Quantum Darwinism posits that the emergence of a classical reality relies onthe spreading of classical information from a quantum system to many parts ofits environment. But what are the essential physical principles of quantumtheory that make this mechanism possible? We address this question byformulating the simplest instance of Darwinism -- CNOT-like fan-outinteractions -- in a class of probabilistic theories that contain classical andquantum theory as special cases. We determine necessary and sufficientconditions for any theory to admit such interactions. We find that everynon-classical theory that admits this spreading of classical information musthave both entangled states and entangled measurements. Furthermore, we showthat Spekkens' toy theory admits this form of Darwinism, and so do allprobabilistic theories that satisfy principles like strong symmetry, or containa certain type of decoherence processes. Our result suggests thecounterintuitive general principle that in the presence of localnon-classicality, a classical world can only emerge if this non-classicalitycan be "amplified" to a form of entanglement.
Majorana braiding gates for topological superconductors in a one dimensional geometryWe propose and analyze a physical system capable of performing topologicalquantum computation with Majorana zero modes (MZM) in a one-dimensionaltopological superconductor (1DTS). One of the leading methods to realizequantum gates in 1DTS is to use T-junctions, which allows one to maneuver MZMssuch as to achieve braiding. In this paper, we propose a scheme that is in apurely one-dimensional geometry and does not require T-junctions, insteadreplacing it with an auxiliary qubit. We show that this allows one to performone and two logical qubit $ Z $ rotations. We first design a topologicallyprotected logical $Z$-gate based entirely on local interactions within the1DTS. Using an auxiliary qubit coupled to the topological superconductors, weextend the $Z$-gate to single and multiqubit arbitrary rotations with partialtopological protection. Finally, to perform universal quantum computing, weintroduce a scheme for performing arbitrary unitary rotations, albeit withouttopological protection. We develop a formalism based on unitary braids whichcreates transitions between different topological phases of the 1DTS system.The unitary formalism can be simply converted to an equivalent adiabaticscheme, which we numerically simulate and show that high fidelity operationsshould be possible with reasonable parameters.
Information flow and error scaling for fully-quantum controlThe optimally designed control of quantum systems is playing an increasinglyimportant role to engineer novel and more efficient quantum technologies. Here,in the scenario represented by controlling an arbitrary quantum system via theinteraction with an another optimally initialized auxiliary quantum system, weshow that the quantum channel capacity sets the scaling behaviour of theoptimal control error. Specifically, we prove that the minimum control error isensured by maximizing the quantum capacity of the channel mapping the initialcontrol state into the target state of the controlled system, i.e., optimizingthe quantum information flow from the controller to the system to becontrolled. Analytical results, supported by numerical evidences, are providedwhen the systems and the controller are either qubits or single Bosonic modesand can be applied to a very large class of platforms for controllable quantumdevices.
Sublinear classical and quantum algorithms for general matrix gamesWe investigate sublinear classical and quantum algorithms for matrix games, afundamental problem in optimization and machine learning, with provableguarantees. Given a matrix $A\in\mathbb{R}^{n\times d}$, sublinear algorithmsfor the matrix game $\min_{x\in\mathcal{X}}\max_{y\in\mathcal{Y}} y^{\top} Ax$were previously known only for two special cases: (1) $\mathcal{Y}$ being the$\ell_{1}$-norm unit ball, and (2) $\mathcal{X}$ being either the $\ell_{1}$-or the $\ell_{2}$-norm unit ball. We give a sublinear classical algorithm thatcan interpolate smoothly between these two cases: for any fixed $q\in (1,2]$,we solve the matrix game where $\mathcal{X}$ is a $\ell_{q}$-norm unit ballwithin additive error $\epsilon$ in time $\tilde{O}((n+d)/{\epsilon^{2}})$. Wealso provide a corresponding sublinear quantum algorithm that solves the sametask in time $\tilde{O}((\sqrt{n}+\sqrt{d})\textrm{poly}(1/\epsilon))$ with aquadratic improvement in both $n$ and $d$. Both our classical and quantumalgorithms are optimal in the dimension parameters $n$ and $d$ up topoly-logarithmic factors. Finally, we propose sublinear classical and quantumalgorithms for the approximate Carathéodory problem and the $\ell_{q}$-marginsupport vector machines as applications.
Cavity quantum electrodynamics and chiral quantum opticsCavity quantum electrodynamics (CQED) investigates the interaction betweenlight confined in a resonator and particles, such as atoms. In recent years,CQED experiments have reached the optical domain resulting in many interestingapplications in the realm of quantum information processing. For many of theseapplication it is necessary to overcome limitations imposed by photon loss. Inthis context whispering-gallery mode (WGM) resonators have obtained significantinterest. Besides their small mode volume and their ultra high quality, theyalso exhibit favorable polarization properties that give rise to chirallight--matter interaction. In this chapter, we will discuss the origin and theconsequences of these chiral features and we review recent achievements in thisarea.
Quantum Phase Transitions in Long-Range Interacting Hyperuniform Spin Chains in a Transverse FieldHyperuniform states of matter are characterized by anomalous suppression oflong-wavelength density fluctuations. While most of interesting cases ofdisordered hyperuniformity are provided by complex many-body systems likeliquids or amorphous solids, classical spin chains with certain long-rangeinteractions have been shown to demonstrate the same phenomenon. It iswell-known that the transverse field Ising model shows a quantum phasetransition (QPT) at zero temperature. Under the quantum effects of a transversemagnetic field, classical hyperuniform spin chains are expected to lose theirhyperuniformity. High-precision simulations of these cases are complicatedbecause of the presence of highly nontrivial long-range interactions. Weperform extensive analysis of these systems using density matrixrenormalization group to study the possibilities of phase transitions and themechanism by which they lose hyperuniformity. We discover first-order QPTs inthe hyperuniform spin chains. An interesting feature of the phase transitionsin these disordered hyperuniform spin chains is that, depending on theparameter values, the presence of transverse magnetic field may remarkably leadto increase in the order of the ground state as measured by the "$\tau$ ordermetric," even if hyperuniformity is lost. Therefore, it would be possible todesign materials to target specific novel quantum behaviors in the presence ofa transverse magnetic field. Our numerical investigations suggest that thesespin chains can show no more than two QPTs. We further analyze the long-rangeinteracting spin chains via the Jordan-Wigner mapping, showing that under thepairwise interacting approximation and a mean-field treatment, there can be atmost two QPTs. Based on these numerical and theoretical explorations, weconjecture that these spin chains can show a maximum of two QPTs at zerotemperature.
Spin qudit tomographyWe consider the task of performing quantum state tomography on a $d$-statespin qudit, using only measurements of spin projection onto differentquantization axes. By an exact mapping onto the classical problem of signalrecovery on the sphere, we prove that full reconstruction of arbitrary quditstates requires a minimal number of measurement axes, $r_d^{\mathrm{min}}$,that is bounded by $2d-1\le r_d^{\mathrm{min}}\le d^2$. We conjecture that$r_d^{\mathrm{min}}=2d-1$, which we verify numerically for all $d\le200$. Wethen provide algorithms with $O(rd^3)$ serial runtime, parallelizable down to$O(rd^2)$, for (i) computing a priori upper bounds on the expected error withwhich spin projection measurements along $r$ given axes can reconstruct anunknown qudit state, and (ii) estimating a posteriori the statistical error ina reconstructed state. Our algorithms motivate a simple randomized tomographyprotocol, for which we find that using more measurement axes can yieldsubstantial benefits that plateau after $r\approx3d$.
Monogamy Relations for Multiqubit SystemsRecently a new class of monogamy relations (actually, exponentially many) wasprovided by Christopher Eltschka et al. in terms of squared concurrence. Theirapproach restricted to the distribution of bipartite entanglement sharedbetween different subsystems of a global state. We have critically analyzedthose monogamy relations in three as well as in four qubit pure states usingsquared negativity. We have been able to prove that in case of pure three qubitstates those relations are always true in terms of squared negativity. However,if we consider the pure four qubit states, the results are not always true.Rather, we find opposite behaviour in some particular classes of four qubitpure states where some of the monogamy relations are violated. We have providedanalytical and numerical evidences in support of our claim.
Geometric scattering in the presence of line defectsA non-relativistic scalar particle moving on a curved surface undergoes ageometric scattering whose behavior is sensitive to the theoretically ambiguousvalues of the intrinsic and extrinsic curvature coefficients entering theexpression for the quantum Hamiltonian operator. This suggests using thescattering data to settle the ambiguity in the definition of the Hamiltonian.It has recently been shown that the inclusion of point defects on the surfaceenhances the geometric scattering effects. We perform a detailed study of thegeometric scattering phenomenon in the presence of line defects for the casethat the particle is confined to move on a Gaussian bump and the defect(s) aremodeled by delta-function potentials supported on a line or a set of parallellines normal to the scattering axis. In contrast to a surface having pointdefects, the scattering phenomenon associated with this system is genericallygeometric in nature in the sense that for a flat surface the scatteringamplitude vanishes for all scattering angles $\theta$ except $\theta=\theta_0$and $\pi-\theta_0$, where $\theta_0$ is the angle of incidence. We show thatthe presence of the line defects amplifies the geometric scattering due to theGaussian bump. This amplification effect is particularly strong when the centerof the bump is placed between two line defects.
Quantum supremacy and quantum phase transitionsDemonstrating the ability of existing quantum platforms to perform certaincomputational tasks intractable to classical computers represents a cornerstonein quantum computing. Despite the growing number of such proposed "quantumsupreme" tasks, it remains an important challenge to identify their directapplications. In this work, we describe how the approach proposed in Ref.[] for demonstrating quantum supremacy in generic driven analogmany-body systems, such as those found in cold atom and ion setups, can beextended to explore dynamical quantum phase transitions. We show how keyquantum supremacy signatures, such as the distance between the outputdistribution and the expected Porter Thomas distribution at the supremacyregime, can be used as effective order parameters. We apply this approach to aperiodically driven disordered 1D Ising model and show that we can accuratelycapture the transition between the driven thermalized and many-body localizedphases. This approach also captures the transition towards the Floquetprethermalized regime for high-frequency driving. Revisiting quantum phases ofmatter under the light of the recent discussions about quantum supremacy drawsa link between complexity theory and analog many-body systems.
Quantum-accelerated multilevel Monte Carlo methods for stochastic differential equations in mathematical financeInspired by recent progress in quantum algorithms for ordinary and partialdifferential equations, we study quantum algorithms for stochastic differentialequations (SDEs). Firstly we provide a quantum algorithm that gives a quadraticspeed-up for multilevel Monte Carlo methods in a general setting. Asapplications, we apply it to compute expection values determined by classicalsolutions of SDEs, with improved dependence on precision. We demonstrate theuse of this algorithm in a variety of applications arising in mathematicalfinance, such as the Black-Scholes and Local Volatility models, and Greeks. Wealso provide a quantum algorithm based on sublinear binomial sampling for thebinomial option pricing model with the same improvement.
A quantum invitation to probability theoryQuantum probability theory and complex analysis for children.
Experimental validation of fully quantum fluctuation theoremsFluctuation theorems are fundamental extensions of the second law ofthermodynamics for small systems. Their general validity arbitrarily far fromequilibrium makes them invaluable in nonequilibrium physics. So far,experimental studies of quantum fluctuation relations do not account forquantum correlations and quantum coherence, two essential quantum properties.We here experimentally verify detailed and integral fully quantum fluctuationtheorems for heat exchange using two quantum-correlated thermal spins-1/2 in anuclear magnetic resonance setup. We confirm, in particular, individualintegral fluctuation relations for quantum correlations and quantum coherence,as well as for the sum of all quantum contributions. These refined formulationsof the second law are important for the investigation of fully quantum featuresin nonequilibrium thermodynamics.
Saving superconducting quantum processors from qubit decay and correlated errors generated by gamma and cosmic raysError-corrected quantum computers can only work if errors are small anduncorrelated. Here I show how cosmic rays or stray background radiation affectssuperconducting qubits by modeling the phonon to electron/quasiparticledown-conversion physics. For present designs, the model predicts about 57\% ofthe radiation energy breaks Cooper pairs into quasiparticles, which thenvigorously suppress the qubit energy relaxation time ($T_1 \sim$ 160 ns) over alarge area (cm) and for a long time (ms). Such large and correlated decay killserror correction. Using this quantitative model, I show how this energy can bechanneled away from the qubit so that this error mechanism can be reduced bymany orders of magnitude. I also comment on how this affects other solid-statequbits.
Quantum battery of interacting spins with environmental noiseA quantum battery is a temporary energy-storage system. We constructed thequantum battery model of an N-spin chain with nearest-neighbor hoppinginteraction and investigated the charging process of the quantum battery. Weobtained the maximum energy in the quantum battery charged by a coherent cavitydriving field or a thermal heat bath. We confirmed that for a finite-lengthspin chain, thermal charging results in a nonzero ergotropy, contradicting aprevious result: that an incoherent heat source cannot charge a single-spinquantum battery. The nearest-neighbor hopping interaction induces energy bandsplitting, which enhances the energy storage and the ergotropy of the quantumbattery. We found a critical point in the energy and ergotropy resulting fromthe ground-state quantum phase transition, after which the energy significantlyenhance. Finally, we also found that disorder increased the energy of thequantum battery.
Relativistic potential of a hydrogen-like system in Poincare invariant quantum mechanicsTo describe a relativistic hydrogen atom we used the Poincare-covariant modelof a two particle system with gauge invariant potential. The kernel of theradial integral equation is obtained which describes a system of two fermionswith electromagnetic interaction.
Decoherence effects in non-classicality tests of gravityThe experimental observation of a clear quantum signature of gravity isbelieved to be out of the grasp of current technology. However several recentpromising proposals to test the possible existence of non-classical features ofgravity seem to be accessible by the state-of-art table-top experiments. Amongthem, some aim at measuring the gravitationally induced entanglement betweentwo masses which would be a distinct non-classical signature of gravity. Weexplicitly study, in two of these proposals, the effects of decoherence on thesystem's dynamics by monitoring the corresponding degree of entanglement. Weidentify the required experimental conditions necessary to perform successfullythe experiments. In parallel, we account also for the possible effects of theContinuous Spontaneous Localization (CSL) model, which is the most known amongthe models of spontaneous wavefunction collapse. We find that any value of theparameters of the CSL model would completely hinder the generation ofgravitationally induced entanglement.
Recursive Generation of The Semi-Classical Expansion in Arbitrary DimensionWe present a recursive procedure, which is based on the small time expansionof the propagator, in order to generate a semi-classical expansion of the\textit{quantum action} for a quantum mechanical potential in arbitrarydimensions. In the method we use the spectral information emerges from thesingularities of the propagator on the complex $t$ plane, which are handled bythe $i\ve$ prescription and basic complex analysis. This feature allows forgeneralization to higher dimensions. We illustrate the procedure by providingsimple examples in non-relativistic quantum mechanics.
The quantum solitons atomtronic interference deviceWe study a quantum many-body system of attracting bosons confined in aring-shaped potential and interrupted by a weak link. With such architecture,the system defines atomtronic quantum interference devices harnessing quantumsolitonic currents. We demonstrate that the system is characterized by specificinterplay between the interaction and the strength of the weak link. Inparticular, we find that, depending on the operating conditions, the currentcan be a universal function of the relative size between the strength of theimpurity and interaction. The low lying many-body states are studied through aquench dynamical protocol that is the atomtronic counterpart of the Ramseyinterferometry. With this approach, we demonstrate how our system defines aqubit. The current states are addressed through the analysis of the momentumdistribution.
Detection of charge states of an InAs nanowire triple quantum dot with an integrated nanowire charge sensorA linear triple quantum dot (TQD) integrated with a quantum dot (QD) chargesensor is realized. The TQD and the charge sensor are built from two adjacentInAs nanowires by fine finger gate technique. The charge state configurationsof the nanowire TQD are studied by measurements of the direct transport signalsof the TQD and by detection of the charge state transitions in the TQD via thenanowire QD sensor. Excellent agreements in the charge stability diagrams ofthe TQD obtained by the direct transport measurements and by the charge-statetransition detection measurements are achieved. It is shown that the chargestability diagrams are featured by three groups of charge state transitionlines of different slopes, corresponding to the changes in the electronoccupation numbers of the three individual QDs in the TQD. It is also shownthat the integrated nanowire QD sensor is highly sensitive and can detect thecharge state transitions in the cases where the direct transport signals of theTQD are too weak to be measurable. Tuning to a regime, where all the three QDsin the TQD are close to be on resonance with the Fermi level of the source anddrain reservoirs and co-existence of triple and quadruple points becomespossible, has also been demonstrated with the help of the charge sensor in theregion where the direct transport signals of the TQD are hardly visible.
Spatial distributions of the fields in guided normal modes of two coupled parallel nanofibersWe study the cross-sectional profiles and spatial distributions of the fieldsin guided normal modes of two coupled parallel nanofibers. We show that thedistributions of the components of the field in a guided normal mode of twoidentical nanofibers are either symmetric or antisymmetric with respect to theradial principal axis $x$ and the tangential principal axis $y$ in thecross-sectional plane of the fibers. The symmetry of the magnetic fieldcomponents with respect to the principal axes is opposite to that of theelectric field components. We show that, in the case of even$\mathcal{E}_z$-cosine modes, the electric intensity distribution is dominantin the area between the fibers, with a saddle point at the two-fiber center.Meanwhile, in the case of odd $\mathcal{E}_z$-sine modes, the electricintensity distribution at the two-fiber center attains a local minimum ofexactly zero. We find that the differences between the results of the coupledmode theory and the exact mode theory are large when the fiber separationdistance is small and either the fiber radius is small or the light wavelengthis large. We show that, in the case where the two nanofibers are not identical,the intensity distribution is symmetric about the radial principal axis $x$ andasymmetric about the tangential principal axis $y$.
Exact Mobility Edges in One-Dimensional Mosaic Lattices Inlaid with Slowly Varying PotentialsWe propose a family of one-dimensional mosaic models inlaid with a slowlyvarying potential $V_n=\lambda\cos(\pi\alpha n^\nu)$, where $n$ is the latticesite index and $0<\nu<1$. Combinating the asymptotic heuristic argument withthe theory of trace map of transfer matrix, mobility edges (MEs) andpseudo-mobility edges (PMEs) in their energy spectra are solvedsemi-analytically, where ME separates extended states from weakly localizedones and PME separates weakly localized states from strongly localized ones.The nature of eigenstates in extended, critical, weakly localized and stronglylocalized is diagnosed by the local density of states, the Lyapunov exponent,and the localization tensor. Numerical calculation results are in excellentquantitative agreement with theoretical predictions.
Full configuration interaction simulations of exchange-coupled donors in silicon using multi-valley effective mass theoryDonor spin in silicon have achieved record values of coherence times andsingle-qubit gate fidelities. The next stage of development involvesdemonstrating high-fidelity two-qubit logic gates, where the most naturalcoupling is the exchange interaction. To aid the efficient design of scalabledonor-based quantum processors, we model the two-electron wave function using afull configuration interaction method within a multi-valley effective masstheory. We exploit the high computational efficiency of our code to investigatethe exchange interaction, valley population, and electron densities for twophosphorus donors in a wide range of lattice positions, orientations, and as afunction of applied electric fields. The outcomes are visualized withinteractive images where donor positions can be swept while watching the valleyand orbital components evolve accordingly. Our results provide a physicallyintuitive and quantitatively accurate understanding of the placement and tuningcriteria necessary to achieve high-fidelity two-qubit gates with donors insilicon.
Von Neumann entropy in a dispersive cavityWe study the von Neumann entropy of the partial trace of a system of twotwo-level atoms (qubits) in a dispersive cavity where the atoms are interactingcollectively with a single mode electromagnetic field in the cavity. We make acontrast of this entanglement entropy with the spin squeezing property of thesystem. We find a close relationship between this von Neumann entropy and thespin squeezing of the system.
Eigenstate thermalization scaling in approaching the classical limitAccording to the eigenstate thermalization hypothesis (ETH), theeigenstate-to-eigenstate fluctuations of expectation values of localobservables should decrease with increasing system size. In approaching thethermodynamic limit - the number of sites and the particle number increasing atthe same rate - the fluctuations should scale as $\sim D^{-1/2}$ with theHilbert space dimension $D$. Here, we study a different limit - the classicalor semiclassical limit - by increasing the particle number in fixed latticetopologies. We focus on the paradigmatic Bose-Hubbard system, which isquantum-chaotic for large lattices and shows mixed behavior for small lattices.We derive expressions for the expected scaling, assuming ideal eigenstateshaving Gaussian-distributed random components. We show numerically that, forlarger lattices, ETH scaling of physical mid-spectrum eigenstates follows theideal (Gaussian) expectation, but for smaller lattices, the scaling occurs viaa different exponent. We examine several plausible mechanisms for thisanomalous scaling.
Long-range Ising chains: eigenstate thermalization and symmetry breaking of excited statesWe use large-scale exact diagonalization to study the quantum Ising chain ina transverse field with long-range power-law interactions decaying withexponent $\alpha$. Analyzing various eigenstate and eigenvalue properties, wefind numerical evidence for ergodic behavior in the thermodynamic limit for$\alpha>0$, \textit{i.~e.} for the slightest breaking of the permutationsymmetry at $\alpha=0$. Considering {an} excited-state fidelity susceptibility,{an} energy-resolved average level-spacing ratio and the eigenstateexpectations of observables, we observe that a behavior consistent witheigenstate thermalization first emerges at high energy densities for finitesystem sizes, as soon as $\alpha>0$. We argue that ergodicity moves towardslower energy densities for increasing system sizes. While we argue the systemto be ergodic for any $\alpha>0$, we also find a peculiar behaviour near$\alpha=2$ suggesting the proximity to a yet unknown integrable point. Wefurther study the symmetry-breaking properties of the eigenstates. We arguethat for weak transverse fields the eigenstates break the $\mathbb{Z}_2$symmetry, and show long-range order, at finite excitation energy densities forall the values of $\alpha$ we can technically address ($\alpha\leq 1.5$). Ourcontribution settles central theoretical questions on long-range quantum Isingchains and are also of direct relevance for the nonequilibrium dynamics in suchsystems such as realized experimentally in systems of trapped ions.
A statistical mechanism for operator growthIt was recently conjectured that in generic quantum many-body systems, thespectral density of local operators has the slowest high-frequency decay aspermitted by locality. We show that the infinite-temperature version of this"universal operator growth hypothesis" holds for the quantum Ising spin modelin $d \ge 2$ dimensions, and for the chaotic Ising chain (with longitudinal andtransverse fields) in one dimension. Moreover, the disordered chaotic Isingchain that exhibits many-body localization can have the same high-frequencyspectral density decay as thermalizing models. Our argument is statistical innature, and is based on the observation that the moments of the spectraldensity can be written as a sign-problem-free sum over paths of Pauli stringoperators.
Entanglement of graph states of spin system with Ising interaction and its quantifying on IBM's quantum computerWe consider graph states generated by operator of evolution with IsingHamiltonian. It is found that the geometric measure of entanglement of thegraph state is related with degree of vertex in the corresponding graph. Thegraph states of spin system with Ising interaction are prepared and theirentanglement is quantified on the 5-qubit IBM's quantum computer, IBM QValencia.
The Zeno and anti-Zeno effects: studying modified decay rates for spin-boson models with both strong and weak system-environment couplingsIn this paper, we look into what happens to a quantum system under repeatedmeasurements if system evolution is removed before each measurement isperformed. Beginning with investigating a single two-level system coupled totwo independent baths of harmonic oscillators, we move to replacing it with alarge collection of such systems, thereby invoking the large spin-boson model.Whereas each of our two-level systems interacts strongly with one of theaforementioned baths, it interacts weakly with the other. A polarontransformation is used to make it possible for the problem in the strongcoupling regime to be treated with perturbation theory. We find that the caseinvolving a single two-level system exhibits qualitative and quantitativedifferences from the case involving a collection of them; however, the generaleffects of strong and weak couplings turn out to be the same as those in thepresence of system evolution, something which allows us to establish thatsystem evolution has no practical bearing on any of these effects.
Transmon platform for quantum computing challenged by chaotic fluctuationsFrom the perspective of many body physics, the transmon qubit architecturescurrently developed for quantum computing are systems of coupled nonlinearquantum resonators. A significant amount of intentional frequency detuning(disorder) is required to protect individual qubit states against thedestabilizing effects of nonlinear resonator coupling. Here we investigate thestability of this variant of a many-body localized (MBL) phase for systemparameters relevant to current quantum processors of two different types, thoseusing untunable qubits (IBM type) and those using tunable qubits (Delft/Googletype). Applying three independent diagnostics of localization theory - aKullback-Leibler analysis of spectral statistics, statistics of many-body wavefunctions (inverse participation ratios), and a Walsh transform of themany-body spectrum - we find that these computing platforms are dangerouslyclose to a phase of uncontrollable chaotic fluctuations.
A general framework for multimode Gaussian quantum optics and photo-detection: application to Hong-Ou-Mandel interference with filtered heralded single photon sourcesThe challenging requirements of large scale quantum information processingusing parametric heralded single photon sources involves maximising theinterference visibility whilst maintaining an acceptable photon generationrate. By developing a general theoretical framework that allows us to includelarge numbers of spatial and spectral modes together with linear and non-linearoptical elements, we investigate the combined effects of spectral and photonnumber impurity on the measured Hong--Ou--Mandel interference visibility ofparametric photon sources, considering both threshold and number resolvingdetectors, together with the effects of spectral filtering. We find that forany degree of spectral impurity, increasing the photon generation ratenecessarily decreases the interference visibility, even when using numberresolving detection. While tight spectral filtering can be used to enforcespectral purity and increased interference visibility at low powers, we findthat the induced photon number impurity results in a decreasing interferencevisibility and heralding efficiency with pump power, while the maximumgeneration rate is also reduced.
An organic quantum batteryQuantum batteries harness the unique properties of quantum mechanics toenhance energy storage compared to conventional batteries. In particular, theyare predicted to undergo superextensive charging, where batteries with largercapacity actually take less time to charge. Up until now however, they have notbeen experimentally demonstrated, due to the challenges in quantum coherentcontrol. Here we implement an array of two-level systems coupled to a photonicmode to realise a Dicke quantum battery. Our quantum battery is constructedwith a microcavity formed by two dielectric mirrors enclosing a thin film of afluorescent molecular dye in a polymer matrix. We use ultrafast opticalspectroscopy to time resolve the charging dynamics of the quantum battery atfemtosecond resolution. We experimentally demonstrate superextensive increasesin both charging power and storage capacity, in agreement with our theoreticalmodelling. We find that decoherence plays an important role in stabilisingenergy storage, analogous to the role that dissipation plays in photosynthesis.This experimental proof-of-concept is a major milestone towards the practicalapplication of quantum batteries in quantum and conventional devices. Our workopens new opportunities for harnessing collective effects in light-mattercoupling for nanoscale energy capture, storage, and transport technologies,including the enhancement of solar cell efficiencies.
Data-Driven System Identification of Linear Quantum Systems Coupled to Time-Varying Coherent InputsIn this paper, we develop a system identification algorithm to identify amodel for unknown linear quantum systems driven by time-varying coherentstates, based on empirical single-shot continuous homodyne measurement data ofthe system's output. The proposed algorithm identifies a model that satisfiesthe physical realizability conditions for linear quantum systems, challengingconstraints not encountered in classical (non-quantum) linear systemidentification. Numerical examples on a multiple-input multiple-output opticalcavity model are presented to illustrate an application of the identificationalgorithm.
How to enhance quantum generative adversarial learning of noisy informationQuantum Machine Learning is where nowadays machine learning meets quantuminformation science. In order to implement this new paradigm for novel quantumtechnologies, we still need a much deeper understanding of its underlyingmechanisms, before proposing new algorithms to feasibly address real problems.In this context, quantum generative adversarial learning is a promisingstrategy to use quantum devices for quantum estimation or generative machinelearning tasks. However, the convergence behaviours of its training process,which is crucial for its practical implementation on quantum processors, havenot been investigated in detail yet. Indeed here we show how different trainingproblems may occur during the optimization process, such as the emergence oflimit cycles. The latter may remarkably extend the convergence time in thescenario of mixed quantum states playing a crucial role in the alreadyavailable noisy intermediate scale quantum devices. Then, we propose newstrategies to achieve a faster convergence in any operating regime. Our resultspave the way for new experimental demonstrations of such hybridclassical-quantum protocols allowing to evaluate the potential advantages overtheir classical counterparts.
Correlated Charge Noise and Relaxation Errors in Superconducting QubitsThe central challenge in building a quantum computer is error correction.Unlike classical bits, which are susceptible to only one type of error, quantumbits ("qubits") are susceptible to two types of error, corresponding to flipsof the qubit state about the $X$- and $Z$-directions. While the HeisenbergUncertainty Principle precludes simultaneous monitoring of $X$- and $Z$-flipson a single qubit, it is possible to encode quantum information in large arraysof entangled qubits that enable accurate monitoring of all errors in thesystem, provided the error rate is low. Another crucial requirement is thaterrors cannot be correlated. Here, we characterize a superconducting multiqubitcircuit and find that charge fluctuations are highly correlated on a lengthscale over 600~$\mu$m; moreover, discrete charge jumps are accompanied by astrong transient suppression of qubit energy relaxation time across themillimeter-scale chip. The resulting correlated errors are explained in termsof the charging event and phonon-mediated quasiparticle poisoning associatedwith absorption of gamma rays and cosmic-ray muons in the qubit substrate.Robust quantum error correction will require the development of mitigationstrategies to protect multiqubit arrays from correlated errors due to particleimpacts.
6-qubit Optimal Clifford CircuitsClifford group lies at the core of quantum computation -- it underliesquantum error correction, its elements can be used to perform magic statedistillation and they form randomized benchmarking protocols, Clifford group isused to study quantum entanglement, and more. The ability to utilize Cliffordgroup elements in practice relies heavily on the efficiency of theircircuit-level implementation. Finding short circuits is a hard problem; despiteClifford group being finite, its size grows quickly with the number of qubits$n$, limiting known optimal implementations to $n{=}4$ qubits. For $n{=}6$, thenumber of Clifford group elements is about $2.1{\cdot}10^{23}$. In this paper,we report a set of algorithms, along with their C/C++ implementation, thatimplicitly synthesize optimal circuits for all 6-qubit Clifford group elementsby storing a subset of the latter in a database of size 2.1TB (1KB=1024B). Wedemonstrate how to extract arbitrary optimal 6-qubit Clifford circuit in$0.0009358$ and $0.0006274$ seconds using consumer- and enterprise-gradecomputers (hardware) respectively, while relying on this database.
Generation of Fock-State Superpositions and Binomial-Code Holonomic Gates via Dressed Intermediate States in the Ultrastrong Light-Matter Coupling RegimeBy using the dressed-state properties of an ultrastrong coupling system, wepropose to generate and manipulate, with high fidelities, arbitrarysuperposition of Fock states. These generated states can form bosonic codes(e.g., binomial codes) to implement nonadiabatic holonomic quantum computation,making the computation fast, robust, and fault-tolerant. The holonomic gatesare induced by geometric phases, which possess a built-in noise-resiliencefeature against local noises. No high-order processes or nonlinear driving areneeded in this work, so that the quantum gates can be implemented in tens ofnanoseconds. Such a fast evolution makes our protocols robust againstdecoherence caused by the decays and dephasings of both the cavity and theatom. Moreover, we design the control fields by a systematic-error-sensitivitynullification method, thus our protocols can be mostly insensitive tosystematic errors caused by pulse imperfections.
Hybrid microwave-optical scanning probe for addressing solid-state spins in nanophotonic cavitiesSpin-photon interfaces based on solid-state atomic defects have enabled avariety of key applications in quantum information processing. To maximize thelight-matter coupling strength, defects are often placed inside nanoscaledevices. Efficiently coupling light and microwave radiation into thesestructures is an experimental challenge, especially in cryogenic or high vacuumenvironments with limited sample access. In this work, we demonstrate afiber-based scanning probe that simultaneously couples light into a planarphotonic circuit and delivers high power microwaves for driving electron spintransitions. The optical portion achieves 46% one-way coupling efficiency,while the microwave portion supplies an AC magnetic field with strength up to 9Gauss. The entire probe can be scanned across a large number of devices insidea $^3$He cryostat without free-space optical access. We demonstrate thistechnique with silicon nanophotonic circuits coupled to single Er$^{3+}$ ions.
Ultra-bright multiplexed energy-time entangled photon generation from lithium niobate on insulator chipHigh-flux entangled photon source is the key resource for quantum opticalstudy and application. Here it is realized in a lithium niobate on isolator(LNOI) chip, with 2.79*10^11 Hz/mW photon pair rate and 1.53*10^9 Hz/nm/mWspectral brightness. These data are boosted by over two orders of magnitudecompared to existing technologies. A 130-nm broad bandwidth is engineered for8-channel multiplexed energy-time entanglement. Harnessed by high-extinctionfrequency correlation and Franson interferences up to 99.17% visibility, suchenergy-time entanglement multiplexing further enhances high-flux data rate, andwarrants broad applications in quantum information processing on a chip.
Quantum compiler for classical dynamical systemsWe present a framework for simulating measure-preserving, ergodic dynamicalsystems on a quantum computer. Our approach is based on a quantum feature maprepresenting classical states by density operators (quantum states) on areproducing kernel Hilbert space (RKHS) $\mathcal H $ of functions on classicalstate space. Simultaneously, a mapping is employed from classical observablesinto self-adjoint operators on $\mathcal H$ such that quantum mechanicalexpectation values are consistent with pointwise function evaluation. Quantumstates and observables on $\mathcal H$ evolve under the action of a unitarygroup of Koopman operators in a compatible manner with classical dynamicalevolution. To achieve quantum parallelism, the state of the quantum system isprojected onto a finite-rank density operator on a $2^N$-dimensional tensorproduct Hilbert space associated with $N$ qubits. By employing discreteFourier-Walsh transforms of spectral functions, the Hamiltonian of thefinite-dimensional quantum system is decomposed into a sum of mutuallycommuting operators of pure tensor product form, implementable as an$N$-channel quantum circuit. In the special case of quasiperiodic dynamics, nointerchannel communication is necessary. Circuits of higher complexity arerequired to simulate chaotic dynamics. The output of the quantum compiler is astochastic simulator of the evolution of classical observables, realizedthrough projective quantum measurements. Numerical examples, including aquantum circuit implementation using the Qiskit software development kit,demonstrate the consistency of the quantum compiler for simple dynamicalsystems.
Solving Inequality-Constrained Binary Optimization Problems on Quantum AnnealerWe propose a new method for solving binary optimization problems underinequality constraints using a quantum annealer. To deal with inequalityconstraints, we often use slack variables, as in previous approaches. When weuse slack variables, we usually conduct a binary expansion, which requiresnumerous physical qubits. Therefore, the problem of the current quantumannealer is limited to a small scale. In this study, we employ the alternatingdirection method of multipliers. This approach allows us to deal with varioustypes using constraints in the current quantum annealer without slackvariables. To test the performance of our algorithm, we use quadratic knapsackproblems (QKPs). We compared the accuracy obtained by our method with asimulated annealer and the optimization and sampling mode of a D-Wave machine.As a result of our experiments, we found that the sampling mode shows the bestaccuracy. We also found that the computational time of our method is fasterthan that of the exact solver when we tackle various QKPs defined on densegraphs.
Universal quantum gates, artificial neurons and pattern recognition simulated by \textit{LC} resonatorsWe propose to simulate quantum gates by \textit{LC} resonators, where theamplitude and the phase of the voltage describe the quantum state. Bycontrolling capacitance or inductance of resonators, it is possible to controlthe phase of the voltage arbitrarily. A set of resonators acts as thephase-shift, the Hadamard and the CNOT gates. They constitute a set ofuniversal quantum gates. We also discuss an application to an artificialneuron. As an example, we study a pattern recognition of numbers and alphabetsby evaluating the similarity between an input and the reference pattern. Wealso study a colored pattern recognition by using a complex neural network.