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Graphs whose normalized Laplacian matrices are separable as density
matrices in quantum mechanics: Recently normalized Laplacian matrices of graphs are studied as density
matrices in quantum mechanics. Separability and entanglement of density
matrices are important properties as they determine the nonclassical behavior
in quantum systems. In this note we look at the graphs whose normalized
Laplacian matrices are separable or entangled. In particular, we show that the
number of such graphs is related to the number of 0-1 matrices that are line
sum symmetric and to the number of graphs with at least one vertex of degree 1.
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quant-ph
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Phase-space formulation of quantum mechanics and quantum state
reconstruction for physical systems with Lie-group symmetries: We present a detailed discussion of a general theory of phase-space
distributions, introduced recently by the authors [J. Phys. A {\bf 31}, L9
(1998)]. This theory provides a unified phase-space formulation of quantum
mechanics for physical systems possessing Lie-group symmetries. The concept of
generalized coherent states and the method of harmonic analysis are used to
construct explicitly a family of phase-space functions which are postulated to
satisfy the Stratonovich-Weyl correspondence with a generalized traciality
condition. The symbol calculus for the phase-space functions is given by means
of the generalized twisted product. The phase-space formalism is used to study
the problem of the reconstruction of quantum states. In particular, we consider
the reconstruction method based on measurements of displaced projectors, which
comprises a number of recently proposed quantum-optical schemes and is also
related to the standard methods of signal processing. A general group-theoretic
description of this method is developed using the technique of harmonic
expansions on the phase space.
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quant-ph
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Optical response of a misaligned and suspended Fabry-Perot cavity: The response to a probe laser beam of a suspended, misaligned and detuned
optical cavity is examined. A five degree of freedom model of the fluctuations
of the longitudinal and transverse mirror coordinates is presented. Classical
and quantum mechanical effects of radiation pressure are studied with the help
of the optical stiffness coefficients and the signals provided by an FM
sideband technique and a quadrant detector, for generic values of the product
$\varpi \tau $ of the fluctuation frequency times the cavity round trip. A
simplified version is presented for the case of small misalignments. Mechanical
stability, mirror position entanglement and ponderomotive squeezing are
accommodated in this model. Numerical plots refer to cavities under test at the
so-called Pisa LF facility.
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quant-ph
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Entangled-state generation and Bell inequality violations in
nanomechanical resonators: We investigate theoretically the conditions under which a multi-mode
nanomechanical resonator, operated as a purely mechanical parametric
oscillator, can be driven into highly nonclassical states. We find that when
the device can be cooled to near its ground state, and certain mode matching
conditions are satisfied, it is possible to prepare distinct resonator modes in
quantum entangled states that violate Bell inequalities with homodyne
quadrature measurements. We analyze the parameter regimes for such Bell
inequality violations, and while experimentally challenging, we believe that
the realization of such states lies within reach. This is a re-imagining of a
quintessential quantum optics experiment by using phonons that represent
tangible mechanical vibrations.
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quant-ph
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A Quantum Computational Semantics for Epistemic Logical Operators. Part
II: Semantics: By using the abstract structures investigated in the first Part of this
article, we develop a semantics for an epistemic language, which expresses
sentences like "Alice knows that Bob does not understand that PI is
irrational". One is dealing with a holistic form of quantum computational
semantics, where entanglement plays a fundamental role, thus, the meaning of a
global expression determines the contextual meanings of its parts, but
generally not the other way around. The epistemic situations represented in
this semantics seem to reflect some characteristic limitations of the real
processes of acquiring information. Since knowledge is not generally closed
under logical consequence, the unpleasant phenomenon of logical omniscience is
here avoided.
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quant-ph
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Coupled Cluster Downfolding Methods: the effect of double commutator
terms on the accuracy of ground-state energies: Downfolding coupled cluster (CC) techniques have recently been introduced
into quantum chemistry as a tool for the dimensionality reduction of the
many-body quantum problem. As opposed to earlier formulations in physics and
chemistry based on the concept of effective Hamiltonians, the appearance of the
downfolded Hamiltonians is a natural consequence of the single-reference
exponential parametrization of the wave function. In this paper, we discuss the
impact of higher-order terms originating in double commutators. In analogy to
previous studies, we consider the case when only one- and two-body interactions
are included in the downfolded Hamiltonians. We demonstrate the efficiency of
the many-body expansions involving single and double commutators for the
unitary extension of the downfolded Hamiltonians on the example of the
beryllium atom, and bond-breaking processes in the Li2 and H2O molecules. For
the H2O system, we also analyze energies obtained with downfolding procedures
as functions of the active space size.
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quant-ph
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Statistical dynamics of a non-Abelian anyonic quantum walk: We study the single particle dynamics of a mobile non-Abelian anyon hopping
around many pinned anyons on a surface. The dynamics is modelled by a discrete
time quantum walk and the spatial degree of freedom of the mobile anyon becomes
entangled with the fusion degrees of freedom of the collective system. Each
quantum trajectory makes a closed braid on the world lines of the particles
establishing a direct connection between statistical dynamics and quantum link
invariants. We find that asymptotically a mobile Ising anyon becomes so
entangled with its environment that its statistical dynamics reduces to a
classical random walk with linear dispersion in contrast to particles with
Abelian statistics which have quadratic dispersion.
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quant-ph
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Continuous-time quantum walks on dynamical percolation graphs: We address continuous-time quantum walks on graphs in the presence of time-
and space-dependent noise. Noise is modeled as generalized dynamical
percolation, i.e. classical time-dependent fluctuations affecting the tunneling
amplitudes of the walker. In order to illustrate the general features of the
model, we review recent results on two paradigmatic examples: the dynamics of
quantum walks on the line and the effects of noise on the performances of
quantum spatial search on the complete and the star graph. We also discuss
future perspectives, including extension to many-particle quantum walk, to
noise model for on-site energies and to the analysis of different noise
spectra. Finally, we address the use of quantum walks as a quantum probe to
characterize defects and perturbations occurring in complex, classical and
quantum, networks.
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quant-ph
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Double exceptional points generated by the strong imaginary coupling of
a non-Hermitian Hamiltonian in an optical microcavity: Exceptional points (EPs) have recently attracted considerable attention in
the study of non-Hermitian systems and in applications such as sensors and mode
switching. In particular, nontrivial topological structures of EPs have been
studied intensively in relation to encircling EPs. Thus, EP generation is
currently an important issue in several fields. To generate multiple EPs,
multiple levels or composite physical systems have been employed with Hermitian
couplings. In this study, we generate multiple EPs on two-level systems in a
single microcavity by adopting the non-Hermitian coupling of a non-Hermitian
Hamiltonian under the imaginary (dominant) coupling. The topological structures
of Riemann surfaces generated by non-Hermitian coupling exhibit features that
are different from those of Riemann surfaces generated by Hermitian coupling.
The features of these topological structures of Riemann surfaces were verified
by encircling multiple EPs and using a Riemann sphere.
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quant-ph
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Eigenvalues and Low Energy Eigenvectors of Quantum Many-Body Systems: I first give an overview of the thesis and Matrix Product States (MPS)
representation of quantum spin chains with an improvement on the conventional
notation.
The rest of this thesis is divided into two parts. The first part is devoted
to eigenvalues of quantum many-body systems (QMBS). I introduce Isotropic
Entanglement, which draws from various tools in random matrix theory and free
probability theory (FPT) to accurately approximate the eigenvalue distribution
of QMBS on a line with generic interactions. Next, I discuss the energy
distribution of one particle hopping random Schr\"odinger operator in 1D from
FPT in context of the Anderson model.
The second part is devoted to ground states and gap of QMBS. I first give the
necessary background on frustration free (FF) Hamiltonians, real and imaginary
time evolution within MPS representation and a numerical implementation. I then
prove the degeneracy and FF condition for quantum spin chains with generic
local interactions, including corrections to our earlier assertions. I then
summarize my efforts in proving lower bounds for the entanglement of the ground
states, which includes some new results, with the hope that they inspire future
work resulting in solving the conjecture given therein. Next I discuss two
interesting measure zero examples where FF Hamiltonians are carefully
constructed to give unique ground states with high entanglement. One of the
examples (i.e., $d=4$) has not appeared elsewhere. In particular, we calculate
the Schmidt numbers exactly, entanglement entropies and introduce a novel
technique for calculating the gap which may be of independent interest. The
last chapter elaborates on one of the measure zero examples (i.e., $d=3$) which
is the first example of a FF translation-invariant spin-1 chain that has a
unique highly entangled ground state and exhibits signatures of a critical
behavior.
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quant-ph
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Spatial entanglement using a quantum walk on a many-body system: The evolution of a many-particle system on a one-dimensional lattice,
subjected to a quantum walk can cause spatial entanglement in the lattice
position, which can be exploited for quantum information/communication
purposes. We demonstrate the evolution of spatial entanglement and its
dependence on the quantum coin operation parameters, the number of particles
present in the lattice and the number of steps of quantum walk on the system.
Thus, spatial entanglement can be controlled and optimized using a
many-particle discrete-time quantum walk.
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quant-ph
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Hybrid quantum linear equation algorithm and its experimental test on
IBM Quantum Experience: We propose a hybrid quantum algorithm based on the Harrow-Hassidim-Lloyd
(HHL) algorithm for solving a system of linear equations. In our hybrid scheme,
a classical information feed-forward is required from the quantum phase
estimation algorithm to reduce a circuit depth from the original HHL algorithm.
In this paper, we show that this hybrid algorithm is functionally identical to
the HHL algorithm under the assumption that the number of qubits used in
algorithms is large enough. In addition, it is experimentally examined with
four qubits in the IBM Quantum Experience setups, and the experimental results
of our algorithm show higher accurate performance on specific systems of linear
equations than that of the HHL algorithm.
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quant-ph
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High-Fidelity Single-Shot Toffoli Gate via Quantum Control: A single-shot Toffoli, or controlled-controlled-NOT, gate is desirable for
classical and quantum information processing. The Toffoli gate alone is
universal for reversible computing and, accompanied by the Hadamard gate, forms
a universal gate set for quantum computing. The Toffoli gate is also a key
ingredient for (non-topological) quantum error correction. Currently Toffoli
gates are achieved by decomposing into sequentially implemented single- and
two-qubit gates, which requires much longer times and yields lower overall
fidelities compared to a single-shot implementation. We develop a
quantum-control procedure to construct a single-shot Toffoli gate for three
nearest-neighbor-coupled superconducting transmon systems such that the
fidelity is 99.9% and is as fast as an entangling two-qubit gate under the same
realistic conditions. The gate is achieved by a non-greedy quantum control
procedure using our enhanced version of the Differential Evolution algorithm.
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quant-ph
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Constructing higher-order topological states in higher dimension: Higher-order topological phase as a generalization of Berry phase attracts an
enormous amount of research. The current theoretical models supporting
higher-order topological phases, however, cannot give the connection between
lower and higher-order topological phases when extending the lattice from lower
to higher dimensions. Here, we theoretically propose and experimentally
demonstrate a topological corner state constructed from the edge states in one
dimensional lattice. The two-dimensional square lattice owns independent
spatial modulation of coupling in each direction, and the combination of edge
states in each direction come up to the higher-order topological corner state
in two-dimensional lattice, revealing the connection of topological phase in
lower and higher dimensional lattices. Moreover, the topological corner states
in two-dimensional lattice can also be viewed as the dimension-reduction from a
four-dimensional topological phase characterized by vector Chern number,
considering two modulation phases as synthetic dimensions in Aubry-Andre-Harper
model discussed as example here. Our work deeps the understanding to
topological phases breaking through the lattice dimension, and provides a
promising tool constructing higher topological phases in higher dimensional
structures.
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quant-ph
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Entanglement generation resonances in XY chains: We examine the maximum entanglement reached by an initially fully aligned
state evolving in an XY Heisenberg spin chain placed in a uniform transverse
magnetic field. Both the global entanglement between one qubit and the rest of
the chain and the pairwise entanglement between adjacent qubits is analyzed. It
is shown that in both cases the maximum is not a monotonous decreasing function
of the aligning field, exhibiting instead a resonant behavior for low
anisotropies, with pronounced peaks (a total of [n/2] peaks in the global
entanglement for an $n$-spin chain), whose width is proportional to the
anisotropy and whose height remains finite in the limit of small anisotropy. It
is also seen that the maximum pairwise entanglement is not a smooth function of
the field even in small finite chains, where it may exhibit narrow peaks above
strict plateaus. Explicit analytical results for small chains, as well as
general exact results for finite n-spin chains obtained through the
Jordan-Wigner mapping, are discussed.
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quant-ph
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Revisiting the damped quantum harmonic oscillator: We reanalyse the quantum damped harmonic oscillator, introducing three less
than common features. These are (i) the use of a continuum model of the
reservoir rather than an ensemble of discrete oscillators, (ii) an exact
diagonalisation of the Hamiltonian by adapting a technique pioneered by Fano,
and (iii) the use of the thermofield technique for describing a finite
temperature reservoir. We recover in this way a number of well-known and some,
perhaps, less familiar results. An example of the latter is an ab initio proof
that the oscillator relaxes to the mean-force Gibbs state. We find that special
care is necessary when comparing the damped oscillator with its undamped
counterpart as the former has two distinct natural frequencies, one associated
with short time evolution and the other with longer times.
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quant-ph
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Quantum-state transfer from an ion to a photon: A quantum network requires information transfer between distant quantum
computers, which would enable distributed quantum information processing and
quantum communication. One model for such a network is based on the
probabilistic measurement of two photons, each entangled with a distant atom or
atomic ensemble, where the atoms represent quantum computing nodes. A second,
deterministic model transfers information directly from a first atom onto a
cavity photon, which carries it over an optical channel to a second atom; a
prototype with neutral atoms has recently been demonstrated. In both cases, the
central challenge is to find an efficient transfer process that preserves the
coherence of the quantum state. Here, following the second scheme, we map the
quantum state of a single ion onto a single photon within an optical cavity.
Using an ion allows us to prepare the initial quantum state in a deterministic
way, while the cavity enables high-efficiency photon generation. The mapping
process is time-independent, allowing us to characterize the interplay between
efficiency and fidelity. As the techniques for coherent manipulation and
storage of multiple ions at a single quantum node are well established, this
process offers a promising route toward networks between ion-based quantum
computers.
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quant-ph
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State of the art and prospects for quantum computing: This is a brief review of the experimental and theoretical quantum computing.
The hopes for eventually building a useful quantum computer rely entirely on
the so-called "threshold theorem". In turn, this theorem is based on a number
of assumptions, treated as axioms, i.e. as being satisfied exactly. Since in
reality this is not possible, the prospects of scalable quantum computing will
remain uncertain until the required precision, with which these assumptions
should be approached, is established. Some related sociological aspects are
also discussed. .
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quant-ph
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Two-player quantum games: When player strategies are via directional
choices: We propose a scheme for a quantum game based on performing an EPR type
experiment and in which each player's spatial directional choices are
considered as their strategies. A classical mixed-strategy game is recovered by
restricting the players' choices to specific spatial trajectories. We show that
for players' directional choices for which the Bell-CHSH inequality is
violated, the players' payoffs in the quantum game have no mapping within the
classical mixed-strategy game. The scheme provides a more direct link between
classical and quantum games.
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quant-ph
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Defining the $p$-wave scattering volume in the presence of dipolar
interactions: The definition of the scattering volume for $p$-wave collisions needs to be
generalized in the presence of dipolar interactions for which the potential
decreases with the interparticle separation as $1/R^3$. Here, we propose a
generalized definition of the scattering volume characterizing the short-range
interactions in odd-parity waves, obtained from an analysis of the $p$-wave
component of the two-body threshold wave function. Our approach uses an
asymptotic model and introduces explicitly the anisotropic dipole-dipole
interaction, which governs the ultracold collision dynamics at long-range. The
short-range interactions, which are essential to describe threshold resonances,
are taken into account by a single parameter which is determined by the
field-free $s$-wave scattering length.
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quant-ph
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The Quantum State of Classical Matter I: Solids and Measurements: Using the kinematic constraints of classical bodies we construct the
allowable wavefunctions corresponding to classical solids. These are shown to
be long lived metastable states that are qualitatively far from eigenstates of
the true Hamiltonian. Extensions of this give an explicit description of phonon
oscillations in terms of the wavefunction itself and some consequences for the
general validity of the quasiparticle picture are presented. An intrinsic
theory of quantum measurement naturally arises based on Schr\"{o}dinger
evolution that is local, consistent with relativity and extends to the case of
noninertial and deformable measurement devices that can have time changing
internal properties. This theory agrees with the Born interpretation in the
limit of static measuring devices. Care is given to the transport of conserved
quantities during measurement.
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quant-ph
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Quantum-Logic Synthesis of Hermitian Gates: In this paper, the problem of synthesizing a general Hermitian quantum gate
into a set of primary quantum gates is addressed. To this end, an extended
version of the Jacobi approach for calculating the eigenvalues of Hermitian
matrices in linear algebra is considered as the basis of the proposed synthesis
method. The quantum circuit synthesis method derived from the Jacobi approach
and its optimization challenges are described. It is shown that the proposed
method results in multiple-control rotation gates around the y axis,
multiple-control phase shift gates, multiple-control NOT gates and a middle
diagonal Hermitian matrix, which can be synthesized to multiple-control Pauli Z
gates. Using the proposed approach, it is shown how multiple-control U gates,
where U is a single-qubit Hermitian quantum gate, can be implemented using a
linear number of elementary gates in terms of circuit lines with the aid of one
auxiliary qubit in an arbitrary state.
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quant-ph
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Decoherence of a Measure of Entanglement: We demonstrate by an explicit model calculation that the decay of
entanglement of two two-state systems (two qubits) is governed by the product
of the factors that measure the degree of decoherence of each of the qubits,
subject to independent sources of quantum noise. This demonstrates an important
physical property that separated open quantum systems can evolve quantum
mechanically on time scales larger than the times for which they remain
entangled.
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quant-ph
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Unextendible maximally entangled bases and mutually unbiased bases in
multipartite systems: We generalize the notion of unextendible maximally entangled basis from
bipartite systems to multipartite quantum systems. It is proved that there do
not exist unextendible maximally entangled bases in three-qubit systems.
Moreover,two types of unextendible maximally entangled bases are constructed in
tripartite quantum systems and proved to be not mutually unbiased.
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quant-ph
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Quantum Algorithms and Simulation for Parallel and Distributed Quantum
Computing: A viable approach for building large-scale quantum computers is to interlink
small-scale quantum computers with a quantum network to create a larger
distributed quantum computer. When designing quantum algorithms for such a
distributed quantum computer, one can make use of the added parallelization and
distribution abilities inherent in the system. An added difficulty to then
overcome for distributed quantum computing is that a complex control system to
orchestrate the various components is required. In this work, we aim to address
these issues. We explicitly define what it means for a quantum algorithm to be
distributed and then present various quantum algorithms that fit the
definition. We discuss potential benefits and propose a high-level scheme for
controlling the system. With this, we present our software framework called
Interlin-q, a simulation platform that aims to simplify designing and verifying
parallel and distributed quantum algorithms. We demonstrate Interlin-q by
implementing some of the discussed algorithms using Interlin-q and layout
future steps for developing Interlin-q into a control system for distributed
quantum computers.
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quant-ph
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Entanglement-Enhanced Quantum Key Distribution: We present and analyze a quantum key distribution protocol based on sending
entangled N-qubit states instead of single-qubit ones as in the trail-blazing
scheme by Bennett and Brassard (BB84). Since the qubits are sent individually,
an eavesdropper is limited to accessing them one by one. In an intercept-resend
attack, this fundamental restriction allows one to make the eavesdropper's
information on the transmitted key vanish if even one of the qubits is not
intercepted. The implied upper bound 1/(2N) for Eve's information is further
shown not to be the lowest since in the case N = 2, the information can be
reduced to less than 30% of that in BB84. In general, the protocol is at least
as secure as BB84.
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quant-ph
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Experimental purification of coherent states: We propose a scheme for optimal Gaussian purification of coherent states from
several imperfect copies. The proposal is experimentally demonstrated for the
case of two copies of a coherent state sent through independent noisy channels.
Our purification protocol relies on only linear optics and an ancilla vacuum
state, rendering this approach an interesting alternative to the more complex
protocols of entanglement distillation and quantum error correction.
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quant-ph
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Variational dynamics of the sub-Ohmic spin-boson model on the basis of
multiple Davydov $\mathrm{D}_1$ states: Dynamics of the sub-Ohmic spin-boson model is investigated by employing a
multitude of the Davydov D$_1$ trial states, also known as the multi-D$_1$
Ansatz. Accuracy in dynamics simulations is improved significantly over the
single D$_1$ Ansatz, especially in the weak system-bath coupling regime. The
reliability of the multi-D$_1$ Ansatz for various coupling strengths and
initial conditions are also systematically examined, with results compared
closely with those of the hierarchy equations of motion and the path integral
Monte Carlo approaches. In addition, a coherent-incoherent phase crossover in
the nonequilibrium dynamics is studied through the multi-D$_1$ Ansatz. The
phase diagram is obtained with a critical point $s_{c}=0.4$. For $s_{c}<s<1$,
the coherent-to-incoherent crossover occurs at a certain coupling strength,
while the coherent state recurs at a much larger coupling strength. For
$s<s_{c}$, only the coherent phase exists.
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quant-ph
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Demonstrating nonclassicality and non-Gaussianity of single-mode fields:
Bell-type tests using generalized phase-space distributions: We present Bell-type tests of nonclassicality and non-Gaussianity for
single-mode fields employing a generalized quasiprobability function. Our
nonclassicality tests are based on the observation that two orthogonal
quadratures in phase space (position and momentum) behave as independent
realistic variables for a coherent state. Taking four (three) points at the
vertices of a rectangle (right triangle) in phase space, our tests detect every
pure nonclassical Gaussian state and a range of mixed Gaussian states. These
tests also set an upper bound for all Gaussian states and their mixtures, which
thereby provide criteria for genuine quantum non-Gaussianity. We optimize the
non-Gaussianity tests by employing a squeezing transformation in phase space
that converts a rectangle (right triangle) to a parallelogram (triangle), which
enlarges the set of non-Gaussian states detectable in our formulation. We
address fundamental and practical limits of our generalized phase-space tests
by looking into their relation with decoherence under a lossy Gaussian channel
and their robustness against finite data and nonoptimal choice of phase-space
points. Furthermore, we demonstrate that our parallelogram test can identify
useful resources for nonlocality testing in phase space.
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quant-ph
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Collective enhancements in many-emitter phonon lasing: We investigate theoretically the many-emitter phonon laser based on optically
driven semiconductor quantum dots within an acoustic nanocavity. We map the
phonon laser Hamiltonian to a Tavis-Cummings type interaction with an
unexpected additional many-emitter energy shift. This many-emitter interaction
with the cavity mode results in a variety of resonances dependent on the number
of participating emitters. We show that the many-emitter phonon laser also
includes the single emitter resonance besides these collective phenomena.
However, we obtain a high quantum yield addressing these collective resonances.
We clearly demonstrate the best setup for maximal enhancement and show that the
output can be increased even more via lasing at the two phonon resonance.
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quant-ph
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Feedback-Induced Steady-State Light Bunching Above the Lasing Threshold: We develop a full quantum-optical approach for optical self-feedback of a
microcavity laser. These miniaturized devices work in a regime between the
quantum and classical limit and are test-beds for the differences between a
quantized theory of optical self-feedback and the corresponding semiclassical
theory. The light intensity and photon statistics are investigated with and
without an external feedback: We show that in the low-gain limit, where
relaxation oscillations do not appear, the recently observed photon bunching in
a quantum dot microcavity laser with optical feedback can be accounted for only
by the fully quantized model. By providing a description of laser devices with
feedback in the quantum limit we reveal novel insights into the origin of
bunching in quantized and semiclassical models.
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quant-ph
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Ising models and topological codes: classical algorithms and quantum
simulation: We present an algorithm to approximate partition functions of 3-body
classical Ising models on two-dimensional lattices of arbitrary genus, in the
real-temperature regime. Even though our algorithm is purely classical, it is
designed by exploiting a connection to topological quantum systems, namely the
color codes. The algorithm performance is exponentially better than other
approaches which employ mappings between partition functions and quantum state
overlaps. In addition, our approach gives rise to a protocol for quantum
simulation of such Ising models by simply measuring local observables on color
codes.
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quant-ph
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Transfer of Nonclassical Properties from A Microscopic Superposition to
Macroscopic Thermal States in The High Temperature Limit: We present several examples where prominent quantum properties are
transferred from a microscopic superposition to thermal states at high
temperatures. Our work is motivated by an analogy of Schrodinger's cat paradox,
where the state corresponding to the virtual cat is a mixed thermal state with
a large average photon number. Remarkably, quantum entanglement can be produced
between thermal states with nearly the maximum Bell-inequality violation even
when the temperatures of both modes approach infinity.
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quant-ph
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Telecom networking with a diamond quantum memory: Practical quantum networks require interfacing quantum memories with existing
channels and systems that operate in the telecom band. Here we demonstrate
low-noise, bidirectional quantum frequency conversion that enables a
solid-state quantum memory to directly interface with telecom-band systems. In
particular, we demonstrate conversion of visible-band single photons emitted
from a silicon-vacancy (SiV) center in diamond to the telecom O-band,
maintaining low noise ($g^2(0)<0.1$) and high indistinguishability
($V=89\pm8\%$). We further demonstrate the utility of this system for quantum
networking by converting telecom-band time-bin pulses, sent across a lossy and
noisy 50 km deployed fiber link, to the visible band and mapping their quantum
states onto a diamond quantum memory with fidelity $\mathcal{F}=87\pm 2.5 \% $.
These results demonstrate the viability of SiV quantum memories integrated with
telecom-band systems for scalable quantum networking applications.
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quant-ph
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Quantum artificial vision for defect detection in manufacturing: In this paper we consider several algorithms for quantum computer vision
using Noisy Intermediate-Scale Quantum (NISQ) devices, and benchmark them for a
real problem against their classical counterparts. Specifically, we consider
two approaches: a quantum Support Vector Machine (QSVM) on a universal
gate-based quantum computer, and QBoost on a quantum annealer. The quantum
vision systems are benchmarked for an unbalanced dataset of images where the
aim is to detect defects in manufactured car pieces. We see that the quantum
algorithms outperform their classical counterparts in several ways, with QBoost
allowing for larger problems to be analyzed with present-day quantum annealers.
Data preprocessing, including dimensionality reduction and contrast
enhancement, is also discussed, as well as hyperparameter tuning in QBoost. To
the best of our knowledge, this is the first implementation of quantum computer
vision systems for a problem of industrial relevance in a manufacturing
production line.
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quant-ph
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Linewidth broadening of a quantum dot coupled to an off-resonant cavity: We study the coupling between a photonic crystal cavity and an off-resonant
quantum dot under resonant excitation of the cavity or the quantum dot.
Linewidths of the quantum dot and the cavity as a function of the excitation
laser power are measured. We show that the linewidth of the quantum dot,
measured by observing the cavity emission, is significantly broadened compared
to the theoretical estimate. This indicates additional incoherent coupling
between the quantum dot and the cavity.
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quant-ph
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Probing Hilbert Space Fragmentation with Strongly Interacting Rydberg
Atoms: Hilbert space fragmentation provides a mechanism to break ergodicity in
closed many-body systems. Here, we propose a realistic scheme to
comprehensively explore this exotic paradigm on a Rydberg quantum simulator. We
show that the Rydberg Ising model in the large detuning regime can be mapped to
a generalized folded XXZ model featuring a strongly fragmented Hilbert space.
The emergent Hamiltonian, however, displays distinct time scales for the
transport of a magnon and a hole excitation. This interesting property
facilitates a continuous tuning of the Krylov-subspace ergodicity, from the
integrable regime, to the Krylov-restricted thermal phase, and eventually to
the statistical bubble localization region. By further introducing nonlocal
interactions, we find that both the fragmentation behavior and the ergodicity
of the Krylov subspace can be significantly enriched. We also examine the role
of atomic position disorders and identify a symmetry-selective many-body
localization transition. We demonstrate that these phenomena manifest
themselves in quench dynamics, which can be readily probed in state-of-the-art
Rydberg array setups.
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quant-ph
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Strong monogamy inequalities for four qubits: We investigate possible generalizations of the Coffman-Kundu-Wootters
monogamy inequality to four qubits, accounting for multipartite entanglement in
addition to the bipartite terms. We show that the most natural extension of the
inequality does not hold in general, and we describe the violations of this
inequality in detail. We investigate alternative ways to extend the monogamy
inequality to express a constraint on entanglement sharing valid for all
four-qubit states, and perform an extensive numerical analysis of randomly
generated four-qubit states to explore the properties of such extensions.
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quant-ph
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Enhancing the expressivity of quantum neural networks with residual
connections: In the recent noisy intermediate-scale quantum era, the research on the
combination of artificial intelligence and quantum computing has been greatly
developed. Inspired by neural networks, developing quantum neural networks with
specific structures is one of the most promising directions for improving
network performance. In this work, we propose a quantum circuit-based algorithm
to implement quantum residual neural networks (QResNets), where the residual
connection channels are constructed by introducing auxiliary qubits to the
data-encoding and trainable blocks of the quantum neural networks. Importantly,
we prove that when this particular network architecture is applied to a
$l$-layer data-encoding, the number of frequency generation forms can be
extended from one, namely the difference of the sum of generator eigenvalues,
to $\mathcal{O}(l^2)$. And the flexibility in adjusting the corresponding
Fourier coefficients can also be improved due to the diversity of spectrum
construction methods and the additional optimization degrees of freedom in the
generalized residual operators. These results indicate that the residual
encoding scheme can achieve better spectral richness and enhance the
expressivity of various parameterized quantum circuits. Extensive numerical
demonstrations in regression tasks of fitting various functions and
applications in image classification with MNIST datasets are offered to present
the expressivity enhancement. Our work lays the foundation for a complete
quantum implementation of the classical residual neural networks and explores a
new strategy for quantum feature map in quantum machine learning.
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quant-ph
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Correlations in Quantum Physics: We provide an historical perspective of how the notion of correlations has
evolved within quantum physics. We begin by reviewing Shannon's information
theory and its first application in quantum physics, due to Everett, in
explaining the information conveyed during a quantum measurement. This
naturally leads us to Lindblad's information theoretic analysis of quantum
measurements and his emphasis of the difference between the classical and
quantum mutual information. After briefly summarising the quantification of
entanglement using these and related ideas, we arrive at the concept of quantum
discord that naturally captures the boundary between entanglement and classical
correlations. Finally we discuss possible links between discord and the
generation of correlations in thermodynamic transformations of coupled harmonic
oscillators.
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quant-ph
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A new method for driven-dissipative problems: Keldysh-Heisenberg
equations: Driven-dissipative systems have recently attracted great attention due to the
existence of novel physical phenomena with no analog in the equilibrium case.
The Keldysh path-integral theory is a powerful tool to investigate these
systems. However, it has still been challenge to study strong nonlinear effects
implemented by recent experiments, since in this case the photon number is few
and quantum fluctuations play a crucial role in dynamics of system. Here we
develop a new approach for deriving exact steady states of driven-dissipative
systems by introducing the Keldysh partition function in the Fock-state basis
and then mapping the standard saddle-point equations into KeldyshHeisenberg
equations. We take the strong Kerr nonlinear resonators with/without the
nonlinear driving as two examples to illustrate our method. It is found that in
the absence of the nonlinear driving, the exact steady state obtained does not
exhibit bistability and agree well with the complex P-representation solution.
While in the presence of the nonlinear driving, the multiphoton resonance
effects are revealed and are consistent with the qualitative analysis. Our
method provides an intuitive way to explore a variety of driven-dissipative
systems especially with strong correlations.
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quant-ph
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Diagrammatic treatment of few-photon scattering from a Rydberg blockaded
atomic ensemble in a cavity: In a previous letter we studied the giant optical nonlinearities of a Rydberg
atomic medium within an optical cavity, in the Schwinger-Keldysh formalism. In
particular, we calculated the non-linear contributions to the spectrum of the
light transmitted through the cavity. In this article we spell out the
essential details of this calculation, and we show how it can be extended to
higher input photon numbers, and higher order correlation functions. As a
relevant example, we calculate and discuss the three-photon correlation
function of the transmitted light, and discuss its physical significance in
terms of the polariton energy levels of the Rydberg medium within the optical
cavity.
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quant-ph
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Finding the ground state of a lattice gauge theory with fermionic tensor
networks: a $2+1d$ $\mathbb{Z}_2$ demonstration: Tensor network states, and in particular Projected Entangled Pair States
(PEPS) have been a strong ansatz for the variational study of complicated
quantum many-body systems, thanks to their built-in entanglement entropy area
law. In this work, we use a special kind of PEPS - Gauged Gaussian Fermionic
PEPS (GGFPEPS) to find the ground state of $2+1d$ dimensional pure
$\mathbb{Z}_2$ lattice gauge theories for a wide range of coupling constants.
We do so by combining PEPS methods with Monte-Carlo computations, allowing for
efficient contraction of the PEPS and computation of correlation functions.
Previously, such numerical computations involved the calculation of the
Pfaffian of a matrix scaling with the system size, forming a severe bottleneck;
in this work we show how to overcome this problem. This paves the way for
applying the method we propose and benchmark here to other gauge groups, higher
dimensions, and models with fermionic matter, in an efficient,
sign-problem-free way.
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quant-ph
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Quantum Torque on a Non-Reciprocal Body out of Thermal Equilibrium and
Induced by a Magnetic Field of Arbitrary Strength: A stationary body that is out of thermal equilibrium with its environment,
and for which the electric susceptibility is non-reciprocal, experiences a
quantum torque. This arises from the spatially non-symmetric electrical
response of the body to its interaction with the non-equilibrium thermal
fluctuations of the electromagnetic field: the non-equilibrium nature of the
thermal field fluctuations results in a net energy flow through the body, and
the spatially non-symmetric nature of the electrical response of the body to
its interaction with these field fluctuations causes that energy flow to be
transformed into a rotational motion. We establish an exact, closed-form,
analytical expression for this torque in the case that the environment is the
vacuum and the material of the body is described by a damped oscillator model,
where the non-reciprocal nature of the electric susceptibility is induced by an
external magnetic field, as for magneto-optical media. We also generalise this
expression to the context in which the body is slowly rotating. By exploring
the high-temperature expansion of the torque, we are able to identify the
separate contributions from the continuous spectral distribution of the
non-reciprocal electric susceptibility, and from the resonance modes. In
particular, we find that the torque persists in the limiting case of zero
damping parameter, due to the contribution of the resonance modes. We also
consider the low-temperature expansion of the torque. This work extends our
previous consideration of this model to an external magnetic field of arbitrary
strength, thereby including non-linear magnetic field effects.
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quant-ph
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Energy absorption by "sparse" systems: beyond linear response theory: The analysis of the response to driving in the case of weakly chaotic or
weakly interacting systems should go beyond linear response theory. Due to the
"sparsity" of the perturbation matrix, a resistor network picture of
transitions between energy levels is essential. The Kubo formula is modified,
replacing the "algebraic" average over the squared matrix elements by a
"resistor network" average. Consequently the response becomes semi-linear
rather than linear. Some novel results have been obtained in the context of two
prototype problems: the heating rate of particles in Billiards with vibrating
walls; and the Ohmic Joule conductance of mesoscopic rings driven by
electromotive force. Respectively, the obtained results are contrasted with the
"Wall formula" and the "Drude formula".
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quant-ph
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Software Mitigation of Crosstalk on Noisy Intermediate-Scale Quantum
Computers: Crosstalk is a major source of noise in Noisy Intermediate-Scale Quantum
(NISQ) systems and is a fundamental challenge for hardware design. When
multiple instructions are executed in parallel, crosstalk between the
instructions can corrupt the quantum state and lead to incorrect program
execution. Our goal is to mitigate the application impact of crosstalk noise
through software techniques. This requires (i) accurate characterization of
hardware crosstalk, and (ii) intelligent instruction scheduling to serialize
the affected operations. Since crosstalk characterization is computationally
expensive, we develop optimizations which reduce the characterization overhead.
On three 20-qubit IBMQ systems, we demonstrate two orders of magnitude
reduction in characterization time (compute time on the QC device) compared to
all-pairs crosstalk measurements. Informed by these characterization, we
develop a scheduler that judiciously serializes high crosstalk instructions
balancing the need to mitigate crosstalk and exponential decoherence errors
from serialization. On real-system runs on three IBMQ systems, our scheduler
improves the error rate of application circuits by up to 5.6x, compared to the
IBM instruction scheduler and offers near-optimal crosstalk mitigation in
practice.
In a broader picture, the difficulty of mitigating crosstalk has recently
driven QC vendors to move towards sparser qubit connectivity or disabling
nearby operations entirely in hardware, which can be detrimental to
performance. Our work makes the case for software mitigation of crosstalk
errors.
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quant-ph
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Multipartite Cellular Automata and the Superposition Principle: Cellular automata can show well known features of quantum mechanics, such as
a linear updating rule that resembles a discretized form of the Schr\"odinger
equation together with its conservation laws. Surprisingly, a whole class of
"natural" Hamiltonian cellular automata, which are based entirely on
integer-valued variables and couplings and derived from an Action Principle,
can be mapped reversibly to continuum models with the help of Sampling Theory.
This results in "deformed" quantum mechanical models with a finite discreteness
scale $l$, which for $l\rightarrow 0$ reproduce the familiar continuum limit.
Presently, we show, in particular, how such automata can form "multipartite"
systems consistently with the tensor product structures of nonrelativistic
many-body quantum mechanics, while maintaining the linearity of dynamics.
Consequently, the Superposition Principle is fully operative already on the
level of these primordial discrete deterministic automata, including the
essential quantum effects of interference and entanglement.
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quant-ph
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Automated detection of laser cooling schemes for ultracold molecules: One of the demanding frontiers in ultracold science is identifying laser
cooling schemes for complex atoms and molecules, out of their vast spectra of
internal states. Motivated by a need to expand the set of available ultracold
molecules for applications in fundamental physics, chemistry, astrochemistry,
and quantum simulation, we propose and demonstrate an automated graph-based
search approach for viable laser cooling schemes. The method is time efficient
and the outcomes greatly surpass the results of manual searches used so far. We
discover new laser cooling schemes for C$_2$, OH$^+$, CN, YO, and CO$_2$ that
can be viewed as surprising or counterintuitive compared to previously
identified laser cooling schemes. In addition, a central insight of this work
is that the reinterpretation of quantum states and transitions between them as
a graph can dramatically enhance our ability to identify new quantum control
schemes for complex quantum systems. As such, this approach will also be
applicable to complex atoms and, in fact, any complex many-body quantum system
with a discrete spectrum of internal states.
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quant-ph
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High-fidelity linear optical quantum computing with polarization
encoding: We show that the KLM scheme [Knill, Laflamme and Milburn, Nature {\bf 409},
46] can be implemented using polarization encoding, thus reducing the number of
path modes required by half. One of the main advantages of this new
implementation is that it naturally incorporates a loss detection mechanism
that makes the probability of a gate introducing a non-detected error, when
non-ideal detectors are considered, dependent only on the detector dark-count
rate and independent of its efficiency. Since very low dark-count rate
detectors are currently available, a high-fidelity gate (probability of error
of order $10^{-6}$ conditional on the gate being successful) can be implemented
using polarization encoding. The detector efficiency determines the overall
success probability of the gate but does not affect its fidelity. This can be
applied to the efficient construction of optical cluster states with very high
fidelity for quantum computing.
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quant-ph
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Controllable dynamics of a dissipative two-level system: We propose a strategy to modulate the decoherence dynamics of a two-level
system, which interacts with a dissipative bosonic environment, by introducing
an assisted degree of freedom. It is revealed that the decay rate of the
two-level system can be significantly suppressed under suitable steers of the
assisted degree of freedom. Our result provides an alternative way to fight
against decoherence and realize a controllable dissipative dynamics.
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quant-ph
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Experimental realization of state transfer by quantum walks with two
coins: Quantum state transfer between different sites is a significant problem for
quantum networks and quantum computers. By selecting quantum walks with two
coins as the basic model and two coin spaces as the communication carriers, we
successfully implement quantum state transfer on various graphs (EPL,
\textbf{124} (2018) 60009) \cite{Shang_2019}. Here, we demonstrate the
experimental implementation of this scheme using IBM quantum experience
platform. In particular, we show the transfer of Bell state, GHZ state and W
state on complete graph on the quantum device. Also, we observe that our
protocol has high fidelity by preforming quantum state tomography.
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quant-ph
|
Ground States of Quantum Many Body Lattice Models via Reinforcement
Learning: We introduce reinforcement learning (RL) formulations of the problem of
finding the ground state of a many-body quantum mechanical model defined on a
lattice. We show that stoquastic Hamiltonians - those without a sign problem -
have a natural decomposition into stochastic dynamics and a potential
representing a reward function. The mapping to RL is developed for both
continuous and discrete time, based on a generalized Feynman-Kac formula in the
former case and a stochastic representation of the Schr\"odinger equation in
the latter. We discuss the application of this mapping to the neural
representation of quantum states, spelling out the advantages over approaches
based on direct representation of the wavefunction of the system.
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quant-ph
|
Single-particle localization in a two-dimensional Rydberg spin system: We study excitation transport in a two-dimensional system of randomly
assembled spins with power-law hopping in two dimensions. This model can be
realized in cold atom quantum simulators with Rydberg atoms. In these
experiments, due to the Rydberg blockade effect, the degree of disorder in the
system is effectively tunable by varying the spin density. We study dynamics
and eigenstate properties of the model as a function of disorder strength and
system size and discuss potential limitations for experiments. At strong
disorder we predominantly observe localized eigenstates with power-law tails.
In this regime the spectral and eigenstate properties can be understood in a
perturbative picture of states localized on small clusters of spins. As the
disorder strength is weakened eigenstates become increasingly delocalized and a
set of seemingly multifractal states appears in the low-energy tail of the
spectrum. A detailed study of the system-size scaling of the eigenstate
properties indicates that in the infinite-size limit all states eventually
become localized. We discuss the feasibility of observing localization effects
experimentally in the spatial spreading of an initially localized excitation
and identify limited system sizes and finite decoherence rates as major
challenges. Our study paves the way towards an experimental observation of
localization effects in Rydberg spin systems with tunable disorder.
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quant-ph
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Selective and efficient quantum process tomography with single photons: We present the results of the first photonic implementation of a new method
for quantum process tomography. The method (originally presented by A.
Bendersky et al, Phys. Rev. Lett 100, 190403 (2008)) enables the estimation of
any element of the chi-matrix that characterizes a quantum process using
resources that scale polynomially with the number of qubits. It is based on the
idea of mapping the estimation of any chi-matrix element onto the average
fidelity of a quantum channel and estimating the latter by sampling randomly
over a special set of states called a 2-design. With a heralded single photon
source we fully implement such algorithm and perform process tomography on a
number of channels affecting the polarization qubit. The method is compared
with other existing ones and its advantages are discussed.
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quant-ph
|
QRAM architectures using superconducting cavities: Quantum random access memory (QRAM) is a common architecture resource for
algorithms with many proposed applications, including quantum chemistry,
windowed quantum arithmetic, unstructured search, machine learning, and quantum
cryptography. Here we propose two bucket-brigade QRAM architectures based on
high-coherence superconducting resonators, which differ in their realizations
of the conditional-routing operations. In the first, we directly construct
controlled-$\mathsf{SWAP}$ ($\textsf{CSWAP}$) operations, while in the second
we utilize the properties of giant-unidirectional emitters (GUEs). For both
architectures we analyze single-rail and dual-rail implementations of a bosonic
qubit. In the single-rail encoding we can detect first-order ancilla errors,
while the dual-rail encoding additionally allows for the detection of photon
losses. For parameter regimes of interest the post-selected infidelity of a
QRAM query in a dual-rail architecture is nearly an order of magnitude below
that of a corresponding query in a single-rail architecture. These findings
suggest that dual-rail encodings are particularly attractive as architectures
for QRAM devices in the era before fault tolerance.
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quant-ph
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The decoherence dynamics of the multipartite entanglement in
non-Markovian environment: We consider four two-level atoms interacting with independent non-Markovian
reservoirs with detuning. We mainly investigate the effects of the detuning and
the length of the reservoir correlation time on the decoherence dynamics of the
multipartite entanglement. We find that the time evolution of the entanglement
of atomic and reservoir subsystems is determined by a parameter, which is a
function of the detuning and the reservoir correlation time. We also find that
the decay and revival of the entanglement of the atomic and reservoir
subsystems are closely related to the sign of the decay rate. We also show that
the cluster state is the most robust to decoherence comparing with Dicke, GHZ,
and W states for this decoherence channel
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quant-ph
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The Dicke model phase transition in the quantum motion of a
Bose-Einstein condensate in an optical cavity: We show that the motion of a laser-driven Bose-Einstein condensate in a
high-finesse optical cavity realizes the spin-boson Dicke-model. The quantum
phase transition of the Dicke-model from the normal to the superradiant phase
corresponds to the self-organization of atoms from the homogeneous into a
periodically patterned distribution above a critical driving strength. The
fragility of the ground state due to photon measurement induced back action is
calculated.
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quant-ph
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Multiphoton controllable transport between remote resonators: We develop a novel method for multiphoton controllable transport between
remote resonators. Specifically, an auxiliary resonator is used to control the
coherent long-range coupling of two spatially separated resonators, mediated by
a coupled-resonator chain of arbitrary length. In this manner, an arbitrary
multiphoton quantum state can be either transmitted through or reflected off
the intermediate chain on demand, with very high fidelity. We find, on using a
time-independent perturbative treatment, that quantum information leakage of an
arbitrary Fock state is limited by two upper bounds, one for the transmitted
case and the other for the reflected case. In principle, the two upper bounds
can be made arbitrarily small, which is confirmed by numerical simulations.
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quant-ph
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Linear position measurements with minimum error-disturbance in each
minimum uncertainty state: In quantum theory, measuring process is an important physical process; it is
a quantum description of the interaction between the system of interest and the
measuring device. Error and disturbance are used to quantitatively check the
performance of the measurement, and are defined by using measuring process.
Uncertainty relations are a general term for relations that provide constraints
on them, and actively studied. However, the true error-disturbance bound for
position measurements is not known yet. Here we concretely construct linear
position measurements with minimum error-disturbance in each minimum
uncertainty state. We focus on an error-disturbance relation (EDR), called the
Branciard-Ozawa EDR, for position measurements. It is based on a quantum
root-mean-square (q-rms) error and a q-rms disturbance. We show the theorem
that gives a necessary and sufficient condition for a linear position
measurement to achieve its lower bound in a minimum uncertainty state, and
explicitly give exactly solvable linear position measurements achieving its
lower bound in the state. We then give probability distributions and states
after the measurement when using them. It is expected to construct measurements
with minimum error-disturbance in a broader class of states in the future,
which will lead to a new understanding of quantum limits, including uncertainty
relations.
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quant-ph
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Particle and anti-particle bosonic entanglement in non-inertial frames: We analyse the entanglement tradeoff between particle and anti-particle modes
of a charged bosonic field between inertial and uniformly accelerated
observers. In contrast with previous results for fermionic fields, we find that
the entanglement redistribution between particle and antiparticle modes does
not prevent the entanglement from vanishing in the infinite acceleration limit.
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quant-ph
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Observation of collective coupling between an engineered ensemble of
macroscopic artificial atoms and a superconducting resonator: The hybridization of distinct quantum systems is now seen as an effective way
to engineer the properties of an entire system leading to applications in
quantum metamaterials, quantum simulation, and quantum metrology. One well
known example is superconducting circuits coupled to ensembles of microscopic
natural atoms. In such cases, the properties of the individual atom are
intrinsic, and so are unchangeable. However, current technology allows us to
fabricate large ensembles of macroscopic artificial atoms such as
superconducting flux qubits, where we can really tailor and control the
properties of individual qubits. Here, we demonstrate coherent coupling between
a microwave resonator and several thousand superconducting flux qubits, where
we observe a large dispersive frequency shift in the spectrum of 250 MHz
induced by collective behavior. These results represent the largest number of
coupled superconducting qubits realized so far. Our approach shows that it is
now possible to engineer the properties of the ensemble, opening up the way for
the controlled exploration of the quantum many-body system.
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quant-ph
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Design of a novel monolithic parabolic-mirror ion-trap to precisely
align the RF null point with the optical focus: We propose a novel ion trap design with the high collection efficiency
parabolic-mirror integrated with the ion trap electrodes. This design has three
radio frequency (RF) electrodes and eight direct current(DC) compensation
electrodes. By carefully adjusting three RF voltages, the parabolic mirror
focus can be made precisely coincident with the RF null point. Thus, the
aberration and the ion micromotion can be minimized at the same time. This
monolithic design can significantly improve the ion-ion entanglement generation
speed by extending the photon collecting solid angle beyond $90\%\cdot4\pi$.
Further analysis of the trapping setup shows that the RF voltage variation
method relexes machining accuracy to a broad range. This design is expected to
be a robust scheme for trapping ion to speed entanglement network node.
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quant-ph
|
Reformulating the Quantum Uncertainty Relation: Uncertainty principle is one of the cornerstones of quantum theory. In the
literature, there are two types of uncertainty relations, the operator form
concerning the variances of physical observables and the entropy form related
to entropic quantities. Both these forms are inequalities involving pairwise
observables, and are found to be nontrivial to incorporate multiple
observables. In this work we introduce a new form of uncertainty relation which
may give out complete trade-off relations for variances of observables in pure
and mixed quantum systems. Unlike the prevailing uncertainty relations, which
are either quantum state dependent or not directly measurable, our bounds for
variances of observables are quantum state independent and immune from the
"triviality" problem of having zero expectation values. Furthermore, the new
uncertainty relation may provide a geometric explanation for the reason why
there are limitations on the simultaneous determination of different
observables in $N$-dimensional Hilbert space.
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quant-ph
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Open source software in quantum computing: Open source software is becoming crucial in the design and testing of quantum
algorithms. Many of the tools are backed by major commercial vendors with the
goal to make it easier to develop quantum software: this mirrors how
well-funded open machine learning frameworks enabled the development of complex
models and their execution on equally complex hardware. We review a wide range
of open source software for quantum computing, covering all stages of the
quantum toolchain from quantum hardware interfaces through quantum compilers to
implementations of quantum algorithms, as well as all quantum computing
paradigms, including quantum annealing, and discrete and continuous-variable
gate-model quantum computing. The evaluation of each project covers
characteristics such as documentation, licence, the choice of programming
language, compliance with norms of software engineering, and the culture of the
project. We find that while the diversity of projects is mesmerizing, only a
few attract external developers and even many commercially backed frameworks
have shortcomings in software engineering. Based on these observations, we
highlight the best practices that could foster a more active community around
quantum computing software that welcomes newcomers to the field, but also
ensures high-quality, well-documented code.
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quant-ph
|
Calculation of Atomic Number States: a Bethe Ansatz Approach: We analyze the conditions for producing atomic number states in a
one-dimensional optical box using the Bethe ansatz method. This approach
provides a general framework, enabling the study of number state production
over a wide range of realistic experimental parameters.
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quant-ph
|
Metrological Detection of Multipartite Entanglement from Young Diagrams: We characterize metrologically useful multipartite entanglement by
representing partitions with Young diagrams. We derive entanglement witnesses
that are sensitive to the shape of Young diagrams and show that Dyson's rank
acts as a resource for quantum metrology. Common quantifiers, such as the
entanglement depth and $k$-separability are contained in this approach as the
diagram's width and height. Our methods are experimentally accessible in a wide
range of atomic systems, as we illustrate by analyzing published data on the
quantum Fisher information and spin-squeezing coefficients.
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quant-ph
|
Quantifying the effects of local many-qubit errors and non-local
two-qubit errors on the surface code: Topological quantum error correction codes are known to be able to tolerate
arbitrary local errors given sufficient qubits. This includes correlated errors
involving many local qubits. In this work, we quantify this level of tolerance,
numerically studying the effects of many-qubit errors on the performance of the
surface code. We find that if increasingly large area errors are at least
moderately exponentially suppressed, arbitrarily reliable quantum computation
can still be achieved with practical overhead. We furthermore quantify the
effect of non-local two-qubit correlated errors, which would be expected in
arrays of qubits coupled by a polynomially decaying interaction, and when using
many-qubit coupling devices. We surprisingly find that the surface code is very
robust to this class of errors, despite a provable lack of a threshold error
rate when such errors are present.
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quant-ph
|
Quantum Energy Teleportation without Limit of Distance: Quantum energy teleportation (QET) is, from an operational viewpoint of
distant protocol users, the transportation of energy via local operations and
classical communication. QET has various links to fundamental research fields,
including black hole physics, the quantum theory of Maxwell's demon, and
condensed-matter entanglement. There are promising signs that QET will be
experimentally verified using the chiral boson fields of quantum Hall edge
currents. In this Letter, we prove that, using the vacuum state of a quantum
field, the upper bound of the amount of energy teleported by QET is inversely
proportional to the transfer distance. This distance bound can be overcome by
using squeezed states with local-vacuum regions.
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quant-ph
|
Translation of "Die Messung quantenmechanischer Operatoren" by
E.P.~Wigner: This is a 'facsimile-style' translation of Wigner's seminal paper on
measurement limitations in the presence of additive conservation laws. A
critical survey of the history of subsequent extensions and variations of what
is now known as the Wigner-Araki-Yanase (WAY) Theorem is provided in a paper
published concurrently.
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quant-ph
|
Semi-device-independent security of one-way quantum key distribution: By testing nonlocality, the security of entanglement-based quantum key
distribution (QKD) can be enhanced to being 'device-independent'. Here we ask
whether such a strong form of security could also be established for one-way
(prepare and measure) QKD. While fully device-independent security is
impossible, we show that security can be guaranteed against individual attacks
in a semi-device-independent scenario. In the latter, the devices used by the
trusted parties are non-characterized, but the dimensionality of the quantum
systems used in the protocol is assumed to be bounded. Our security proof
relies on the analogies between one-way QKD, dimension witnesses and
random-access codes.
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quant-ph
|
State Independent Proof of Kochen-Specker Theorem with Thirty Rank-Two
Projectors: The Kochen-Specker theorem states that noncontextual hidden variable theories
are incompatible with quantum mechanics. We provide a state independent proof
of the Kochen-Specker theorem using the smallest number of projectors, i.e.,
thirty rank-2 projectors, associated with the Mermin pentagram for a
three-qubit system.
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quant-ph
|
Bohmian particle trajectories contradict quantum mechanics: The Bohmian interpretation of quantum mechanics adds particle trajectories to
the wave function and ensures that the probability distribution of the particle
positions agrees with quantum mechanics at any time. This is not sufficient to
avoid contradictions with quantum mechanics. There are correlations between
particle positions at different times which cannot be reproduced with real
particle trajectories. A simple rearrangement of an experimental test of the
Bell-CHSH inequality demonstrates this.
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quant-ph
|
Time-of-arrival probabilities for general particle detectors: We develop a general framework for the construction of probabilities for the
time of arrival in quantum systems. The time of arrival is identified with the
time instant when a transition in the detector's degrees of freedom takes
place. Thus, its definition is embedded within the larger issue of defining
probabilities with respect to time for general quantum transitions. The key
point in our analysis is that we manage to reduce the problem of defining a
quantum time observable to a mathematical model where time is associated to a
transition from a subspace of the Hilbert space of the total system to its
complementary subspace. This property makes it possible to derive a general
expression for the probability for the time of transition, valid for any
quantum system, with the only requirement that the time of transition is
correlated with a definite macroscopic record.
The framework developed here allows for the consideration of any experimental
configuration for the measurement of the time of arrival and it also applies to
relativistic systems with interactions described by quantum field theory. We
use the method in order to describe time-of-arrival measurements in high-energy
particle reactions and for a rigorous derivation of the time-integrated
probabilities in particle oscillations.
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quant-ph
|
No labeling quantum mechanics of indiscernible particles: Our aim in this paper is to show an example of the formalism we have
developed to avoid the label-tensor-product-vector-space-formalism of quantum
mechanics when dealing with indistinguishable quanta. States in this new vector
space, that we call the Q-space, refer only to occupation numbers and
permutation operators act as the identity operator on them, reflecting in the
formalism the unobservability of permutations, a goal of quasi-set theory.
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quant-ph
|
Spin in Compton scattering with pronounced polarization dynamics: We theoretically investigate a scattering configuration in Compton
scattering, in which the orientation of the electron spin is reversed and
simultaneously, the photon polarization changes from linear polarization into
circular polarization. The intrinsic angular momentum of electron and photon
are computed along the coincident propagation direction of the incoming and
outgoing photon. We find that this intrinsic angular momentum is not conserved
in the considered scattering process. We also discuss the generation of
entanglement for the considered scattering setup and present an angle dependent
investigation of the corresponding differential cross section, Stokes
parameters and spin expectation.
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quant-ph
|
Unified simulation methods for quantum acoustic devices: In circuit quantum acoustodynamics (cQAD), superconducting circuits are
combined with acoustic resonators to create and control non-classical states of
mechanical motion. Simulating these systems is challenging due to the extreme
difference in scale between the microwave and mechanical wavelengths. All
existing techniques simulate the electromagnetic and mechanical subsystems
separately. However, this approach may not be adequate for all cQAD devices.
Here, we demonstrate a single simulation of a superconducting qubit coupled to
an acoustic and a microwave resonator and introduce two methods for using this
simulation to predict the frequencies, coupling rates, and energy-participation
ratios of the electromechanical modes of the hybrid system. We also discuss how
these methods can be used to investigate important dissipation channels and
quantify the nontrivial effects of mode hybridization in our device. Our
methodology is flexible and can be extended to other acoustic resonators and
quantum degrees of freedom, providing a valuable new tool for designing hybrid
quantum systems.
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quant-ph
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Star-quantization of an infinite wall: In deformation quantization (a.k.a. the Wigner-Weyl-Moyal formulation of
quantum mechanics), we consider a single quantum particle moving freely in one
dimension, except for the presence of one infinite potential wall. Dias and
Prata pointed out that, surprisingly, its stationary-state Wigner function does
not obey the naive equation of motion, i.e. the naive stargenvalue (*-genvalue)
equation. We review our recent work on this problem, that treats the infinite
wall as the limit of a Liouville potential. Also included are some new results:
(i) we show explicitly that the Wigner-Weyl transform of the usual density
matrix is the physical solution, (ii) we prove that an effective-mass treatment
of the problem is equivalent to the Liouville one, and (iii) we point out that
self-adjointness of the operator Hamiltonian requires a boundary potential, but
one different from that proposed by Dias and Prata.
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quant-ph
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Efficient Simulation of Quantum Many-body Thermodynamics by Tailoring
Zero-temperature Tensor Network: Numerical annealing and renormalization group have conceived various
successful approaches to study the thermodynamics of strongly-correlated
systems where perturbation or expansion theories fail to work. As the process
of lowering the temperatures is usually involved in different manners, these
approaches in general become much less efficient or accurate at the low
temperatures. In this work, we propose to access the finite-temperature
properties from the tensor network (TN) representing the zero-temperature
partition function. We propose to "scissor" a finite part from such an
infinite-size TN, and "stitch" it to possess the periodic boundary condition
along the imaginary-time direction. We dub this approach as TN tailoring.
Exceptional accuracy is achieved with a fine-tune process, surpassing the
previous methods including the linearized tensor renormalization group [Phys.
Rev. Lett. 106, 127202 (2011)], continuous matrix product operator [Phys. Rev.
Lett. 125, 170604 (2020)], and etc. High efficiency is demonstrated, where the
time cost is nearly independent of the target temperature including the
extremely-low temperatures. The proposed idea can be extended to
higher-dimensional systems of bosons and fermions.
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quant-ph
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Moment maps and Galois orbits in quantum information theory: SIC-POVMs are configurations of points or rank-one projections arising from
the action of a finite Heisenberg group on $\mathbb C^d$. The resulting
equations are interpreted in terms of moment maps by focussing attention on the
orbit of a cyclic subgroup and the maximal torus in $\mathrm U(d)$ that
contains it. The image of a SIC-POVM under the associated moment map lies in an
intersection of real quadrics, which we describe explicitly. We also elaborate
the conjectural description of the related number fields and describe the
structure of Galois orbits of overlap phases.
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quant-ph
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Nonclassical 2-photon interference with separate intrinsically
narrowband fibre sources: In this paper, we demonstrate a source of photon pairs based on
four-wave-mixing in photonic crystal fibres. Careful engineering of the phase
matching conditions in the fibres enables us to create photon pairs at 597 nm
and 860 nm in an intrinsically factorable state showing no spectral
correlations. This allows for heralding one photon in a pure state and hence
renders narrow band filtering obsolete. The source is narrow band, bright and
achieves an overall detection efficiency of up to 21% per photon. For the first
time, a Hong-Ou-Mandel interference with unfiltered photons from separate fibre
sources is presented.
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quant-ph
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Quantum battery charging by non-equilibrium steady-state currents: We present an analysis of the availability and maximum extractable work of
quantum batteries in the presence of charge and/or heat steady-state currents.
Quantum batteries are modelled as non-interacting open quantum systems
(mesoscopic systems) strongly coupled to two thermal and particle reservoirs
within the framework of non-equilibrium Green's function theory in a
steady-state regime. We found that the battery can be charged manifestly by a
steady-state charge current compared to heat one, especially, in an
off-resonant transport regime. It allows us to reliably access the performance
of the quantum batteries in the high bias-charging regime.
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quant-ph
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Wigner representation of the rotational dynamics of rigid tops: We propose a methodology to design Wigner representations in phase spaces
with nontrivial topology having evolution equations with desired mathematical
properties. As an illustration, two representations of molecular rotations are
developed to facilitate the analysis of molecular alignment in moderately
intense laser fields, reaction dynamics, scattering phenomena and dissipative
processes.
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quant-ph
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Analysis of a controlled phase gate using circular Rydberg states: We propose and analyze the implementation of a two qubit quantum gate using
circular Rydberg states with maximum orbital angular momentum. The intrinsic
quantum gate error is limited by the finite Rydberg lifetime and finite Rydberg
blockade shift. Circular states have much longer radiative lifetimes than low
orbital angular momentum states and are therefore candidates for high fidelity
gate operations. We analyze the dipole-dipole interaction of two circular state
Rydberg atoms and present numerical simulations of quantum process tomography
to find the intrinsic fidelity of a Rydberg blockade controlled phase gate. Our
analysis shows that the intrinsic gate error can be less than $9 \times10^{-6}$
for circular Cs atoms in a cryogenic environment.
|
quant-ph
|
A Perturbative Approach to Continuous-Time Quantum Error Correction: We present a novel discussion of the continuous-time quantum error correction
introduced by Paz and Zurek in 1998 [Paz and Zurek, Proc. R. Soc. A 454, 355
(1998)]. We study the general Lindbladian which describes the effects of both
noise and error correction in the weak-noise (or strong-correction) regime
through a perturbative expansion. We use this tool to derive quantitative
aspects of the continuous-time dynamics both in general and through two
illustrative examples: the 3-qubit and the 5-qubit stabilizer codes, which can
be independently solved by analytical and numerical methods and then used as
benchmarks for the perturbative approach. The perturbatively accessible time
frame features a short initial transient in which error correction is
ineffective, followed by a slow decay of the information content consistent
with the known facts about discrete-time error correction in the limit of fast
operations. This behavior is explained in the two case studies through a
geometric description of the continuous transformation of the state space
induced by the combined action of noise and error correction.
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quant-ph
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Optomechanical quantum entanglement mediated by acoustic phonon fields: We present exact solutions for the quantum time evolution of two spatially
separated, local inductor-capacitor (LC) oscillators that are coupled
optomechanically to a long elastic strip that functions as a quantum thermal
acoustic field environment. We show that the optomechanical coupling to the
acoustic environment gives rise to causal entanglement dynamics between the two
LC oscillators in the absence of resonant photon exchange between them, and
that significant entanglement develops regardless of the environment
temperature. Such a process establishes that distributed entanglement may be
generated between superconducting qubits via a connected phonon bus bar,
without the need for resonant phonon release and capture.
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quant-ph
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Violation of the "information-disturbance relationship" in finite-time
quantum measurements: The effect of measurement attributes (quantum level of precision, finite
duration) on the classical and quantum correlations is analysed for a pair of
qubits immersed in a common reservoir. We show that the quantum discord is
enhanced as the precision of the measuring instrument is increased, and both
the classical correlation and the quantum discord experience noticeable changes
during finite-time measurements performed on a neighboring partition of the
entangled system. The implications of these results on the
"information-disturbance relationship" are examined, with critical analysis of
the delicate roles played by quantum non-locality and non-Markovian dynamics in
the violation of this relationship, which appears surprisingly for a range of
measurement attributes. This work highlights that the fundamental limits of
quantum mechanical measurements can be altered by exchanges of non-classical
correlations such as the quantum discord with external sources, which has
relevance for cryptographic technology.
|
quant-ph
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Environment-assisted analog quantum search: Two main obstacles for observing quantum advantage in noisy
intermediate-scale quantum computers (NISQ) are the finite precision effects
due to control errors, or disorders, and decoherence effects due to thermal
fluctuations. It has been shown that dissipative quantum computation is
possible in presence of an idealized fully-engineered bath. However, it is not
clear, in general, what performance can be achieved by NISQ when internal bath
degrees of freedom are not controllable. In this work, we consider the task of
quantum search of a marked node on a complete graph of $n$ nodes in the
presence of both static disorder and non-zero coupling to an environment. We
show that, given fixed and finite levels of disorder and thermal fluctuations,
there is an optimal range of bath temperatures that can significantly improve
the success probability of the algorithm. Remarkably for a fixed disorder
strength $\sigma$, the system relaxation time decreases for higher temperatures
within a robust range of parameters. In particular, we demonstrate that for
strong disorder, the presence of a thermal bath increases the success
probability from $1/(n \sigma^2)$ to at least $1/2$. While the asymptotic
running time is approximately maintained, the need to repeat the algorithm many
times and issues associated with unitary over-rotations can be avoided as the
system relaxes to an absorbing steady state. Furthermore, we discuss for what
regimes of disorder and bath parameters quantum speedup is possible and mention
conditions for which similar phenomena can be observed in more general families
of graphs. Our work highlights that in the presence of static disorder, even
non-engineered environmental interactions can be beneficial for a quantum
algorithm.
|
quant-ph
|
Measurement-Device-Independenization of Quantum Key Distribution
Protocols: Quantum key distribution(QKD) allows the legitimate partner to establish a
secret key whose security only depends on physical laws. In recent years,
research on QKD by employing insecure measurement devices, namely
measurement-device-independent QKD (MDI-QKD) is increased. MDI-QKD removes all
attacks on measurement devices and thus an untrusted third party can be
employed for measuring. However, a weakness of previous MDI-QKD protocols is
the need for joint measurements such as Bell measurements whose efficiency is
low in practice. On the other hand, can all QKD protocols become
measurement-device-independent remains a problem. In this paper, we present a
scheme making prepare-measure QKD protocols become MDI-QKD protocols, called
$'measurement-device-independenization'$, which does not need to employ joint
measurements and could be efficiently implemented by weak coherence sources.
The protocol might look like the detector-device-independent(DDI) protocols but
it is also secure under the Trojan horse attack. To illustrate this, we
investigate the photon-number-adding(PNA) attack and present a scheme, called
$'photon-number-purification'$, which can also be employed to close loopholes
for previous protocols such as DDI and plug-and-play ones.
|
quant-ph
|
Velocity-like maximum polarization: irreversibility and quantum
measurements: The polarization emerging in the subsequent scattering processes can never
exceed $1$ which corresponds to the fully polarized pure state. This property
is shown to be provided by the addition rule similar to that for relativistic
velocities never exceeding the speed of light. The cases of spin $1/2$ and $1$
are considered. The photon linear polarization in Thomson scattering is
monotonically increasing. This directness is shown to be a consequence of spin
measurement procedure and may be the particular example of ithe anticipated
relation between quantum measurement and time irreversibility. The emergent
polarization may be considered as a case of opposing time's arrows
corresponding to microscopic (spin) and macroscopic (momentum) degrees of
freedom, respectively.
|
quant-ph
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Witnessing quantumness of a system by observing only its classical
features: Witnessing non-classicality in the gravitational field has been claimed to be
practically impossible. This constitutes a deep problem, which has even lead
some researchers to question whether gravity should be quantised, due to the
weakness of quantum effects. To counteract these claims, we propose a thought
experiment that witnesses non-classicality of a physical system by probing it
with a qubit. Remarkably, this experiment does not require any quantum control
of the system, involving only measuring a single classical observable on that
system. In addition, our scheme does not even assume any specific dynamics.
That non-classicality of a system can be established indirectly, by coupling it
to a qubit, opens up the possibility that quantum gravitational effects could
in fact be witnessed in the lab.
|
quant-ph
|
Measurement noise susceptibility in quantum estimation: Fisher Information is a key notion in the whole field of quantum metrology.
It allows for a direct quantification of maximal achievable precision of
estimation of parameters encoded in quantum states using the most general
quantum measurement. It fails, however, to quantify the robustness of quantum
estimation schemes against measurement imperfections, which are always present
in any practical implementations. Here, we introduce a new concept of Fisher
Information Measurement Noise Susceptibility that quantifies the potential loss
of Fisher Information due to small measurement disturbance. We derive an
explicit formula for the quantity, and demonstrate its usefulness in analysis
of paradigmatic quantum estimation schemes, including interferometry and
super-resolution optical imaging.
|
quant-ph
|
Hybrid Entangled Entanglement in Vector Vortex Beams: Light beams having a vectorial field structure - or polarization - that
varies over the transverse profile and a central optical singularity are called
vector-vortex (VV) beams and may exhibit specific properties, such as focusing
into "light needles" or rotation invariance, with applications ranging from
microscopy and light trapping to communication and metrology. Individual
photons in such beams exhibit a form of single-particle quantum entanglement
between different degrees of freedom. On the other hand, the quantum states of
two photons can be also entangled with each other. Here we combine these two
concepts and demonstrate the generation of quantum entanglement between two
photons that are both in VV states - a new form of quantum "entangled
entanglement". This result may lead to quantum-enhanced applications of VV
beams as well as to quantum-information protocols fully exploiting the
vectorial features of light.
|
quant-ph
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Neural-network quantum state tomography: We revisit the application of neural networks techniques to quantum state
tomography. We confirm that the positivity constraint can be successfully
implemented with trained networks that convert outputs from standard
feed-forward neural networks to valid descriptions of quantum states. Any
standard neural-network architecture can be adapted with our method. Our
results open possibilities to use state-of-the-art deep-learning methods for
quantum state reconstruction under various types of noise.
|
quant-ph
|
Combating fluctuations in relaxation times of fixed-frequency transmon
qubits with microwave-dressed states: With the long coherence time, the fixed-frequency transmon qubit is a
promising qubit modality for quantum computing. Currently, diverse qubit
architectures that utilize fixed-frequency transmon qubits have been
demonstrated with high-fidelity gate performance. Nevertheless, the relaxation
times of transmon qubits can have large temporal fluctuations, causing
instabilities in gate performance. The fluctuations are often believed to be
caused by nearly on-resonance couplings with sparse two-level-system (TLS)
defects. To mitigate their impact on qubit coherence and gate performance, one
direct approach is to tune the qubits away from these TLSs. In this work, to
combat the potential TLS-induced performance fluctuations in a tunable-bus
architecture unitizing fixed-frequency transmon qubits, we explore the
possibility of using an off-resonance microwave drive to effectively tuning the
qubit frequency through the ac-Stark shift while implementing universal gate
operations on the microwave-dressed qubit. We show that the qubit frequency can
be tuned up to 20 MHz through the ac-stark shift while keeping minimal impacts
on the qubit control. Besides passive approaches that aim to remove these TLSs
through more careful treatments of device fabrications, this work may offer an
active approach towards mitigating the TLS-induced performance fluctuations in
fixed-frequency transmon qubit devices.
|
quant-ph
|
Ordering of Trotterization: Impact on Errors in Quantum Simulation of
Electronic Structure: Trotter-Suzuki decompositions are frequently used in the quantum simulation
of quantum chemistry. They transform the evolution operator into a form
implementable on a quantum device, while incurring an error---the Trotter
error. The Trotter error can be made arbitrarily small by increasing the
Trotter number. However, this increases the length of the quantum circuits
required, which may be impractical. It is therefore desirable to find methods
of reducing the Trotter error through alternate means. The Trotter error is
dependent on the order in which individual term unitaries are applied. Due to
the factorial growth in the number of possible orderings with respect to the
number of terms, finding an optimal strategy for ordering Trotter sequences is
difficult. In this paper, we propose three ordering strategies, and assess
their impact on the Trotter error incurred. Initially, we exhaustively examine
the possible orderings for molecular hydrogen in a STO-3G basis. We demonstrate
how the optimal ordering scheme depends on the compatibility graph of the
Hamiltonian, and show how it varies with increasing bond length. We then use 44
molecular Hamiltonians to evaluate two strategies based on coloring their
incompatibility graphs, while considering the properties of the obtained
colorings. We find that the Trotter error for most systems involving heavy
atoms, using a reference magnitude ordering, is less than 1 kcal/mol. Relative
to this, the difference between ordering schemes can be substantial, being
approximately on the order of millihartrees. The coloring-based ordering
schemes are reasonably promising, however further work is required. Finally, we
consider ordering strategies based on the norm of the Trotter error operator,
including an iterative method for generating the new error operator terms added
upon insertion of a term into an ordered Hamiltonian.
|
quant-ph
|
Efficient Hamiltonian Simulation for Solving Option Price Dynamics: Pricing financial derivatives, in particular European-style options at
different time-maturities and strikes, means a relevant problem in finance. The
dynamics describing the price of vanilla options when constant volatilities and
interest rates are assumed, is governed by the Black-Scholes model, a linear
parabolic partial differential equation with terminal value given by the
pay-off of the option contract and no additional boundary conditions. Here, we
present a digital quantum algorithm to solve Black-Scholes equation on a
quantum computer by mapping it to the Schr\"odinger equation. The non-Hermitian
nature of the resulting Hamiltonian is solved by embedding its propagator into
an enlarged Hilbert space by using only one additional ancillary qubit.
Moreover, due to the choice of periodic boundary conditions, given by the
definition of the discretized momentum operator, we duplicate the initial
condition, which substantially improves the stability and performance of the
protocol. The algorithm shows a feasible approach for using efficient
Hamiltonian simulation techniques as Quantum Signal Processing to solve the
price dynamics of financial derivatives on a digital quantum computer. Our
approach differs from those based on Monte Carlo integration, exclusively
focused on sampling the solution assuming the dynamics is known. We report
expected accuracy levels comparable to classical numerical algorithms by using
9 qubits to simulate its dynamics on a fault-tolerant quantum computer, and an
expected success probability of the post-selection procedure due to the
embedding protocol above 60%.
|
quant-ph
|
The quark-gluon plasma, turbulence, and quantum mechanics: Quark-gluon plasmas formed in heavy ion collisions at high energies are well
described by ideal classical fluid equations with nearly zero viscosity. It is
believed that a similar fluid permeated the entire universe at about three
microseconds after the big bang. The estimated Reynolds number for this
quark-gluon plasma at 3 microseconds is approximately 10^19. The possibility
that quantum mechanics may be an emergent property of a turbulent proto-fluid
is tentatively explored. A simple relativistic fluid equation which is
consistent with general relativity and is based on a cosmic dust model is
studied. A proper time transformation transforms it into an inviscid Burgers
equation. This is analyzed numerically using a spectral method. Soliton-like
solutions are demonstrated for this system, and these interact with the known
ergodic behavior of the fluid to yield a stochastic and chaotic system which is
time reversible. Various similarities to quantum mechanics are explored.
|
quant-ph
|
Wigner Inequalities for Test of Hypothesis of Realism and Concepts of
Macroscopic and Local Realism: We propose a new Wigner inequality suitable for test of the hypothesis of
realism. We show that this inequality is not identical neither to the
well-known Wigner inequality nor to the Leggett-Garg inequality in Wigner form.
The obtained inequality is suitable for test of realism not only in quantum
mechanical systems, but also in quantum field systems.
Also we propose a mathematically consistent derivation of the Leggett--Garg
inequality in Wigner form, which was recently presented in the literature, for
three and $n$ distinct moments of time. Contrary to these works, our rigor
derivation uses Kolmogorov axiomatics of probability theory. We pay special
attention to the construction and studies of the spaces of elementary outcomes.
Basing on the the Leggett--Garg inequality in Wigner form for $n$ distinct
moments of time we prove that any unitary evolution of a quantum system
contradicts the concept of macroscopic realism. We show that application of the
concept of macroscopic realism to any quantum system leads to ``freezing'' of
the system in the initial state.
It is shown that for a particle with an infinite number of observables the
probability to find a pair of the observables in some defined state is zero,
even if the operators of these observables commute. This fact might serve as an
additional logical argument for the contradiction between quantum theory and
classical realism.
|
quant-ph
|
Quantum particles trapped in a position-dependent mass barrier; a
d-dimensional recipe: We consider a free particle,V(r)=0, with position-dependent mass
m(r)=1/(1+zeta^2*r^2)^2 in the d-dimensional schrodinger equation. The
effective potential turns out to be a generalized Poschl-Teller potential that
admits exact solution.
|
quant-ph
|
Modeling and Harmonic Balance Analysis of Parametric Amplifiers for
Qubit Read-out: Predicting the performance of traveling-wave parametric amplifiers (TWPAs)
based on nonlinear elements like superconducting Josephson junctions (JJs) is
vital for qubit read-out in quantum computers. The purpose of this article is
twofold: (a) to demonstrate how nonlinear inductors based on combinations of
JJs can be modeled in commercial circuit simulators, and (b) to show how the
harmonic balance (HB) is used in the reliable prediction of the amplifier
performance e.g., gain and pump harmonic power conversion. Experimental
characterization of two types of TWPA architectures is compared with
simulations to showcase the reliability of the HB method. We disseminate the
modeling know-how and techniques to new designers of parametric amplifiers.
|
quant-ph
|
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