Showing papers in "Physical Review A in 2018"
TL;DR: In this paper, a classical-quantum hybrid algorithm for machine learning on near-term quantum processors, called quantum circuit learning, is proposed, which can approximate nonlinear functions.
Abstract: We propose a classical-quantum hybrid algorithm for machine learning on near-term quantum processors, which we call quantum circuit learning. A quantum circuit driven by our framework learns a given task by tuning parameters implemented on it. The iterative optimization of the parameters allows us to circumvent the high-depth circuit. Theoretical investigation shows that a quantum circuit can approximate nonlinear functions, which is further confirmed by numerical simulations. Hybridizing a low-depth quantum circuit and a classical computer for machine learning, the proposed framework paves the way toward applications of near-term quantum devices for quantum machine learning.
947 citations
TL;DR: In this paper, a quantum-classical algorithm was proposed to study the dynamics of the two-spatial-site Schwinger model on IBM's quantum computers using rotational symmetries, total charge, and parity.
Abstract: We present a quantum-classical algorithm to study the dynamics of the two-spatial-site Schwinger model on IBM's quantum computers. Using rotational symmetries, total charge, and parity, the number of qubits needed to perform computation is reduced by a factor of $\ensuremath{\sim}5$, removing exponentially large unphysical sectors from the Hilbert space. Our work opens an avenue for exploration of other lattice quantum field theories, such as quantum chromodynamics, where classical computation is used to find symmetry sectors in which the quantum computer evaluates the dynamics of quantum fluctuations.
383 citations
TL;DR: This work extends adversarial training to the quantum domain and shows how to construct generative adversarial networks using quantum circuits, as well as showing how to compute gradients -- a key element in generatives adversarial network training -- using another quantum circuit.
Abstract: Quantum machine learning is expected to be one of the first potential general-purpose applications of near-term quantum devices. A major recent breakthrough in classical machine learning is the notion of generative adversarial training, where the gradients of a discriminator model are used to train a separate generative model. In this work and a companion paper, we extend adversarial training to the quantum domain and show how to construct generative adversarial networks using quantum circuits. Furthermore, we also show how to compute gradients---a key element in generative adversarial network training---using another quantum circuit. We give an example of a simple practical circuit ansatz to parametrize quantum machine learning models and perform a simple numerical experiment to demonstrate that quantum generative adversarial networks can be trained successfully.
309 citations
TL;DR: In this paper, a geometrical interpretation of the half integers of the winding number of a non-Hermitian system is given, and the existence of left and right zero-mode edge states is related to the second winding number or energy vorticity.
Abstract: We unveil the geometrical meaning of winding number and utilize it to characterize the topological phases in one-dimensional chiral non-Hermitian systems While chiral symmetry ensures the winding number of Hermitian systems are integers, it can take half integers for non-Hermitian systems We give a geometrical interpretation of the half integers by demonstrating that the winding number $\ensuremath{
u}$ of a non-Hermitian system is equal to half of the summation of two winding numbers ${\ensuremath{
u}}_{1}$ and ${\ensuremath{
u}}_{2}$ associated with two exceptional points, respectively The winding numbers ${\ensuremath{
u}}_{1}$ and ${\ensuremath{
u}}_{2}$ represent the times of the real part of the Hamiltonian in momentum space encircling the exceptional points and can only take integers We further find that the difference of ${\ensuremath{
u}}_{1}$ and ${\ensuremath{
u}}_{2}$ is related to the second winding number or energy vorticity By applying our scheme to a non-Hermitian Su-Schrieffer-Heeger model and an extended version of it, we show that the topologically different phases can be well characterized by winding numbers Furthermore, we demonstrate that the existence of left and right zero-mode edge states is closely related to the winding number ${\ensuremath{
u}}_{1}$ and ${\ensuremath{
u}}_{2}$
297 citations
TL;DR: It is shown how a multi-time non-Markovian process can be reconstructed experimentally, and that it has a natural representation as a many body quantum state, where temporal correlations are mapped to spatial ones.
Abstract: Currently, there is no systematic way to describe a quantum process with memory solely in terms of experimentally accessible quantities However, recent technological advances mean we have control over systems at scales where memory effects are non-negligible The lack of such an operational description has hindered advances in understanding physical, chemical, and biological processes, where often unjustified theoretical assumptions are made to render a dynamical description tractable This has led to theories plagued with unphysical results and no consensus on what a quantum Markov (memoryless) process is Here, we develop a universal framework to characterize arbitrary non-Markovian quantum processes We show how a multitime non-Markovian process can be reconstructed experimentally, and that it has a natural representation as a many-body quantum state, where temporal correlations are mapped to spatial ones Moreover, this state is expected to have an efficient matrix-product-operator form in many cases Our framework constitutes a systematic tool for the effective description of memory-bearing open-system evolutions
290 citations
TL;DR: In this paper, a new family of quantum circuits based on exchange-type gates was proposed to enable accurate calculations while keeping the gate count (i.e., the circuit depth) low.
Abstract: In this work we investigate methods to improve the efficiency and scalability of quantum algorithms for quantum chemistry applications. We propose a transformation of the electronic structure Hamiltonian in the second quantization framework into the particle-hole picture, which offers a better starting point for the expansion of the system wave function. The state of the molecular system at study is parametrized so as to constrain the sampling of the corresponding wave function within the sector of the molecular Fock space that contains the desired solution. To this end, we explore different mapping schemes to encode the molecular ground state wave function in a quantum register. Taking advantage of known post-Hartree-Fock quantum chemistry approaches and heuristic Hilbert space search quantum algorithms, we propose a new family of quantum circuits based on exchange-type gates that enable accurate calculations while keeping the gate count (i.e., the circuit depth) low. The particle-hole implementation of the unitary coupled-cluster (UCC) method within the variational quantum eigensolver approach gives rise to an efficient quantum algorithm, named q-UCC, with important advantages compared to the straightforward translation of the classical coupled-cluster counterpart. In particular, we show how a single Trotter step in the expansion of the system wave function can accurately and efficiently reproduce the ground-state energy of simple molecular systems.
282 citations
TL;DR: In this article, the authors proposed a sending or not sending (Sending or Not sending) protocol based on the twin-field quantum key distribution (TF-QKD), which can tolerate large misalignment error.
Abstract: Based on the novel idea of twin-field quantum key distribution [TF-QKD; Lucamarini et al., Nature (London) 557, 400 (2018)], we present a protocol named the ``sending or not sending TF-QKD'' protocol, which can tolerate large misalignment error. A revolutionary theoretical breakthrough in quantum communication, TF-QKD changes the channel-loss dependence of the key rate from linear to square root of channel transmittance. However, it demands the challenging technology of long-distance single-photon interference, and also, as stated in the original paper, the security proof was not finalized there due to the possible effects of the later announced phase information. Here we show by a concrete eavesdropping scheme that the later phase announcement does have important effects and the traditional formulas of the decoy-state method do not apply to the original protocol. We then present our ``sending or not sending'' protocol. Our protocol does not take postselection for the bits in $Z$-basis (signal pulses), and hence the traditional decoy-state method directly applies and automatically resolves the issue of security proof. Most importantly, our protocol presents a negligibly small error rate in $Z$-basis because it does not request any single-photon interference in this basis. Thus our protocol greatly improves the tolerable threshold of misalignment error in single-photon interference from the original a few percent to more than $45%$. As shown numerically, our protocol exceeds a secure distance of 700, 600, 500, or 300 km even though the single-photon interference misalignment error rate is as large as $15%, 25%, 35%$, or $45%$.
266 citations
TL;DR: An essential singularity is found in the entanglement fidelity of GKP codes in the limit of vanishing loss rate, and a generalization of spin-coherent states is introduced, extending the characterization to qudit binomial codes and yielding a multiqudit code.
Abstract: The early Gottesman, Kitaev, and Preskill (GKP) proposal for encoding a qubit in an oscillator has recently been followed by cat- and binomial-code proposals. Numerically optimized codes have also been proposed, and we introduce codes of this type here. These codes have yet to be compared using the same error model; we provide such a comparison by determining the entanglement fidelity of all codes with respect to the bosonic pure-loss channel (i.e., photon loss) after the optimal recovery operation. We then compare achievable communication rates of the combined encoding-error-recovery channel by calculating the channel's hashing bound for each code. Cat and binomial codes perform similarly, with binomial codes outperforming cat codes at small loss rates. Despite not being designed to protect against the pure-loss channel, GKP codes significantly outperform all other codes for most values of the loss rate. We show that the performance of GKP and some binomial codes increases monotonically with increasing average photon number of the codes. In order to corroborate our numerical evidence of the cat-binomial-GKP order of performance occurring at small loss rates, we analytically evaluate the quantum error-correction conditions of those codes. For GKP codes, we find an essential singularity in the entanglement fidelity in the limit of vanishing loss rate. In addition to comparing the codes, we draw parallels between binomial codes and discrete-variable systems. First, we characterize one- and two-mode binomial as well as multiqubit permutation-invariant codes in terms of spin-coherent states. Such a characterization allows us to introduce check operators and error-correction procedures for binomial codes. Second, we introduce a generalization of spin-coherent states, extending our characterization to qudit binomial codes and yielding a multiqudit code.
257 citations
TL;DR: In this article, the Liouvillian spectral gap has been studied in the critical region of the steady-state density matrix and the eigenmatrix of the spectral gap.
Abstract: A state of an open quantum system is described by a density matrix, whose dynamics is governed by a Liouvillian superoperator. Within a general framework, we explore fundamental properties of both first-order dissipative phase transitions and second-order dissipative phase transitions associated with a symmetry breaking. In the critical region, we determine the general form of the steady-state density matrix and of the Liouvillian eigenmatrix whose eigenvalue defines the Liouvillian spectral gap. We illustrate our exact results by studying some paradigmatic quantum optical models exhibiting critical behavior.
246 citations
TL;DR: A resource theory for continuous-variable systems grounded on operations routinely available within current quantum technologies, which lends itself to quantify both quantum non-Gaussianity and Wigner negativity as resources, depending on the choice of the free-state set.
Abstract: We develop a resource theory for continuous-variable systems grounded on operations routinely available within current quantum technologies. In particular, the set of free operations is convex and includes quadratic transformations and conditional coarse-grained measurements. The present theory lends itself to quantify both quantum non-Gaussianity and Wigner negativity as resources, depending on the choice of the free-state set---i.e., the convex hull of Gaussian states or the states with positive Wigner function, respectively. After showing that the theory admits no maximally resourceful state, we define a computable resource monotone---the Wigner logarithmic negativity. We use the latter to assess the resource content of experimentally relevant states---e.g., photon-added, photon-subtracted, cubic-phase, and cat states---and to find optimal working points of some resource concentration protocols. We envisage applications of this framework to subuniversal and universal quantum information processing over continuous variables.
225 citations
TL;DR: The parameter landscape is numerically investigated and it is shown that it is a simple one in the sense of having no local optima, which greatly simplifies numerical search for the optimal values of the parameters.
Abstract: Farhi et al. recently proposed a class of quantum algorithms, the Quantum Approximate Optimization Algorithm (QAOA), for approximately solving combinatorial optimization problems. A level-p QAOA circuit consists of steps in which a classical Hamiltonian, derived from the cost function, is applied followed by a mixing Hamiltonian. The 2p times for which these two Hamiltonians are applied are the parameters of the algorithm. As p increases, however, the parameter search space grows quickly. The success of the QAOA approach will depend, in part, on finding effective parameter-setting strategies. Here, we analytically and numerically study parameter setting for QAOA applied to MAXCUT. For level-1 QAOA, we derive an analytical expression for a general graph. In principle, expressions for higher p could be derived, but the number of terms quickly becomes prohibitive. For a special case of MAXCUT, the Ring of Disagrees, or the 1D antiferromagnetic ring, we provide an analysis for arbitrarily high level. Using a Fermionic representation, the evolution of the system under QAOA translates into quantum optimal control of an ensemble of independent spins. This treatment enables us to obtain analytical expressions for the performance of QAOA for any p. It also greatly simplifies numerical search for the optimal values of the parameters. By exploring symmetries, we identify a lower-dimensional sub-manifold of interest; the search effort can be accordingly reduced. This analysis also explains an observed symmetry in the optimal parameter values. Further, we numerically investigate the parameter landscape and show that it is a simple one in the sense of having no local optima.
TL;DR: This work devise an efficient gradient-based learning algorithm for the quantum circuit Born machine by minimizing the kerneled maximum mean discrepancy loss and simulated generative modeling of the Bars-and-Stripes dataset and Gaussian mixture distributions using deep quantum circuits.
Abstract: Quantum circuit Born machines are generative models which represent the probability distribution of classical dataset as quantum pure states. Computational complexity considerations of the quantum sampling problem suggest that the quantum circuits exhibit stronger expressibility compared to classical neural networks. One can efficiently draw samples from the quantum circuits via projective measurements on qubits. However, similar to the leading implicit generative models in deep learning, such as the generative adversarial networks, the quantum circuits cannot provide the likelihood of the generated samples, which poses a challenge to the training. We devise an efficient gradient-based learning algorithm for the quantum circuit Born machine by minimizing the kerneled maximum mean discrepancy loss. We simulated generative modeling of the BARS-AND-STRIPES dataset and Gaussian mixture distributions using deep quantum circuits. Our experiments show the importance of circuit depth and the gradient-based optimization algorithm. The proposed learning algorithm is runnable on near-term quantum device and can exhibit quantum advantages for probabilistic generative modeling.
TL;DR: This work presents a quantum algorithm for the Monte Carlo pricing of financial derivatives and shows how the amplitude estimation algorithm can be applied to achieve a quadratic quantum speedup in the number of steps required to obtain an estimate for the price with high confidence.
Abstract: This work presents a quantum algorithm for the Monte Carlo pricing of financial derivatives. We show how the relevant probability distributions can be prepared in quantum superposition, the payoff functions can be implemented via quantum circuits, and the price of financial derivatives can be extracted via quantum measurements. We show how the amplitude estimation algorithm can be applied to achieve a quadratic quantum speedup in the number of steps required to obtain an estimate for the price with high confidence. This work provides a starting point for further research at the interface of quantum computing and finance.
TL;DR: In this paper, the authors investigate the performance of error mitigation via measurement of conserved symmetries on near-term devices and present two protocols to measure conserved symmetry during the bulk of an experiment, and develop a third, zero-cost, post-processing protocol which is equivalent to a variant of the quantum subspace expansion.
Abstract: We investigate the performance of error mitigation via measurement of conserved symmetries on near-term devices. We present two protocols to measure conserved symmetries during the bulk of an experiment, and develop a third, zero-cost, post-processing protocol which is equivalent to a variant of the quantum subspace expansion. We develop methods for inserting global and local symmetries into quantum algorithms, and for adjusting natural symmetries of the problem to boost the mitigation of errors produced by different noise channels. We demonstrate these techniques on two- and four-qubit simulations of the hydrogen molecule (using a classical density-matrix simulator), finding up to an order of magnitude reduction of the error in obtaining the ground-state dissociation curve.
TL;DR: In this paper, the structure and dynamics of one-dimensional binary Bose gases forming quantum droplets are studied by solving the corresponding amended Gross-Pitaevskii equation, and two physically different regimes are identified, corresponding to small droplets of an approximately Gaussian shape and large ''puddles'' with a broad flat-top plateau.
Abstract: The structure and dynamics of one-dimensional binary Bose gases forming quantum droplets is studied by solving the corresponding amended Gross-Pitaevskii equation. Two physically different regimes are identified, corresponding to small droplets of an approximately Gaussian shape and large ``puddles'' with a broad flat-top plateau. Small droplets collide quasielastically, featuring the solitonlike behavior. On the other hand, large colliding droplets may merge or suffer fragmentation, depending on their relative velocity. The frequency of a breathing excited state of droplets, as predicted by the dynamical variational approximation based on the Gaussian ansatz, is found to be in good agreement with numerical results. Finally, the stability diagram for a single droplet with respect to shape excitations with a given wave number is drawn, being consistent with preservation of the Weber number for large droplets.
TL;DR: The Permutational-Invariant Quantum Solver (PIQS) as mentioned in this paper is an open-source library in python, which can be used to study several important physical phenomena in the presence of local incoherent processes, in which each degree of freedom couples to its own reservoir.
Abstract: The permutational invariance of identical two-level systems allows for an exponential reduction in the computational resources required to study the Lindblad dynamics of coupled spin-boson ensembles evolving under the effect of both local and collective noise. Here we take advantage of this speedup to study several important physical phenomena in the presence of local incoherent processes, in which each degree of freedom couples to its own reservoir. Assessing the robustness of collective effects against local dissipation is paramount to predict their presence in different physical implementations. We have developed an open-source library in python, the Permutational-Invariant Quantum Solver (PIQS), which we use to study a variety of phenomena in driven-dissipative open quantum systems. We consider both local and collective incoherent processes in the weak-, strong-, and ultrastrong-coupling regimes. Using PIQS, we reproduce a series of known physical results concerning collective quantum effects and extend their study to the local driven-dissipative scenario. Our work addresses the robustness of various collective phenomena, e.g., spin squeezing, superradiance, and quantum phase transitions, against local dissipation processes.
TL;DR: In this paper, the authors study experimentally various physical limitations and technical imperfections that lead to damping and finite contrast of optically driven Rabi oscillations between ground and Rydberg states of a single atom.
Abstract: We study experimentally various physical limitations and technical imperfections that lead to damping and finite contrast of optically driven Rabi oscillations between ground and Rydberg states of a single atom. Finite contrast is due to preparation and detection errors, and we show how to model and measure them accurately. Part of these errors originates from the finite lifetime of Rydberg states, and we observe its n 3 scaling with the principal quantum number n. To explain the damping of Rabi oscillations, we use simple numerical models taking into account independently measured experimental imperfections and show that the observed damping actually results from the accumulation of several small effects, each at the level of a few percent. We discuss prospects for improving the coherence of ground-Rydberg Rabi oscillations in view of applications in quantum simulation and quantum information processing with arrays of single Rydberg atoms.
TL;DR: In this article, a distributed sensing scheme that uses continuous-variable multipartite entanglement to enhance distributed sensing of field-quadrature displacement is described, which can be used to calibrate continuous variable quantum key distribution networks, to perform multiple-sensor cold-atom temperature measurements, and to do distributed interferometric phase sensing.
Abstract: Distributed quantum sensing uses quantum correlations between multiple sensors to enhance the measurement of unknown parameters beyond the limits of unentangled systems. We describe a sensing scheme that uses continuous-variable multipartite entanglement to enhance distributed sensing of field-quadrature displacement. By dividing a squeezed-vacuum state between multiple homodyne-sensor nodes using a lossless beam-splitter array, we obtain a root-mean-square (rms) estimation error that scales inversely with the number of nodes (Heisenberg scaling), whereas the rms error of a distributed sensor that does not exploit entanglement is inversely proportional to the square root of the number of nodes (standard quantum limit scaling). Our sensor's scaling advantage is destroyed by loss, but it nevertheless retains an rms-error advantage in settings in which there is moderate loss. Our distributed sensing scheme can be used to calibrate continuous-variable quantum key distribution networks, to perform multiple-sensor cold-atom temperature measurements, and to do distributed interferometric phase sensing.
TL;DR: In this article, the authors scrutinize the validity of the local-constant field approximation in the case of nonlinear Compton scattering focusing on the role played by the energy of the emitted photon on the formation length of this process.
Abstract: In the calculation of probabilities of physical processes occurring in a background classical field, the local-constant-field approximation (LCFA) relies on the possibility of neglecting the space-time variation of the external field within the region of formation of the process. This approximation is widely employed in strong-field QED as it allows one to evaluate probabilities of processes occurring in arbitrary electromagnetic fields starting from the corresponding quantities computed in a constant electromagnetic field. Here, we scrutinize the validity of the LCFA in the case of nonlinear Compton scattering focusing on the role played by the energy of the emitted photon on the formation length of this process. In particular, we derive analytically the asymptotic behavior of the emission probability per unit of photon light-cone energy ${k}_{\ensuremath{-}}$ and show that it tends to a constant for ${k}_{\ensuremath{-}}\ensuremath{\rightarrow}0$. With numerical codes being an essential tool for the interpretation of present and upcoming experiments in strong-field QED, we obtained an improved approximation for the photon emission probability, implemented it numerically, and showed that it amends the inaccurate behavior of the LCFA in the infrared region, such that it is in qualitative and good quantitative agreement with the full strong-field QED probability also in the infrared region.
TL;DR: This work obtains an analytical key rate formula for the loss-only scenario, confirming the square root scaling and also showing the loss limit, and simulates the key rate for realistic imperfections and shows that PM-MDI QKD can overcome the repeaterless bound with currently available technology.
Abstract: Variations of phase-matching measurement-device-independent quantum key distribution (PM-MDI QKD) protocols have been investigated before, but it was recently discovered that this type of protocol (under the name of twin-field QKD) can beat the linear scaling of the repeaterless bound on secret key capacity. We propose a variation of PM-MDI QKD protocol, which reduces the sifting cost and uses non-phase-randomized coherent states as test states. We provide a security proof in the infinite key limit. Our proof is conceptually simple and gives tight key rates. We obtain an analytical key rate formula for the loss-only scenario, confirming the square root scaling and also showing the loss limit. We simulate the key rate for realistic imperfections and show that PM-MDI QKD can overcome the repeaterless bound with currently available technology.
TL;DR: In this article, the authors revisited the derivation of Rabi-and Dicke-type models for the study of quantum light-matter interactions in cavity and circuit QED.
Abstract: We revisit the derivation of Rabi- and Dicke-type models, which are commonly used for the study of quantum light-matter interactions in cavity and circuit QED. We demonstrate that the validity of the two-level approximation, which is an essential step in this derivation, depends explicitly on the choice of gauge once the system enters the ultrastrong-coupling regime. In particular, while in the electric dipole gauge the two-level approximation can be performed as long as the Rabi frequency remains much smaller than the energies of all higher-lying levels, it can dramatically fail in the Coulomb gauge, even for systems with an extremely anharmonic spectrum. We extensively investigate this phenomenon both in the single-dipole (Rabi) and multidipole (Dicke) case, and consider the specific examples of dipoles confined by double-well and square-well potentials, and of circuit QED systems with flux qubits coupled to an LC resonator.
TL;DR: In this article, the authors consider a spin chain with physically realistic two-body interactions and show that the spin-spin interactions can yield an advantage in charging power over the noninteracting case.
Abstract: Recently, it has been shown that energy can be deposited on a collection of quantum systems at a rate that scales superextensively. Some of these schemes for quantum batteries rely on the use of global many-body interactions that take the batteries through a correlated shortcut in state space. Here we extend the notion of a quantum battery from a collection of a priori isolated systems to a many-body quantum system with intrinsic interactions. Specifically, we consider a one-dimensional spin chain with physically realistic two-body interactions. We find that the spin-spin interactions can yield an advantage in charging power over the noninteracting case and we demonstrate that this advantage can grow superextensively when the interactions are long ranged. However, we show that, unlike in previous work, this advantage is a mean-field interaction effect that does not involve correlations and that relies on the interactions being intrinsic to the battery.
TL;DR: In this article, a multiscale simulation of solid-state high-order-harmonic generation was performed for dielectrics and it was shown that mesoscopic effects of the extended system, in particular the realistic sampling of the entire Brillouin zone, the pulse propagation in the dense medium, and the inhomogeneous illumination of the crystal, have a strong effect on the harmonic spectra.
Abstract: High-order-harmonic generation by a highly nonlinear interaction of infrared laser fields with matter allows for the generation of attosecond pulses in the XUV spectral regime This process, well established for atoms, has been recently extended to the condensed phase Remarkably well-pronounced harmonics up to order $\ensuremath{\sim}30$ have been observed for dielectrics We establish a route toward an ab initio multiscale simulation of solid-state high-order-harmonic generation We find that mesoscopic effects of the extended system, in particular the realistic sampling of the entire Brillouin zone, the pulse propagation in the dense medium, and the inhomogeneous illumination of the crystal, have a strong effect on the harmonic spectra Our results provide an explanation for the formation of clean harmonics and have implications for a wide range of nonlinear optical processes in dense media
TL;DR: In this article, the Born-Huang expansion was applied to the full nucleus-electron-photon Hamiltonian of nonrelativistic quantum electrodynamics (QED) in the long-wavelength approximation.
Abstract: By applying the Born-Huang expansion, originally developed for coupled nucleus-electron systems, to the full nucleus-electron-photon Hamiltonian of nonrelativistic quantum electrodynamics (QED) in the long-wavelength approximation, we deduce an exact set of coupled equations for electrons on photonic energy surfaces and the nuclei on the resulting polaritonic energy surfaces. This theory describes seamlessly many-body interactions among nuclei, electrons, and photons including the quantum fluctuation of the electromagnetic field and provides a proper first-principle framework to describe QED-chemistry phenomena, namely polaritonic and cavity chemistry effects. Since the photonic surfaces and the corresponding nonadiabatic coupling elements can be solved analytically, the resulting expansion can be brought into a compact form, which allows us to analyze aspects of coupled nucleus-electron-photon systems in a simple and intuitive manner. Furthermore, we discuss structural differences between the exact quantum treatment and Floquet theory, show how existing implementations of Floquet theory can be adjusted to adhere to QED, and highlight how standard drawbacks of Floquet theory can be overcome. We then highlight, by assuming that the relevant photonic frequencies of a prototypical cavity QED experiment are in the energy range of the electrons, how from this generalized Born-Huang expansion an adapted Born-Oppenheimer approximation for nuclei on polaritonic surfaces can be deduced. This form allows a direct application of first-principle methods of quantum chemistry such as coupled-cluster or configuration interaction approaches to QED chemistry. By restricting the basis set of this generalized Born-Oppenheimer approximation, we furthermore bridge quantum chemistry and quantum optics by recovering simple models of coupled matter-photon systems employed in quantum optics and polaritonic chemistry. We finally highlight numerically that simple few-level models can lead to physically wrong predictions, even in weak-coupling regimes, and show how the presented derivations from first principles help to check and derive physically reliable simplified models.
TL;DR: In this article, it was shown that the resulting quantum-limited signal to noise at EPs is proportional to the perturbation, and comparable to other sensors, thus providing the same precision.
Abstract: Recently, sensors with resonances at exceptional points (EPs) have been suggested to have a vastly improved sensitivity due to the extraordinary scaling of the complex frequency splitting of the n initially degenerate modes with the n-th root of the perturbation. We show here that the resulting quantum-limited signal to noise at EPs is proportional to the perturbation, and comparable to other sensors, thus providing the same precision. The complex frequency splitting close to EPs is therefore not suited to estimate the precision of EP sensors. The underlying reason of this counter-intuitive result is that the mode �elds, described by the eigenvectors, are equal for all modes at the EP, and are strongly changing with the perturbation.
IBM1
TL;DR: Two quantities are proposed: the leakage and seepage rates, which together with average gate fidelity allow for characterizing the average performance of quantum gates in the presence of leakage and show how the randomized benchmarking protocol can be modified to enable the robust estimation of all three quantities for a Clifford gate set.
Abstract: We present a general framework for the quantification and characterization of leakage errors that result when a quantum system is encoded in the subspace of a larger system. To do this we introduce metrics for quantifying the coherent and incoherent properties of the resulting errors and we illustrate this framework with several examples relevant to superconducting qubits. In particular, we propose two quantities, the leakage and seepage rates, which together with average gate fidelity allow for characterizing the average performance of quantum gates in the presence of leakage and show how the randomized benchmarking protocol can be modified to enable the robust estimation of all three quantities for a Clifford gate set.
TL;DR: In this paper, it was shown that three-dimensional non-Hermitian Hamiltonian systems have generic band touching along one-dimensional closed contours, forming exceptional rings and links in reciprocal space.
Abstract: The generic nature of band touching points in three-dimensional band structures is at the heart of the rich phenomenology, topological stability, and novel Fermi arc surface states associated with Weyl semimetals. Here we report on the corresponding scenario emerging in systems effectively described by non-Hermitian Hamiltonians. Remarkably, three-dimensional non-Hermitian systems have generic band touching along one-dimensional closed contours, forming exceptional rings and links in reciprocal space. The associated Seifert surfaces support open ``Fermi ribbons'' where the real part of the energy gap vanishes, providing a novel class of higher-dimensional bulk generalizations of Fermi arcs which are characterized by an integer twist number. These results have possible applications to a plethora of physical settings, ranging from mechanical systems and optical metamaterials with loss and gain to heavy fermion materials with finite-lifetime quasiparticles. In particular, photonic crystals provide fertile ground for simulating the exuberant phenomenology of exceptional links and their concomitant Fermi ribbons.
TL;DR: In this paper, a generic cavity-QED system where a set of (artificial) two-level dipoles is coupled to the electric field of a single-mode $LC$ resonator was studied.
Abstract: We study a generic cavity-QED system where a set of (artificial) two-level dipoles is coupled to the electric field of a single-mode $LC$ resonator. This setup is used to derive a minimal quantum mechanical model for cavity QED, which accounts for both dipole-field and direct dipole-dipole interactions. The model is applicable for arbitrary coupling strengths and allows us to extend the usual Dicke model into the nonperturbative regime of QED, where the dipole-field interaction can be associated with an effective fine-structure constant of order unity. In this regime, we identify three distinct classes of normal, superradiant, and subradiant vacuum states and discuss their characteristic properties and the transitions between them. Our findings reconcile many of the previous, often contradictory predictions in this field and establish a common theoretical framework to describe ultrastrong-coupling phenomena in a diverse range of cavity-QED platforms.
TL;DR: A monotone is introduced to quantify the genuine non-Gaussianity of resource states, in analogy to the stabilizer theory, and a protocol is given that allows the distillation of cubic phase states, which enables universal quantum computation when combined with free operations.
Abstract: Continuous-variable systems realized in quantum optics play a major role in quantum information processing, and it is also one of the promising candidates for a scalable quantum computer. We introduce a resource theory for continuous-variable systems relevant to universal quantum computation. In our theory, easily implementable operations---Gaussian operations combined with feed-forward---are chosen to be the free operations, making the convex hull of the Gaussian states the natural free states. Since our free operations and free states cannot perform universal quantum computation, genuine non-Gaussian states---states not in the convex hull of Gaussian states---are the necessary resource states for universal quantum computation together with free operations. We introduce a monotone to quantify the genuine non-Gaussianity of resource states, in analogy to the stabilizer theory. A direct application of our resource theory is to bound the conversion rate between genuine non-Gaussian states. Finally, we give a protocol that probabilistically distills genuine non-Gaussianity---increases the genuine non-Gaussianity of resource states---only using free operations and postselection on Gaussian measurements, where our theory gives an upper bound for the distillation rate. In particular, the same protocol allows the distillation of cubic phase states, which enable universal quantum computation when combined with free operations.
TL;DR: By introducing a classical technique for operating the Hopfield network, this work can leverage quantum algorithms to obtain a quantum computational complexity that is logarithmic in the dimension of the data.
Abstract: Neural networks, ubiquitous in machine learning, are generalized to the quantum realm The method results in a network that can be exploited to offer exponential speedup on many applications, such as image processing and optimization, thus with a wider interest in neuroscience and medicine