from simple computational basis states.
|
quant-ph
|
Fault tolerant Quantum Information Processing with Holographic control: We present a fault-tolerant semi-global control strategy for universal
quantum computers. We show that N-dimensional array of qubits where only
(N-1)-dimensional addressing resolution is available is compatible with
fault-tolerant universal quantum computation. What is more, we show that
measurements and individual control of qubits are required only at the
boundaries of the fault-tolerant computer, i.e. holographic fault-tolerant
quantum computation. Our model alleviates the heavy physical conditions on
current qubit candidates imposed by addressability requirements and represents
an option to improve their scalability.
|
quant-ph
|
Classical simulation of two spin-$S$ singlet state correlations
involving spin measurements: We give a classical protocol to exactly simulate quantum correlations implied
by a spin-$s$ singlet state for the infinite sequence of spins satisfying $(2s
+ 1) = 2^{n}$, in the worst-case scenario, where $n$ is a positive integer. The
class of measurements we consider here are only those corresponding to spin
observables. The required amount of communication is found to be $log_{2}d$
where $d = 2s + 1$ is the dimension of the spin-$s$ Hilbert space.
|
quant-ph
|
Quantum cryptography based on Wheeler's delayed choice experiment: We describe a cryptographic protocol in which Wheeler's delayed choice
experiment is used to generate the key distribution. The protocol, which uses
photons polarized only along one axis, is secure against general attacks.
|
quant-ph
|
Optimizing the number of CNOT gates in one-dimensional nearest-neighbor
quantum Fourier transform circuit: The physical limitations of quantum hardware often require nearest-neighbor
qubit structures, in which two-qubit gates are required to construct
nearest-neighbor quantum circuits. However, two-qubit gates are considered a
major cost of quantum circuits because of their high error rate as compared
with single-qubit gates. The controlled-not (CNOT) gate is the typical choice
of a two-qubit gate for universal quantum circuit implementation together with
the set of single-qubit gates. In this study, we construct a one-dimensional
nearest-neighbor circuit of quantum Fourier transform (QFT), which is one of
the most frequently used quantum algorithms. Compared with previous studies on
n-qubit one-dimensional nearest-neighbor QFT circuits, it is found that our
method reduces the number of CNOT gates by ~60%. Additionally, we showed that
our results for the one-dimensional nearest-neighbor circuit can be applied to
quantum amplitude estimation.
|
quant-ph
|
Uncontrolled disorder effects in fabricating photonic quantum simulators
on a kagome geometry: A projected-entangled pair state versus exact
digonalization analysis: We propose a flexible numerical framework for extracting the energy spectra
and photon transfer dynamics of a unit kagome cell with disordered
cavity-cavity couplings under realistic experimental conditions. A
projected-entangled pair state (PEPS) ansatz to the many-photon wavefunction
allows to gain a detailed understanding of the effects of undesirable disorder
in fabricating well-controlled and scalable photonic quantum simulators. The
correlation functions associated with the propagation of two-photon excitations
reveal intriguing interference patterns peculiar to the kagome geometry and
promise at the same time a highly tunable quantum interferometry device with a
signature for the formation of resonant or Fabry-Pe\'rot-like transmission of
photons. Our results justify the use of the proposed PEPS technique for
addressing the role of disorder in such quantum simulators in the microwave
regime and promises a sophisticated numerical machinery for yet further
explorations of the scalability of the resulting kagome arrays. The introduced
methodology and the physical results may also pave the way for unraveling
exotic phases of correlated light on a kagome geometry.
|
quant-ph
|
Quantum Coding Theorems for Arbitrary Sources, Channels and Entanglement
Resources: The information spectrum approach gives general formulae for optimal rates of
various information theoretic protocols, under minimal assumptions on the
nature of the sources, channels and entanglement resources involved. This paper
culminates in the derivation of the dense coding capacity for a noiseless
quantum channel, assisted by arbitrary shared entanglement, using this
approach. We also review the currently known coding theorems, and their
converses, for protocols such as data compression for arbitrary quantum sources
and transmission of classical information through arbitrary quantum channels.
In addition, we derive the optimal rate of data compression for a mixed source
|
quant-ph
|
Approximation Algorithms for Quantum Max-$d$-Cut: We initiate the algorithmic study of the Quantum Max-$d$-Cut problem, a
quantum generalization of the well-known Max-$d$-Cut problem. The Quantum
Max-$d$-Cut problem involves finding a quantum state that maximizes the
expected energy associated with the projector onto the antisymmetric subspace
of two, $d$-dimensional qudits over all local interactions. Equivalently, this
problem is physically motivated by the $SU(d)$-Heisenberg model, a spin glass
model that generalized the well-known Heisenberg model over qudits. We develop
a polynomial-time randomized approximation algorithm that finds product-state
solutions of mixed states with bounded purity that achieve non-trivial
performance guarantees. Moreover, we prove the tightness of our analysis by
presenting an algorithmic gap instance for Quantum Max-d-Cut problem with $d
\geq 3$.
|
quant-ph
|
Global and short-range entanglement properties in excited, many-body
localized spin chains: We explore the use of short-range entanglement measures, such as concurrence
and negativity, and global entanglement measures such as geometric
entanglement, as indicators of many-body localization (MBL) in the spectra of
disordered spin systems. From the perspective of entanglement monogamy, the two
types of entanglement behave oppositely in the thermalized and MBL phases. In a
recent work, the concurrence of subsystems, a measure of local entanglement,
was used in a study of many-body localization in a one-dimensional spin-$1/2$
system (Bera and Lakshminarayan, 2016). We show numerically that the negativity
displays notably similar behavior for this system, with the advantage that it
can also be extended to systems of higher local dimension. We then demonstrate
this extension in practice by using it to predict the existence of an MBL phase
in a disordered a spin-1 system. In terms of global entanglement, the geometric
entanglement of both spin-$1/2$ and spin-1 systems is also shown to behave as a
complementary indicator of the MBL phenomenon.
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quant-ph
|
Introduction to quantum information theory and outline of two
applications to physics: the black hole information paradox and the
renormalization group information flow: This review paper is intended for scholars with different backgrounds,
possibly in only one of the subjects covered, and therefore little background
knowledge is assumed. The first part is an introduction to classical and
quantum information theory (CIT, QIT): basic definitions and tools of CIT are
introduced, such as the information content of a random variable, the typical
set, and some principles of data compression. Some concepts and results of QIT
are then introduced, such as the qubit, the pure and mixed states, the Holevo
theorem, the no-cloning theorem, and the quantum complementarity. In the second
part, two applications of QIT to open problems in theoretical physics are
discussed. The black hole (BH) information paradox is related to the phenomenon
of the Hawking radiation (HR). Consid- ering a BH starting in a pure state,
after its complete evaporation only the Hawking radiation will remain, which is
shown to be in a mixed state. This either describes a non-unitary evolution of
an isolated system, contradicting the evolution postulate of quantum mechanics
and violating the no-cloning theorem, or it implies that the initial
information content can escape the BH, therefore contradicting general
relativity. The progress toward the solution of the paradox is discussed. The
renormalization group (RG) aims at the extraction of the macroscopic
description of a physical system from its microscopic description. This passage
from microscopic to macroscopic can be described in terms of several steps from
one scale to another, and is therefore formalized as the action of a group. The
c-theorem proves the existence, under certain conditions, of a function which
is monotonically decreasing along the group transformations. This result
suggests an interpretation of this function as entropy, and its use to study
the information flow along the RG transformations.
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quant-ph
|
Simultaneous gates in frequency-crowded multilevel systems using fast,
robust, analytic control shapes: We present a few-parameter ansatz for pulses to implement a broad set of
simultaneous single-qubit rotations in frequency-crowded multilevel systems.
Specifically, we consider a system of two qutrits whose working and leakage
transitions suffer from spectral crowding (detuned by $\delta$). In order to
achieve precise controllability, we make use of two driving fields (each having
two quadratures) at two different tones to implement arbitrary simultaneous
rotations. Expanding the waveforms in terms of Hanning windows, we show how
analytic pulses containing smooth and composite-pulse features can easily
achieve gate errors less than $10^{-4}$ and considerably outperform known
adiabatic techniques. Moreover, we find a generalization of the WahWah method
by Schutjens et al. [Phys. Rev. A 88, 052330 (2013)] that allows precise
separate single-qubit rotations for all gate times beyond a quantum speed
limit. We find in all cases a quantum speed limit slightly below $2\pi/\delta$
for the gate time and show that our pulses are robust against variations in
system parameters and filtering due to transfer functions, making them suitable
for experimental implementations.
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quant-ph
|
Quantum decoherence in the rotation of small molecules: The dynamics of non-polar diatomic molecules interacting with a far-detuned
narrow-band laser field, that only may drive rotational transitions, is
studied. The rotation of the molecule is considered both classically and
quantum mechanically, providing links to features known from the heavy
symmetric top. In particular, quantum decoherence in the molecular rotation,
being induced by spontaneous Raman processes, is addressed. It is shown how
this decoherence modifies the rotational dynamics in phase space.
|
quant-ph
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The SLH framework for modeling quantum input-output networks: Many emerging quantum technologies demand precise engineering and control
over networks consisting of quantum mechanical degrees of freedom connected by
propagating electromagnetic fields, or quantum input-output networks. Here we
review recent progress in theory and experiment related to such quantum
input-output networks, with a focus on the SLH framework, a powerful modeling
framework for networked quantum systems that is naturally endowed with
properties such as modularity and hierarchy. We begin by explaining the
physical approximations required to represent any individual node of a network,
eg. atoms in cavity or a mechanical oscillator, and its coupling to quantum
fields by an operator triple $(S,L,H)$. Then we explain how these nodes can be
composed into a network with arbitrary connectivity, including coherent
feedback channels, using algebraic rules, and how to derive the dynamics of
network components and output fields. The second part of the review discusses
several extensions to the basic SLH framework that expand its modeling
capabilities, and the prospects for modeling integrated implementations of
quantum input-output networks. In addition to summarizing major results and
recent literature, we discuss the potential applications and limitations of the
SLH framework and quantum input-output networks, with the intention of
providing context to a reader unfamiliar with the field.
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quant-ph
|
Is absolute separability determined by the partial transpose?: The absolute separability problem asks for a characterization of the quantum
states $\rho \in M_m\otimes M_n$ with the property that $U\rho U^\dagger$ is
separable for all unitary matrices $U$. We investigate whether or not it is the
case that $\rho$ is absolutely separable if and only if $U\rho U^\dagger$ has
positive partial transpose for all unitary matrices $U$. In particular, we
develop an easy-to-use method for showing that an entanglement witness or
positive map is unable to detect entanglement in any such state, and we apply
our method to many well-known separability criteria, including the range
criterion, the realignment criterion, the Choi map and its generalizations, and
the Breuer-Hall map. We also show that these two properties coincide for the
family of isotropic states, and several eigenvalue results for entanglement
witnesses are proved along the way that are of independent interest.
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quant-ph
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Quantum simulation of three-body interactions in weakly driven quantum
systems: The realization of effective Hamiltonians featuring many-body interactions
beyond pairwise coupling would enable the quantum simulation of central models
underpinning topological physics and quantum computation. We overcome crucial
limitations of perturbative Floquet engineering and discuss the highly accurate
realization of a purely three-body Hamiltonian in superconducting circuits and
molecular nanomagnets.
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quant-ph
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The concept of weak measurements and the super-efficiency of quantum
tomography: The quantum measurement procedure based on the Lorentz transformation
formalism and weak perturbation of the system is considered. In the simple case
of a single-qubit it turns out that one can perform 4-dimension pseudo-rotation
along with ordinary 3-dimension rotations on the Bloch sphere. These
pseudo-rotations are similar to the Lorentz transformation in special
relativity theory. The extension of the Lorentz transformation for many-qubit
systems is also considered. The quantum measurement protocols based on the
Lorentz transformation are proposed. It has been shown that these protocols
cease to form the decomposition of unity and could be superefficient providing
the fidelity higher than any POVM-measurement protocol. However, one can
perform the complement of the Lorentz protocol to POVM-protocol by an
additional measurement operator. If the initial mixed state is close to the
pure one this operator corresponds to weak perturbation of the state while the
original Lorentz protocol sets the strong perturbations. As the result, the
feedback provides an effective control of a quantum system introducing weak
perturbations to the quantum state. The results of this research are essential
for the development of methods for the control of quantum information
technologies.
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quant-ph
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Quantum two and three person duels: In game theory, a popular model of a struggle for survival among three
competing agents is a truel, or three person generalization of a duel. Adopting
the ideas recently developed in quantum game theory, we present a quantum
scheme for the problems of duels and truels. In the classical case, the outcome
is sensitive to the precise rules under which the truel is performed and can be
counter intuitive. These aspects carry over into our quantum scheme, but
interference amongst the players' strategies can arise, leading to game
equilibria different from the classical case.
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quant-ph
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Reconstruction of diagonal elements of density matrix using maximum
likelihood estimation: The data of the experiment of Schiller et al., Phys. Rev. Lett. 77 (1996)
2933, are alternatively evaluated using the maximum likelihood estimation. The
given data are fitted better than by the standard deterministic approach.
Nevertheless, the data are fitted equally well by a whole family of states.
Standard deterministic predictions correspond approximately to the envelope of
these maximum likelihood solutions.
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quant-ph
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Robust quantum gates and a bus architecture for quantum computing with
rare-earth-ion doped crystals: We present a composite pulse controlled phase gate which together with a bus
architecture improves the feasibility of a recent quantum computing proposal
based on rare-earth-ion doped crystals. Our proposed gate operation is tolerant
to variations between ions of coupling strengths, pulse lengths, and frequency
shifts, and it achieves worst case fidelities above 0.999 with relative
variations in coupling strength as high as 10% and frequency shifts up to
several percent of the resonant Rabi frequency of the laser used to implement
the gate. We outline an experiment to demonstrate the creation and detection of
maximally entangled states in the system.
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quant-ph
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Analysis and improvement of Tian-Zhang-Li voting protocol based on
controlled quantum teleportation: Recently Tian, Zhang and Li (TZL) have proposed a protocol for voting based
on controlled quantum teleportation (Int. J. Theor. Phys. DOI
10.1007/s10773-015-2868-8). We have critically analyzed the protocol and have
shown that it's neither efficient nor secure. Further, it is shown that in the
TZL protocol, the scrutineer Charlie does not have the required control over
the voting process. Apart from showing the limitations of TZL protocol, two
improved protocols for quantum voting along the line of TZL protocol are
proposed here. One of the proposed protocols is designed using a standard
scheme of controlled deterministic secure quantum communication, and the other
one is designed using the idea of quantum cryptographic switch which uses a
technique known as permutation of particles (PoP). A few possible alternative
approaches to accomplish the same task have also been discussed. Further, the
efficiencies of the proposed protocols are reported, and it is shown that the
proposed protocols are free from the limitations of the TZL protocol, and they
are more efficient than the TZL protocol.
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quant-ph
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Harmonic Oscillator SUSY Partners and Evolution Loops: Supersymmetric quantum mechanics is a powerful tool for generating exactly
solvable potentials departing from a given initial one. If applied to the
harmonic oscillator, a family of Hamiltonians ruled by polynomial Heisenberg
algebras is obtained. In this paper it will be shown that the SUSY partner
Hamiltonians of the harmonic oscillator can produce evolution loops. The
corresponding geometric phases will be as well studied.
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quant-ph
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Impossibility of Classically Simulating One-Clean-Qubit Computation: Deterministic quantum computation with one quantum bit (DQC1) is a restricted
model of quantum computing where the input state is the completely mixed state
except for a single clean qubit, and only a single output qubit is measured at
the end of the computing. It is proved that the restriction of quantum
computation to the DQC1 model does not change the complexity classes NQP and
SBQP. As a main consequence, it follows that the DQC1 model cannot be
efficiently simulated by classical computers unless the polynomial-time
hierarchy collapses to the second level (more precisely, to AM), which answers
the long-standing open problem posed by Knill and Laflamme under the very
plausible complexity assumption. The argument developed in this paper also
weakens the complexity assumption necessary for the existing impossibility
results on classical simulation of various sub-universal quantum computing
models, such as the IQP model and the Boson sampling.
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quant-ph
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Quasi-set theory for bosons and fermions: quantum distributions: Quasi-set theory provides a mathematical background for dealing with
collections of indistinguishable elementary particles. In this paper, we show
how to obtain the quantum statistics into the scope of quasi-set theory and
discuss the Helium atom, which represents the simplest example where
indistinguishability plays an important role. A brief discussion about
indistinguishability and interference is also presented as well as other
related lines of work. One of the advantages of our approach is that one of the
most basic principles of quantum theory, namely, the Indistinguishability
Postulate, does not need to be assumed even implicetely in the axiomatic basis
of quantum mechanics.
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quant-ph
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Linear optical scheme to demonstrate genuine multipartite entanglement
for single-particle W states: We consider the method of entanglement witness operator to verify genuine
multipartite entanglement for single-particle W states involving N parties. In
particular, linear optical schemes using photo detectors and beam splitters are
proposed to implement two different types of witness operator in experiment.
The first scheme that requires only a single measurement setting is shown to
detect genuine multipartite entanglement for the overall efficiency beyond
1-1/N. On the other hand, the second scheme with N+1 measurement settings
achieves success at a significantly lowered efficiency than 1-1/N.
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quant-ph
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Quantum Entanglement involved in Grover's and Shor's algorithms: the
four-qubit case: In this paper, we study the nature of entanglement in quantum Grover's and
Shor's algorithms. So far, the authors who have been interested in this problem
have approached the question quantitatively by introducing entanglement
measures (numerical ones most of the time). One can ask a different question:
what about a qualitative measure of entanglement ? In other words, we try to
find what are the different entanglement SLOCC classes that can be generated by
these two algorithms. We treat in this article the case of pure four-qubit
systems.
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quant-ph
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Addressing a single NV$^{-}$ spin with a macroscopic dielectric
microwave cavity: We present a technique for addressing single NV$^{-}$ center spins in diamond
over macroscopic distances using a tunable dielectric microwave cavity. We
demonstrate optically detected magnetic resonance (ODMR) for a single NV$^{-}$
center in a nanodiamond (ND) located directly under the macroscopic microwave
cavity. By moving the cavity relative to the ND, we record the ODMR signal as a
function of position, mapping out the distribution of the cavity magnetic field
along one axis. In addition, we argue that our system could be used to
determine the orientation of the NV$^{-}$ major axis in a straightforward
manner.
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quant-ph
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Ground state cooling of a nanomechanical resonator in the
weak-confinement regime via quantum interference: Ground state cooling of a nanomechanical resonator coupled to a
superconducting flux qubit is discussed. We show that by inducing quantum
interference to cancel detrimental carrier excitations, ground state cooling
becomes possible in the weak-confinement or non-resolved regime. The qubit is
modelled as a three-level system in lambda configuration, and the driving
fluxes are applied such that the qubit absorption spectrum exhibits
electromagnetically induced transparency, thereby cancelling the unwanted
carrier excitation. As our interference-based scheme allows to apply strong
cooling fields, fast and efficient cooling can be achieved.
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quant-ph
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Preparation of spin squeezed atomic states by optical phase shift
measurement: In this paper we present a state vector analysis of the generation of atomic
spin squeezing by measurement of an optical phase shift. The frequency
resolution is improved when a spin squeezed sample is used for spectroscopy in
place of an uncorrelated sample. When light is transmitted through an atomic
sample some photons will be scattered out of the incident beam, and this has a
destructive effect on the squeezing. We present quantitative studies for three
limiting cases: the case of a sample of atoms of size smaller than the optical
wavelength, the case of a large dilute sample and the case of a large dense
sample.
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quant-ph
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Calculating potential energy surfaces with quantum computers by
measuring only the density along adiabatic transitions: We show that chemically-accurate potential energy surfaces (PESs) can be
generated from quantum computers by measuring the density along an adiabatic
transition between different molecular geometries. In lieu of using phase
estimation, the energy is evaluated by performing line-integration using the
inverted TDDFT Kohn-Sham potential obtained from the time-varying densities.
The accuracy of this method depends on the validity of the adiabatic evolution
itself and the potential inversion process (which is theoretically exact but
can be numerically unstable), whereas total evolution time is the defining
factor for the precision of phase estimation. We examine the method with a
one-dimensional system of two electrons for both the ground and first triplet
state in first quantization, as well as the ground state of three- and four-
electron systems in second quantization. It is shown that few accurate
measurements can be utilized to obtain chemical accuracy across the full
potential energy curve, with shorter propagation time than may be required
using phase estimation for a similar accuracy. We also show that an accurate
potential energy curve can be calculated by making many imprecise density
measurements (using few shots) along the time evolution and smoothing the
resulting density evolution. We discuss how one can generate full PESs using
either sparse grid representations or machine learning density functionals
where it is known that training the functional using the density (along with
the energy) generates a more transferable functional than only using the
energy. Finally, it is important to note that the method is able to classically
provide a check of its own accuracy by comparing the density resulting from a
time-independent Kohn-Sham calculation using the inverted potential, with the
measured density.
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quant-ph
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Self-ordering and cavity cooling using a train of ultrashort pulses: A thin atomic gas in an optical resonator exhibits a phase transition from a
homogeneous density to crystalline order when laser illuminated orthogonal to
the resonator axis. We study this well-known self-organization phenomenon for a
generalized pumping scheme using a femtosecond pulse train with a frequency
spectrum spanning a large bandwidth covering many cavity modes. We show that
due to simultaneous scattering into adjacent longitudinal cavity modes the
induced light forces and the atomic dynamics becomes nearly
translation-invariant along the cavity axis. In addition the laser bandwidth
introduces a new correlation length scale within which clustering of the atoms
is energetically favorable. Numerical simulations allow us to determine the
self-consistent ordering threshold power as function of bandwidth and atomic
cloud size. We find strong evidence for a change from a second order to a first
order self-ordering phase transition with growing laser bandwidth when the size
of the atomic cloud gets bigger than the clustering length. An analysis of the
cavity output reveals a corresponding transition from a single to a double
pulse traveling within the cavity. This doubles the output pulse repetition
rate and creates a new time crystal structure in the cavity output. Simulations
also show that multi-mode operation significantly improves cavity cooling
generating lower kinetic temperatures at a much faster cooling rate.
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quant-ph
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The squeezed thermal reservoir as a generalized equilibrium reservoir: We explore the perspective of considering the squeezed thermal reservoir as
an equilibrium reservoir in a generalized Gibbs ensemble with two non-commuting
conserved quantities. We outline the main properties of such a reservoir in
terms of the exchange of energy, both heat and work, and entropy, giving some
key examples to clarify its physical interpretation. This new paradigm allows
for a correct and insightful interpretation of all thermodynamical features of
the squeezed thermal reservoir, as well as other similar non-thermal
reservoirs, including the characterization of reversibility and the first and
second laws of thermodynamics.
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quant-ph
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Wading through the void: Exploring quantum friction and nonequilibrium
fluctuations: When two or more objects move relative to one another in vacuum, they
experience a drag force which, at zero temperature, usually goes under the name
of quantum friction. This contactless non-conservative interaction is mediated
by the fluctuations of the material-modified quantum electrodynamic vacuum and,
hence, is purely quantum in nature. Numerous investigations have revealed the
richness of the mechanisms at work, thereby stimulating novel theoretical and
experimental approaches and identifying challenges as well as opportunities. In
this article, we provide an overview of the physics surrounding quantum
friction and a perspective on recent developments.
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quant-ph
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Impact of dark states on the stationary properties of quantum particles
with off-centered interactions in one dimension: We present a generalization of the two-body contact interaction for
non-relativistic particles trapped in one dimension. The particles interact
only when they are a distance c apart. The competition of the interaction
length scale with the oscillator length leads to three regimes identified from
the energy spectra. When c is less than the oscillator length, particles avoid
each other, whereas in the opposite case bunching occurs. In the intermediate
region where the oscillator length is comparable to c, both exclusion and
bunching are manifested. All of these regions are separated by dark states,
i.e. bosonic or fermionic states which are not affected by the interactions.
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quant-ph
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Coexistence of extended and localized states in one-dimensional systems: Mobility edge transitions from localized to extended states have been
observed in two and three dimensional systems, for which sound theoretical
explanations have also been derived. One-dimensional lattice models have failed
to predict their emergence, offering no clues on how to actually probe this
phenomenon in lower dimensions. This work reports results for a class of
tight-binding models with electron-mass position dependence, for which
localized-extended wave function transitions can be identified. We show that it
is possible to control the density of localized and extended states by tuning
the transition-related parameter for a continuous range of energy values.
Mathematically exact results for extended or localized states are derived in
two extreme conditions of this parameter, as well as an exact energy value for
the mobility edge transition in the intermediate regime. Our framework provides
a clear point of view on the phenomena and can also be harnessed for setting up
experiments to probe to precisely evaluate the associated mobility edges using
state-of-the-art technology.
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quant-ph
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Quantum Annealing vs. QAOA: 127 Qubit Higher-Order Ising Problems on
NISQ Computers: Quantum annealing (QA) and Quantum Alternating Operator Ansatz (QAOA) are
both heuristic quantum algorithms intended for sampling optimal solutions of
combinatorial optimization problems. In this article we implement a rigorous
direct comparison between QA on D-Wave hardware and QAOA on IBMQ hardware.
These two quantum algorithms are also compared against classical simulated
annealing. The studied problems are instances of a class of Ising models, with
variable assignments of $+1$ or $-1$, that contain cubic $ZZZ$ interactions
(higher order terms) and match both the native connectivity of the Pegasus
topology D-Wave chips and the heavy hexagonal lattice of the IBMQ chips. The
novel QAOA implementation on the heavy hexagonal lattice has a CNOT depth of
$6$ per round and allows for usage of an entire heavy hexagonal lattice.
Experimentally, QAOA is executed on an ensemble of randomly generated Ising
instances with a grid search over $1$ and $2$ round angles using all 127
programmable superconducting transmon qubits of ibm_washington. The error
suppression technique digital dynamical decoupling is also tested on all QAOA
circuits. QA is executed on the same Ising instances with the programmable
superconducting flux qubit devices D-Wave Advantage_system4.1 and
Advantage_system6.1 using modified annealing schedules with pauses. We find
that QA outperforms QAOA on all problem instances. We also find that dynamical
decoupling enables 2-round QAOA to marginally outperform 1-round QAOA, which is
not the case without dynamical decoupling.
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quant-ph
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Emergent measure-dependent probabilities from modified quantum dynamics
without state-vector reduction: Counting outcomes is the obvious algorithm for generating probabilities in
quantum mechanics without state-vector reduction (i.e. many-worlds). This
procedure has usually been rejected because for purely linear dynamics it gives
results in disagreement with experiment. Here it is shown that if non-linear
decoherence effects (previously proposed by other authors) are combined with an
exponential time dependence of the scale for the non-linear effects, the
correct measure-dependent probabilities can emerge via outcome counting,
without the addition of any stochastic fields or metaphysical hypotheses.
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quant-ph
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Implementing the sine transform of fermionic modes as a tensor network: Based on the algebraic theory of signal processing, we recursively decompose
the discrete sine transform of first kind (DST-I) into small orthogonal block
operations. Using a diagrammatic language, we then second-quantize this
decomposition to construct a tensor network implementing the DST-I for
fermionic modes on a lattice. The complexity of the resulting network is shown
to scale as $\frac 54 n \log n$ (not considering swap gates), where $n$ is the
number of lattice sites. Our method provides a systematic approach of
generalizing Ferris' spectral tensor network for non-trivial boundary
conditions.
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quant-ph
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Statistical Properties and Algebraic Characteristics of Quantum
Superpositions of Negative Binomial States: We introduce new kinds of states of quantized radiation fields, which are the
superpositions of negative binomial states. They exhibit remarkable
non-classical properties and reduce to Schr\"odinger cat states in a certain
limit. The algebras involved in the even and odd negative binomial states turn
out to be generally deformed oscillator algebras. It is found that the even and
odd negative binomial states satisfy a same eigenvalue equation with a same
eigenvalue and they can be viewed as two-photon nonlinear coherent states. Two
methods of generating such states are proposed.
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quant-ph
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Simultaneous position and state measurement of Rydberg atoms: We present a technique for state-selective position detection of cold Rydberg
atoms. Ground state Rb atoms in a magneto-optical trap are excited to a Rydberg
state and are subsequently ionized with a tailored electric field pulse. This
pulse selectively ionizes only atoms in e.g. the 54d state and not in the 53d
state. The released electrons are detected after a slow flight towards a micro
channel plate. From the time of flight of the electrons the position of the
atoms is deduced. The state selectivity is about 20:1 when comparing 54d with
53d and the one-dimensional position resolution ranges from 6 to 40 $\mu$m over
a range of 300 $\mu$m. This state selectivity and position resolution are
sufficient to allow for the observation of coherent quantum excitation
transport.
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quant-ph
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Exploiting fermion number in factorized decompositions of the electronic
structure Hamiltonian: Achieving an accurate description of fermionic systems typically requires
considerably many more orbitals than fermions. Previous resource analyses of
quantum chemistry simulation often failed to exploit this low fermionic number
information in the implementation of Trotter-based approaches and overestimated
the quantum-computer runtime as a result. They also depended on numerical
procedures that are computationally too expensive to scale up to large systems
of practical interest. Here we propose techniques that solve both problems by
using various factorized decompositions of the electronic structure
Hamiltonian. We showcase our techniques for the uniform electron gas, finding
substantial (over 100x) improvements in Trotter error for low-filling fraction
and pushing to much higher numbers of orbitals than is possible with existing
methods. Finally, we calculate the T-count to perform phase-estimation on
Jellium. In the low-filling regime, we observe improvements in gate complexity
of over 10x compared to the best Trotter-based approach reported to date. We
also report gate counts competitive with qubitization-based approaches for
Wigner-Seitz values of physical interest.
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quant-ph
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Unscrambling the Omelette of Quantum Contextuality (PART 1): Preexistent
Properties or Measurement Outcomes?: In this paper we attempt to analyze the physical and philosophical meaning of
quantum contextuality. We will argue that there exists a general confusion
within the foundational literature arising from the improper "scrambling" of
two different meanings of quantum contextuality. While the first one,
introduced by Bohr, is related to an epistemic interpretation of contextuality
which stresses the incompatibility (or complementarity) of certain measurement
situations described in classical terms; the second meaning of contextuality is
related to a purely formal understanding of contextuality as exposed by the
Kochen-Specker (KS) theorem which focuses instead on the constraints of the
orthodox quantum formalism in order to interpret projection operators as
preexistent or actual (definite valued) properties. We will show how these two
notions have been scrambled together creating an "omelette of contextuality"
which has been fully widespread through a popularized "epistemic explanation"
of the KS theorem according to which: The measurement outcome of the observable
A when measured together with B or together with C will necessarily differ in
case [A, B] = [A, C] = 0, and [B, C] /= 0. We will show why this statement is
not only improperly scrambling epistemic and formal perspectives, but is also
physically and philosophically meaningless. Finally, we analyze the
consequences of such widespread epistemic reading of KS theorem as related to
statistical statements of measurement outcomes.
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quant-ph
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Experimental Test of Contextuality based on State Discrimination with a
Single Qubit: Exploring quantum phenomena beyond predictions of any classical model has
fundamental importance to understand the boundary of classical and quantum
descriptions of nature. As a typical property that a quantum system behaves
distinctively from a classical counterpart, contextuality has been studied
extensively and verified experimentally in systems composed of at least three
levels (qutrit). Here we extend the scope of experimental test of contextuality
to a minimal quantum system of only two states (qubit) by implementing the
minimum error state discrimination on a single $^{171}$Yb$^+$ ion. We observe a
substantial violation of a no-go inequality derived by assuming
non-contextuality, and firmly conclude that the measured results of state
discrimination cannot be reconciled with any non-contextual description. We
also quantify the contextual advantage of state discrimination and the
tolerance against quantum noises.
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quant-ph
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Stimulated emission quantum state tomography for frequency
non-degenerate entangled photon pairs: Frequency non-degenerate entangled photon pairs have been employed in quantum
communication, imaging, and sensing. To characterize quantum entangled state
with long-wavelength (infrared, IR or even terahertz, THz) photon, one needs to
either develop the single-photon detectors at the corresponding wavelengths or
use novel tomography technique, which does not rely on single-photon
detections, such as stimulated emission tomography (SET). We use standard
quantum state tomography and SET to measure the density matrix of entangled
photon pairs, with one photon at 1550 nm and the other one at 810 nm, and
obtain highly consistent results, showing the reliability of SET. Our work
paves the way for efficient measurement of entangled photons with highly
dissimilar frequencies, even to the frequencies where single-photon detections
are not available.
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quant-ph
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Localization of Quantum States at the Cyclotron Resonance: A new type of localization - localization over the quantum resonance cells -
in an intrinsically degenerate system is explored by using the quasienergy
eigenstates.
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quant-ph
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Designing a Fast and Flexible Quantum State Simulator: This paper describes the design and implementation of Spinoza, a fast and
flexible quantum simulator written in Rust. Spinoza simulates the evolution of
a quantum system's state by applying quantum gates, with the core design
principle being that a single-qubit gate applied to a target qubit preserves
the probability of pairs of amplitudes corresponding to measurement outcomes
that differ only in the target qubit. Multiple strategies are employed for
selecting pairs of amplitudes, depending on the gate type and other parameters,
to optimize performance. Specific optimizations are also implemented for
certain gate types and target qubits.
Spinoza is intended to enable the development of quantum computing solutions
by offering developers a simple, flexible, and fast tool for classical
simulation. In this paper we provide details about the design and usage
examples. Furthermore, we compare Spinoza's performance against several other
open-source simulators to demonstrate its strengths.
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quant-ph
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The Unreasonable Success of Quantum Probability I: Quantum Measurements
as Uniform Fluctuations: We introduce a 'uniform tension-reduction' (UTR) model, which allows to
represent the probabilities associated with an arbitrary measurement situation
and use it to explain the emergence of quantum probabilities (the Born rule) as
'uniform' fluctuations on this measurement situation. The model exploits the
geometry of simplexes to represent the states, in a way that the measurement
probabilities can be derived as the 'Lebesgue measure' of suitably defined
convex subregions of the simplexes. We consider a very simple and evocative
physical realization of the abstract model, using a material point particle
which is acted upon by elastic membranes, which by breaking and collapsing
produce the different possible outcomes. This easy to visualize mechanical
realization allows one to gain considerable insight into the possible hidden
structure of an arbitrary measurement process. We also show that the UTR-model
can be further generalized into a 'general tension-reduction' (GTR) model,
describing conditions of lack of knowledge generated by 'non-uniform'
fluctuations. In this ampler framework, particularly suitable to describe
experiments in cognitive science, we define and motivate a notion of 'universal
measurement', describing the most general possible condition of lack of
knowledge in a measurement, emphasizing that the uniform fluctuations
characterizing quantum measurements can also be understood as an average over
all possible forms of non-uniform fluctuations which can be actualized in a
measurement context. This means that the Born rule of quantum mechanics can be
understood as a first order approximation of a more general non-uniform theory,
thus explaining part of the great success of quantum probability in the
description of different domains of reality. This is the first part of a
two-part article.
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quant-ph
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Native approach to controlled-Z gates in inductively coupled fluxonium
qubits: The fluxonium qubits have emerged as a promising platform for gate-based
quantum information processing. However, their extraordinary protection against
charge fluctuations comes at a cost: when coupled capacitively, the qubit-qubit
interactions are restricted to XX-interactions. Consequently, effective XX- or
XZ-interactions are only constructed either by temporarily populating
higher-energy states, or by exploiting perturbative effects under microwave
driving. Instead, we propose and demonstrate an inductive coupling scheme,
which offers a wide selection of native qubit-qubit interactions for fluxonium.
In particular, we leverage a built-in, flux-controlled ZZ-interaction to
perform qubit entanglement. To combat the increased flux-noise-induced
dephasing away from the flux-insensitive position, we use a continuous version
of the dynamical decoupling scheme to perform noise filtering. Combining these,
we demonstrate a 20 ns controlled-Z (CZ) gate with a mean fidelity of 99.53%.
More than confirming the efficacy of our gate scheme, this high-fidelity result
also reveals a promising but rarely explored parameter space uniquely suitable
for gate operations between fluxonium qubits.
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quant-ph
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Violation of a Leggett-Garg inequality with ideal non-invasive
measurements: The quantum superposition principle states that an entity can exist in two
different states simultaneously, counter to our 'classical' intuition. Is it
possible to understand a given system's behaviour without such a concept? A
test designed by Leggett and Garg can rule out this possibility. The test,
originally intended for macroscopic objects, has been implemented in various
systems. However to-date no experiment has employed the 'ideal negative result'
measurements that are required for the most robust test. Here we introduce a
general protocol for these special measurements using an ancillary system which
acts as a local measuring device but which need not be perfectly prepared. We
report an experimental realisation using spin-bearing phosphorus impurities in
silicon. The results demonstrate the necessity of a non-classical picture for
this class of microscopic system. Our procedure can be applied to systems of
any size, whether individually controlled or in a spatial ensemble.
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quant-ph
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Experimental analysis of quantum annealers and hybrid solvers using
benchmark optimization problems: This paper studies the Hamiltonian Cycle Problem (HCP) and the Traveling
Salesman Problem (TSP) on D-Wave's quantum systems. Initially, motivated by the
fact that most libraries present their benchmark instances in terms of
adjacency matrices, we develop a novel matrix formulation for the HCP and TSP
Hamiltonians, which enables the seamless and automatic integration of benchmark
instances in quantum platforms. our extensive experimental tests have led us to
some interesting conclusions. D-Wave's {\tt Advantage\_system4.1} is more
efficient than {\tt Advantage\_system1.1} both in terms of qubit utilization
and quality of solutions. Finally, we experimentally establish that D-Wave's
Hybrid solvers always provide a valid solution to a problem, without violating
the QUBO constraints, even for arbitrarily big problems, of the order of $120$
nodes. When solving TSP instances, the solutions produced by the quantum
annealer are often invalid, in the sense that they violate the topology of the
graph. To address this use we advocate the use of \emph{min-max normalization}
for the coefficients of the TSP Hamiltonian. Finally, we present a thorough
mathematical analysis on the precise number of constraints required to express
the HCP and TSP Hamiltonians. This analysis, explains quantitatively why,
almost always, running incomplete graph instances requires more qubits than
complete instances. It turns out that incomplete graph require more quadratic
constraints than complete graphs, a fact that has been corroborated by a series
of experiments.
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quant-ph
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Signatures of Hong-Ou-Mandel Interference at Microwave Frequencies: Two-photon quantum interference at a beam splitter, commonly known as
Hong-Ou-Mandel interference, was recently demonstrated with
\emph{microwave-frequency} photons by Lang \emph{et
al.}\,\cite{lang:microwaveHOM}. This experiment employed circuit QED systems as
sources of microwave photons, and was based on the measurement of second-order
cross-correlation and auto-correlation functions of the microwave fields at the
outputs of the beam splitter. Here we present the calculation of these
correlation functions for the cases of inputs corresponding to: (i) trains of
\emph{pulsed} Gaussian or Lorentzian single microwave photons, and (ii)
resonant fluorescent microwave fields from \emph{continuously-driven} circuit
QED systems. The calculations include the effects of the finite bandwidth of
the detection scheme. In both cases, the signature of two-photon quantum
interference is a suppression of the second-order cross-correlation function
for small delays. The experiment described in Ref.
\onlinecite{lang:microwaveHOM} was performed with trains of \emph{Lorentzian}
single photons, and very good agreement between the calculations and the
experimental data was obtained.
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quant-ph
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Adaptive Perturbation Method in Quantum Mechanics: The adaptive perturbation chooses a non-standard decomposition. The
Hamiltonian becomes a sum of solvable and perturbation parts. We calculate the
spectrum using the adaptive perturbation method at the leading-order to compare
to numerical solutions. The maximum deviation is around $5\%$ for different
coupling regions. A perturbation study relies on whether a choice of
leading-order is suitable. Our result with different parameters should show
that the adaptive perturbation method provides appropriate saddle points to all
coupling regions. In the end, we show that the perturbation parameters should
not be a coupling constant.
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quant-ph
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Fisher information and multiparticle entanglement: The Fisher information $F$ gives a limit to the ultimate precision achievable
in a phase estimation protocol. It has been shown recently that the Fisher
information for a linear two-mode interferometer cannot exceed the number of
particles if the input state is separable. As a direct consequence, with such
input states the shot-noise limit is the ultimate limit of precision. In this
work, we go a step further by deducing bounds on $F$ for several multiparticle
entanglement classes. These bounds imply that genuine multiparticle
entanglement is needed for reaching the highest sensitivities in quantum
interferometry. We further compute similar bounds on the average Fisher
information $\bar F$ for collective spin operators, where the average is
performed over all possible spin directions. We show that these criteria detect
different sets of states and illustrate their strengths by considering several
examples, also using experimental data. In particular, the criterion based on
$\bar F$ is able to detect certain bound entangled states.
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quant-ph
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Not all entangled states are useful for ancilla-assisted quantum process
tomography: It is well known that one can extract all the information of an unknown
quantum channel by means of quantum process tomography, such as standard
quantum-process tomography and ancilla-assisted quantum process tomography
(AAQPT). Furthermore, it has been shown that entanglement is not necessary for
AAQPT, there exist separable states which are also useful for it. Surprisingly,
in this work we find that not all entangled states are useful for AAQPT, there
also exist some entangled states which are useless. The realignment operation
used in entanglement detection can be related to the question whether a
bipartite state is useful for AAQPT. We derive the relationship between them
and show the process of extracting the complete information of an unknown
channel by the realignment operation. Based on this relationship, we present
examples of a two-qutrit entangled state and a two-qutrit bound entangled
state. Both of these two examples are entangled but they cannot be used for
AAQPT. Last but not least, experimental verification has also been performed on
the IBM platform.
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quant-ph
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Quantum supervaluationist account of the EPR paradox: In the paper, the EPR paradox is explored by the approach of quantum
supervaluationism that leads to a "gappy" semantics with the propositions
giving rise to truth-value gaps. Within this approach, the statement, which
asserts that in the singlet state the system of two (i.e., A and B) spin-1/2
particles possesses the a priori property "spin A is up and spin B is down
along the same axis" or "spin A is down and spin B is up along the same axis",
does not have the truth-value at all. Consequently, after the verification of,
say, the proposition "spin A is up along the z-axis", the statistical
population describing the valuation of the logical connective "spin B is down
along the z-axis and spin B is up (down) along the x-axis" would have no
elements.
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quant-ph
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Long-lived storage of orbital angular momentum quantum states: Quantum memories are indispensible for establishing a long-distance quantum
network. High-dimensional quantum memories enable a higher channel capacity
compared to a quantum memory working in a two-dimensional space, and have a
lower requirement for storage lifetime in the field of quantum coomunication.
The photonic transverse spatial modes such as Laguerra-Gaussian modes orbital
angular momentum (OAM) are ideal candidates for encoding high-dimensional
information, because it can form an infinite-dimensional Hilbert space.
Although the faithful storage of an OAM qubit or qutrit has been realized in
pioneering works, the longest storage lifetime for the former is only in the
order of a few microseconds, and hundreds of nano-seconds for the latter. Here
we implement a quantum memory for OAM qubits and qutrits using a cold atomic
ensemble, the experimental results clearly show that our memory can still beat
the classical limit after a storage time of $400\mu s$,which is two orders of
magnitude higher than the previous work. The retrieval efficiency at this time
equals to $44\%$ of the value when the storage time is set to be $10\mu s$. Our
work is very promising for establishing a high dimensional quantum network.
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quant-ph
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Optimized noise-assisted simulation of the Lindblad equation with
time-dependent coefficients on a noisy quantum processor: Noise in quantum devices is generally considered detrimental to computational
accuracy. However, the recent proposal of noise-assisted simulation has
demonstrated that noise can be an asset in digital quantum simulations of open
systems on Noisy Intermediate-Scale Quantum (NISQ) devices. In this context, we
introduce an optimized decoherence rate control scheme that can significantly
reduce computational requirements by multiple orders of magnitude, in
comparison to the original noise-assisted simulation. We further extend this
approach to encompass Lindblad equations with time-dependent coefficients,
using only quantum error characterization and mitigation techniques. This
extension allows for the perturbative simulation of non-Markovian dynamics on
NISQ devices, eliminating the need for ancilla qubits or mid-circuit
measurements. Our contributions are validated through numerical experiments on
an emulated IBMQ device. Overall, our work offers valuable optimizations that
bring current quantum processors closer to effectively simulating realistic
open systems.
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quant-ph
|
Experimental generation of 6 dB continuous variable entanglement from a
nondegenerate optical parametric amplifier: We experimentally demonstrated that the quantum correlations of amplitude and
phase quadratures between signal and idler beams produced from a non-degenerate
optical parametric amplifier (NOPA) can be significantly improved by using a
mode cleaner in the pump field and reducing the phase fluctuations in phase
locking systems. Based on the two technical improvements the quantum
entanglement measured with a two-mode homodyne detector is enhanced from ~ 4 dB
to ~ 6 dB below the quantum noise limit using the same NOPA and nonlinear
crystal.
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quant-ph
|
Non-critical slowing down of photonic condensation: We investigate the response of a photonic gas interacting with a reservoir of
pumped dye-molecules to quenches in the pump power. In addition to the expected
dramatic critical slowing down of the equilibration time around phase
transitions we find extremely slow equilibration even far away from phase
transitions. This non-critical slowing down can be accounted for quantitatively
by fierce competition among cavity modes for access to the molecular
environment, and we provide a quantitative explanation for this non-critical
slowing down.
|
quant-ph
|
Local random quantum circuits form approximate designs on arbitrary
architectures: We consider random quantum circuits (RQC) on arbitrary connected graphs whose
edges determine the allowed $2$-qudit interactions. Prior work has established
that such $n$-qudit circuits with local dimension $q$ on 1D, complete, and
$D$-dimensional graphs form approximate unitary designs, that is, they generate
unitaries from distributions close to the Haar measure on the unitary group
$U(q^n)$ after polynomially many gates. Here, we extend those results by
proving that RQCs comprised of $O(\mathrm{poly}(n,k))$ gates on a wide class of
graphs form approximate unitary $k$-designs. We prove that RQCs on graphs with
spanning trees of bounded degree and height form $k$-designs after
$O(|E|n\,\mathrm{poly}(k))$ gates, where $|E|$ is the number of edges in the
graph. Furthermore, we identify larger classes of graphs for which RQCs
generate approximate designs in polynomial circuit size. For $k \leq 4$, we
show that RQCs on graphs of certain maximum degrees form designs after
$O(|E|n)$ gates, providing explicit constants. We determine our circuit size
bounds from the spectral gaps of local Hamiltonians. To that end, we extend the
finite-size (or Knabe) method for bounding gaps of frustration-free
Hamiltonians on regular graphs to arbitrary connected graphs. We further
introduce a new method based on the Detectability Lemma for determining the
spectral gaps of Hamiltonians on arbitrary graphs. Our methods have wider
applicability as the first method provides a succinct alternative proof of
[Commun. Math. Phys. 291, 257 (2009)] and the second method proves that RQCs on
any connected architecture form approximate designs in quasi-polynomial circuit
size.
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quant-ph
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Hamiltonian design to prepare arbitrary states of four-level systems: We propose a method to manipulate, possibly faster than adiabatically,
four-level systems with time-dependent couplings and constant energy shifts
(detunings in quantum-optical realizations). We inversely engineer the
Hamiltonian, in ladder, tripod, or diamond configurations, to prepare arbitrary
states using the geometry of four-dimensional rotations to set the state
populations, specifically we use Cayley's factorization of a general rotation
into right- and left-isoclinic rotations.
|
quant-ph
|
Quantum resonant activation: Quantum resonant activation is investigated for the archetype setup of an
externally driven two-state (spin-boson) system subjected to strong dissipation
by means of both analytical and extensive numerical calculations. The
phenomenon of resonant activation emerges in the presence of either randomly
fluctuating or deterministic periodically varying driving fields. Addressing
the incoherent regime, a characteristic minimum emerges in the mean first
passage time to reach an absorbing neighboring state whenever the intrinsic
time scale of the modulation matches the characteristic time scale of the
system dynamics. For the case of deterministic periodic driving, the first
passage time probability density function (pdf) displays a complex,
multi-peaked behavior, which depends crucially on the details of initial phase,
frequency, and strength of the driving. As an interesting feature we find that
the mean first passage time enters the resonant activation regime at a critical
frequency $\nu^*$ which depends very weakly on the strength of the driving.
Moreover, we provide the relation between the first passage time pdf and the
statistics of residence times.
|
quant-ph
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Multi-stability and condensation of exciton-polaritons below threshold: Exciton-polaritons can condense to a macroscopic quantum state through a
non-equilibrium process of pumping and decay. In recent experiments, polariton
condensates are used to observe, for a short time, nonlinear Josephson
phenomena by coupling two condensates. However, it is still not clear how these
phenomena are affected by the pumping and decay at long times and how the
coupling alters the polariton condensation. Here, we consider a polariton
Josephson junction pumped on one side and study its dynamics within a
mean-field theory. The Josephson current is found to give rise to
multi-stability of the stationary states, which are sensitive to the initial
conditions and incoherent noises. These states can be attributed to either the
self-trapping effect or the parity-time (PT) symmetry of the system. These
results can be used to explain the emission spectra and the $\pi$-phase locking
observed in recent experiments. We further predict that the multi-stability can
reduce to the self-trapped state if the PT symmetry is broken. Moreover, the
polaritons can condense even below the threshold, exhibiting hysteresis.
|
quant-ph
|
Equilibration of quantum chaotic systems: Quantum ergordic theorem for a large class of quantum systems was proved by
von Neumann [Z. Phys. {\bf 57}, 30 (1929)] and again by Reimann [Phys. Rev.
Lett. {\bf 101}, 190403 (2008)] in a more practical and well-defined form.
However, it is not clear whether the theorem applies to quantum chaotic
systems. With the rigorous proof still elusive, we illustrate and verify this
theorem for quantum chaotic systems with examples. Our numerical results show
that a quantum chaotic system with an initial low-entropy state will
dynamically relax to a high-entropy state and reach equilibrium. The quantum
equilibrium state reached after dynamical relaxation bears a remarkable
resemblance to the classical micro-canonical ensemble. However, the
fluctuations around equilibrium are distinct: the quantum fluctuations are
exponential while the classical fluctuations are Gaussian.
|
quant-ph
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Mitigating depolarizing noise on quantum computers with noise-estimation
circuits: A significant problem for current quantum computers is noise. While there are
many distinct noise channels, the depolarizing noise model often appropriately
describes average noise for large circuits involving many qubits and gates. We
present a method to mitigate the depolarizing noise by first estimating its
rate with a noise-estimation circuit and then correcting the output of the
target circuit using the estimated rate. The method is experimentally validated
on the simulation of the Heisenberg model. We find that our approach in
combination with readout-error correction, randomized compiling, and zero-noise
extrapolation produces results close to exact results even for circuits
containing hundreds of CNOT gates.
|
quant-ph
|
Identifying overparameterization in Quantum Circuit Born Machines: In machine learning, overparameterization is associated with qualitative
changes in the empirical risk landscape, which can lead to more efficient
training dynamics. For many parameterized models used in statistical learning,
there exists a critical number of parameters, or model size, above which the
model is constructed and trained in the overparameterized regime. There are
many characteristics of overparameterized loss landscapes. The most significant
is the convergence of standard gradient descent to global or local minima of
low loss. In this work, we study the onset of overparameterization transitions
for quantum circuit Born machines, generative models that are trained using
non-adversarial gradient-based methods. We observe that bounds based on
numerical analysis are in general good lower bounds on the overparameterization
transition. However, bounds based on the quantum circuit's algebraic structure
are very loose upper bounds. Our results indicate that fully understanding the
trainability of these models remains an open question.
|
quant-ph
|
Counterexample to "Sufficient Conditions for uniqueness of the Weak
Value" by J. Dressel and A. N. Jordan, arXiv:1106.1871v1: The abstract of "Contextual Values of Observables in Quantum Measurements" by
J. Dressel, S. Agarwal, and A. N. Jordan [Phys. Rev. Lett. 104 240401 (2010)]
(called DAJ below), states: "We introduce contextual values as a generalization
of the eigenvalues of an observable that takes into account both the system
observable and a general measurement procedure. This technique leads to a
natural definition of a general conditioned average that converges uniquely to
the quantum weak value in the minimal disturbance limit." A counterexample to
the claim of the last sentence was presented in Version 1. Subsequently Dressel
and Jordan placed in the arXiv the paper of the title (called DJ below) which
attempts to prove the claim of DAJ quoted above under stronger hypotheses than
given in DAJ, hypotheses which the counterexample does not satisfy. The present
work (Version 6) presents a new counterexample to this revised claim of DJ. A
brief introduction to "contextual values" is included. Also included is a
critical analysis of DJ.
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quant-ph
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Deterministic nonlinear gates with oscillators mediated by a qubit: Quantum nonlinear operations for harmonic oscillator systems play a key role
in the development of analog quantum simulators and computers. Since a variety
of strong highly nonlinear operations are unavailable in the existing physical
systems, it is a common practice to approximate them by using conditional
measurement-induced methods. The conditional approach has several drawbacks,
the most severe of which is the exponentially decreasing success rate of the
strong and complex nonlinear operations. We show that by using a suitable two
level system sequentially interacting with the oscillator, it is possible to
resolve these issues and implement a nonlinear operation both nearly
deterministically and nearly perfectly. We explicitly demonstrate the approach
by constructing self-Kerr and cross-Kerr couplings in a realistic situation,
which require a feasible dispersive coupling between the two-level system and
the oscillator.
|
quant-ph
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Rydberg-induced optical nonlinearities from a cold atomic ensemble
trapped inside a cavity: We experimentally characterize the optical nonlinear response of a cold
atomic medium placed inside an optical cavity, and excited to Rydberg states.
The excitation to S and D Rydberg levels is carried out via a two-photon
transition in an EIT (electromagnetically induced transparency) configuration,
with a weak (red) probe beam on the lower transition, and a strong (blue)
coupling beam on the upper transition. The observed optical nonlinearities
induced by S states for the probe beam can be explained using a semi-classical
model with van der Waals' interactions. For the D states, it appears necessary
to take into account a dynamical decay of Rydberg excitations into a long-lived
dark state. We show that the measured nonlinearities can be explained by using
a Rydberg bubble model with a dynamical decay.
|
quant-ph
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Efficient atomic quantum memory for photonic qubits in cavity QED: We investigate a scheme of atomic quantum memory to store photonic qubits of
polarization in cavity QED. It is observed that the quantum-state swapping
between a single-photon pulse and a $ \Lambda $-type atom can be made via
scattering in an optical cavity [T. W. Chen, C. K. Law, P. T. Leung, Phys. Rev.
A {\bf 69} (2004) 063810]. This swapping operates limitedly in the strong
coupling regime for $ \Lambda $-type atoms with equal dipole couplings. We
extend this scheme in cavity QED to present a more feasible and efficient
method for quantum memory combined with projective measurement. This method
works without requiring such a condition on the dipole couplings. The fidelity
is significantly higher than that of the swapping, and even in the moderate
coupling regime it reaches almost unity by narrowing sufficiently the
photon-pulse spectrum. This high performance is rather unaffected by the atomic
loss, cavity leakage or detunings, while a trade-off is paid in the success
probability for projective measurement.
|
quant-ph
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A Survey of Classical And Quantum Sequence Models: Our primary objective is to conduct a brief survey of various classical and
quantum neural net sequence models, which includes self-attention and recurrent
neural networks, with a focus on recent quantum approaches proposed to work
with near-term quantum devices, while exploring some basic enhancements for
these quantum models. We re-implement a key representative set of these
existing methods, adapting an image classification approach using quantum
self-attention to create a quantum hybrid transformer that works for text and
image classification, and applying quantum self-attention and quantum recurrent
neural networks to natural language processing tasks. We also explore different
encoding techniques and introduce positional encoding into quantum
self-attention neural networks leading to improved accuracy and faster
convergence in text and image classification experiments. This paper also
performs a comparative analysis of classical self-attention models and their
quantum counterparts, helping shed light on the differences in these models and
their performance.
|
quant-ph
|
Cavityless self-organization of ultracold atoms due to the
feedback-induced phase transition: Feedback is a general idea of modifying system behaviour depending on the
measurement outcomes. It spreads from natural sciences, engineering, and
artificial intelligence to contemporary classical and rock music. Recently,
feedback has been suggested as a tool to induce phase transitions beyond the
dissipative ones and tune their universality class. Here, we propose and
theoretically investigate a system possessing such a feedback-induced phase
transition. The system contains a Bose-Einstein condensate placed in an optical
potential with the depth that is feedback-controlled according to the intensity
of the Bragg-reflected probe light. We show that there is a critical value of
the feedback gain where the uniform gas distribution loses its stability and
the ordered periodic density distribution emerges. Due to the external
feedback, the presence of a cavity is not necessary for this type of atomic
self-organization. We analyze the dynamics after a sudden change of the
feedback control parameter. The feedback time constant is shown to determine
the relaxation above the critical point. We show as well that the control
algorithm with the derivative of the measured signal dramatically decreases the
transient time.
|
quant-ph
|
Scalable Architecture for Adiabatic Quantum Computing of NP-Hard
Problems: We present a comprehensive review of past research into adiabatic quantum
computation and then propose a scalable architecture for an adiabatic quantum
computer that can treat NP-hard problems without requiring local coherent
operations. Instead, computation can be performed entirely by adiabatically
varying a magnetic field applied to all the qubits simultaneously. Local
(incoherent) operations are needed only for: (1) switching on or off certain
pairwise, nearest-neighbor inductive couplings in order to set the problem to
be solved and (2) measuring some subset of the qubits in order to obtain the
answer to the problem.
|
quant-ph
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Strong coupling corrections in quantum thermodynamics: Quantum systems strongly coupled to many-body systems equilibrate to the
reduced state of a global thermal state, deviating from the local thermal state
of the system as it occurs in the weak-coupling limit. Taking this insight as a
starting point, we study the thermodynamics of systems strongly coupled to
thermal baths. First, we provide strong-coupling corrections to the second law
applicable to general systems in three of its different readings: As a
statement of maximal extractable work, on heat dissipation, and bound to the
Carnot efficiency. These corrections become relevant for small quantum systems
and always vanish in first order in the interaction strength. We then move to
the question of power of heat engines, obtaining a bound on the power
enhancement due to strong coupling. Our results are exemplified on the
paradigmatic situation of non-Markovian quantum Brownian motion.
|
quant-ph
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Markovian and non-Markovian dynamics in quantum and classical systems: We discuss the conceptually different definitions used for the
non-Markovianity of classical and quantum processes. The well-established
definition for non-Markovianity of a classical stochastic process represents a
condition on the Kolmogorov hierarchy of the n-point joint probability
distributions. Since this definition cannot be transferred to the quantum
regime, quantum non-Markovianity has recently been defined and quantified in
terms of the underlying quantum dynamical map, using either its divisibility
properties or the behavior of the trace distance between pairs of initial
states. Here, we investigate and compare these definitions and their relations
to the classical notion of non-Markovianity by employing a large class of
non-Markovian processes, known as semi-Markov processes, which admit a natural
extension to the quantum case. A number of specific physical examples is
constructed which allow to study the basic features of the classical and the
quantum definitions and to evaluate explicitly the measures for quantum
non-Markovianity. Our results clearly demonstrate several fundamental
distinctions between the classical and the quantum notion of non-Markovianity,
as well as between the various quantum measures for non-Markovianity.
|
quant-ph
|
Quantum Key Distribution over 67 km with a plug & play system: We present a fibre-optical quantum key distribution system. It works at
1550nm and is based on the plug & play setup. We tested the stability under
field conditions using aerial and terrestrial cables and performed a key
exchange over 67 km between Geneva and Lausanne.
|
quant-ph
|
Stabilizing Preparation of Quantum Gaussian States via Continuous
Measurement: This paper provides a stabilizing preparation method for quantum Gaussian
states by utilizing continuous measurement. The stochastic evolution of the
open quantum system is described in terms of the quantum stochastic master
equation. We present necessary and sufficient conditions for the system to have
a unique stabilizing steady Gaussian state. The conditions are much weaker than
those existing results presented in the approach of preparing Gaussian states
through environment engineering. Parametric conditions of how to prepare an
arbitrary pure Gaussian state are provided. This approach provides more degrees
of freedom to choose the system Hamiltonian and the system-environment coupling
operators, as compared with the case where dissipation-induced approach is
employed. The stabilizing conditions for the case of imperfect measurement
efficiency are also presented. These results may benefit practical experimental
implementation in preparing quantum Gaussian states.
|
quant-ph
|
Interference and complementarity for two-photon hybrid entangled states: In this work we generate two-photon hybrid entangled states (HES), where the
polarization of one photon is entangled with the transverse spatial degree of
freedom of the second photon. The photon pair is created by parametric
down-conversion in a polarization-entangled state. A birefringent double-slit
couples the polarization and spatial degrees of freedom of these photons and
finally, suitable spatial and polarization projections generate the HES. We
investigate some interesting aspects of the two-photon hybrid interference, and
present this study in the context of the complementarity relation that exists
between the visibilities of the one- and two-photon interference patterns.
|
quant-ph
|
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