The 100 most-cited articles in Physical Review A, 2018

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.

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.

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.

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.

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…

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 $\ensuremath{\nu}$ of a non-Hermitian system is equal to half of the summation of two winding numbers ${\ensuremath{\nu}}_{1}$ and ${\ensuremath{\nu}}_{2}$ associated with two exceptional points, respectively. The winding numbers ${\ensuremath{\nu}}_{1}$ and ${\ensuremath{\nu}}_{2}$ 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 ${\ensuremath{\nu}}_{1}$ and ${\ensuremath{\nu}}_{2}$ 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…

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…

Farhi et al. recently proposed a class of quantum algorithms, the quantum approximate optimization algorithm (QAOA), for approximately solving combinatorial optimization problems (E. Farhi et al., arXiv:1411.4028; arXiv:1412.6062; arXiv:1602.07674). A level-$p$ QAOA circuit consists of $p$ steps; in each step 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, which are to be optimized classically for the best performance. As $p$ increases, parameter optimization becomes inefficient due to the curse of dimensionality. 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 the QAOA applied to MaxCut. For the 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…

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.

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…

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…

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…

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.

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.

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 $n\mathrm{th}$ 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 for this counterintuitive result is that the mode fields, described by the eigenvectors, are equal for all modes at the EP, and are strongly changing with the perturbation.

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.

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.

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…

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…

Arrays of single atoms promoted to Rydberg states offer a versatile platform for quantum simulation and implementation of two-qubit gates. A comprehensive account of the limiting factors and sources of errors in their experimental preparation is presented.

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.

It was recently found that the Lee-Huang-Yang (LHY) correction to the mean-field Hamiltonian of binary atomic boson condensates suppresses the collapse and creates stable localized modes (two-component quantum droplets, QDs) in two and three dimensions (2D and 3D). In particular, the LHY effect modifies the effective Gross-Pitaevskii equation (GPE) in 2D by adding a logarithmic factor to the usual cubic term. In the framework of the accordingly modified two-component GPE system, we construct 2D self-trapped modes in the form of QDs with vorticity $S$ embedded into each component. Because of the effect of the logarithmic factor, the QDs feature a flat-top shape, which expands with the increase of $S$ and norm $N$. An essential finding, produced by a systematic numerical investigation and analytical estimates, is that the vortical QDs are stable (which is a critical issue for vortex solitons in nonlinear models) up to $S=5$, for $N$ exceeding a certain threshold value, which is predicted to scale as ${N}_{\mathrm{th}}\ensuremath{\sim}{S}^{4}$ for large $S$ (for three-dimensional QDs,…

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…

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.

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…

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.

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.

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…

Studies of quantum metrology have shown that the use of many-body entangled states can lead to an enhancement in sensitivity when compared with unentangled states. In this paper, we quantify the metrological advantage of entanglement in a setting where the measured quantity is a linear function of parameters individually coupled to each qubit. We first generalize the Heisenberg limit to the measurement of nonlocal observables in a quantum network, deriving a bound based on the multiparameter quantum Fisher information. We then propose measurement protocols that can make use of Greenberger-Horne-Zeilinger (GHZ) states or spin-squeezed states and show that in the case of GHZ states the protocol is optimal, i.e., it saturates our bound. We also identify nanoscale magnetic resonance imaging as a promising setting for this technology.

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.

We propose a superconducting circuit to implement a two-photon quantum Rabi model in a solid-state device, where a qubit and a resonator are coupled by a two-photon interaction. We analyze the input-output relations for this circuit in the strong-coupling regime and find that fundamental quantum-optical phenomena are qualitatively modified. For instance, two-photon interactions are shown to yield a single- or two-photon blockade when a pumping field is either applied to the cavity mode or to the qubit, respectively. In addition, we derive an effective Hamiltonian for perturbative ultrastrong two-photon couplings in the dispersive regime, where two-photon interactions introduce a qubit-state-dependent Kerr term. Finally, we analyze the spectral collapse of the multiqubit two-photon quantum Rabi model and find a scaling of the critical coupling with the number of qubits. Using realistic parameters with the circuit proposed, three qubits are sufficient to reach the collapse point.

Robust quantum state transfer (QST) is an indispensable ingredient in scalable quantum information processing. Here we present an experimentally feasible mechanism for realizing robust QST via topologically protected edge states in superconducting qubit chains. Using superconducting Xmon qubits with tunable couplings, we construct generalized Su-Schrieffer-Heeger models and analytically derive the wave functions of topological edge states. We find that such edge states can be employed as a quantum channel to realize robust QST between remote qubits. With a numerical simulation, we show that both single-qubit states and two-qubit entangled states can be robustly transferred in the presence of sizable imperfections in the qubit couplings. The transfer fidelity demonstrates a wide plateau at the value of unity in the imperfection magnitude. This approach is general and can be implemented in a variety of quantum computing platforms.

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…

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.

The geometry of the quantum set of correlations is studied with standard tools from the convex geometry. Examples of counterintuitive features are found in the simplest nontrivial Bell scenario, and more complex features are shown to persist in more sophisticated Bell scenarios.

A method for the creation of three-dimensional (3D) solitary topological modes, corresponding to vortical droplets of a two-component dilute superfluid, is presented. We use the recently introduced system of nonlinearly coupled Gross-Pitaevskii equations, which include contact attraction between the components, and quartic repulsion stemming from the Lee-Huang-Yang correction to the mean-field energy. Self-trapped vortex tori, carrying the topological charges ${m}_{1}={m}_{2}=1$ or ${m}_{1}={m}_{2}=2$ in their components, are constructed by means of numerical and approximate analytical methods. The analysis reveals stability regions for the vortex droplets (in broad and relatively narrow parameter regions for ${m}_{1,2}=1$ and ${m}_{1,2}=2$, respectively). The results provide a scenario for the creation of stable 3D self-trapped states with the double vorticity (${m}_{1,2}=2$). The stable modes are shaped as flat-top ones, with the space between the inner hole, induced by the vorticity, and the outer boundary filled by a nearly constant density. On the other hand, all modes with…

We demonstrate that the open quantum Rabi model (QRM) exhibits a second-order dissipative phase transition (DPT) and propose a method to observe this transition with trapped ions. The interplay between the ultrastrong qubit-oscillator coupling and the oscillator damping brings the system into a steady state with a diverging number of excitations, in which a DPT is allowed to occur even with a finite number of system components. The universality class of the open QRM, modified from the closed QRM by a Markovian bath, is identified by finding critical exponents and scaling functions using the Keldysh functional integral approach. We propose to realize the open QRM with two trapped ions where the coherent coupling and the rate of dissipation can be individually controlled and adjusted over a wide range. Thanks to this controllability, our work opens a possibility to investigate potentially rich dynamics associated with a dissipative phase transition.

Two topics, evolving rapidly in separate fields, were combined recently: the out-of-time-ordered correlator (OTOC) signals quantum-information scrambling in many-body systems. The Kirkwood-Dirac (KD) quasiprobability represents operators in quantum optics. The OTOC was shown to equal a moment of a summed quasiprobability [Yunger Halpern, Phys. Rev. A 95, 012120 (2017)]. That quasiprobability, we argue, is an extension of the KD distribution. We explore the quasiprobability's structure from experimental, numerical, and theoretical perspectives. First, we simplify and analyze Yunger Halpern's weak-measurement and interference protocols for measuring the OTOC and its quasiprobability. We decrease, exponentially in system size, the number of trials required to infer the OTOC from weak measurements. We also construct a circuit for implementing the weak-measurement scheme. Next, we calculate the quasiprobability (after coarse graining) numerically and analytically: we simulate a transverse-field Ising model first. Then, we calculate the quasiprobability averaged over random circuits,…

Anomaly detection is used for identifying data that deviate from ``normal'' data patterns. Its usage on classical data finds diverse applications in many important areas such as finance, fraud detection, medical diagnoses, data cleaning, and surveillance. With the advent of quantum technologies, anomaly detection of quantum data, in the form of quantum states, may become an important component of quantum applications. Machine-learning algorithms are playing pivotal roles in anomaly detection using classical data. Two widely used algorithms are the kernel principal component analysis and the one-class support vector machine. We find corresponding quantum algorithms to detect anomalies in quantum states. We show that these two quantum algorithms can be performed using resources that are logarithmic in the dimensionality of quantum states. For pure quantum states, these resources can also be logarithmic in the number of quantum states used for training the machine-learning algorithm. This makes these algorithms potentially applicable to big quantum data applications.

Optical clocks operated on satellites are expected to open up new opportunities in time transfer, geodesy, fundamental physics, and satellite navigation. Here we demonstrate an important first step towards this goal: a modular, compact, optical lattice clock (OLC) system that achieves $2.0\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$ fractional uncertainty. The clock is operated with bosonic strontium and improves the performance of bosonic OLCs by a factor of 30. This has important implications for future use of bosonic OLCs in fundamental physics and metrology. We make use of the clock's metrological performance to measure, with independent clocks, the isotope shift of the $^{1}S_{0}\ensuremath{\rightarrow}^{3}P_{0}$ transitions of $^{88}\mathrm{Sr}$ and $^{87}\mathrm{Sr}$, with an uncertainty of 12 mHz. The ratio of the transition frequencies is thus determined with $3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$ fractional uncertainty.

Grid (or comb) states are an interesting class of bosonic states introduced by Gottesman, Kitaev, and Preskill [D. Gottesman, A. Kitaev, and J. Preskill, Phys. Rev. A 64, 012310 (2001)] to encode a qubit into an oscillator. A method to generate or ``breed'' a grid state from Schr\"odinger cat states using beam splitters and homodyne measurements is known [H. M. Vasconcelos, L. Sanz, and S. Glancy, Opt. Lett. 35, 3261 (2010)], but this method requires postselection. In this paper we show how postprocessing of the measurement data can be used to entirely remove the need for postselection, making the scheme much more viable. We bound the asymptotic behavior of the breeding procedure and demonstrate the efficacy of the method numerically.

In closed quantum systems, dynamical phase transitions are identified by the nonanalytic behavior of the return probability as a function of time. In this work, we study the nonunitary dynamics following quenches across exceptional points in a non-Hermitian lattice realizable by optical resonators. Dynamical quantum phase transitions with topological signatures are found when an isolated exceptional point is crossed during the quench. A winding number defined by a real, noncyclic geometric phase is introduced, whose value features quantized jumps at critical times of these phase transitions and remains constant elsewhere, playing the role of a topological order parameter. This work provides a simple framework to study dynamical and topological quantum phase transitions in non-Hermitian systems.

A method is proposed to detect some candidates of dark matter with a network of precision-measurement devices such as atomic clocks. Spatiotemporal correlation functions of the ultralight dark-matter fields are derived for formalizing the proposed scheme.

We present a method to exponentiate nonsparse indefinite low-rank matrices on a quantum computer. Given access to the elements of the matrix, our method allows one to determine the singular values and their associated singular vectors in time exponentially faster in the dimension of the matrix than known classical algorithms. The method extends to non-Hermitian and nonsquare matrices via matrix embedding. Moreover, our method preserves the phase relations between the singular spaces allowing for efficient algorithms that require operating on the entire singular-value decomposition of a matrix. As an example of such an algorithm, we discuss the Procrustes problem of finding a closest isometry to a given matrix.

We study topological properties of one-dimensional non-Hermitian systems without chiral symmetry and give phase diagrams characterized by topological invariants ${\ensuremath{\nu}}_{E}$ and ${\ensuremath{\nu}}_{\mathrm{tot}}$, associated with complex energy vorticity and summation of Berry phases of complex bands, respectively. In the absence of chiral symmetry, we find that the phase diagram determined by ${\ensuremath{\nu}}_{E}$ is different from ${\ensuremath{\nu}}_{\mathrm{tot}}$. While the transition between phases with different ${\ensuremath{\nu}}_{E}$ is closely related to the band-touching point, the transition between different ${\ensuremath{\nu}}_{\mathrm{tot}}$ is irrelevant to the band-touching condition. We give an interpretation for the discrepancy from the geometrical view by analyzing the relation of topological invariants with the winding numbers associated with exception points of the system. We then generalize the fidelity approach to study the phase transition in the non-Hermitian system and find that transition between phases with different…

We investigate the ultimate precision achievable in Gaussian quantum metrology. We derive general analytical expressions for the quantum Fisher information matrix and for the measurement compatibility condition, ensuring asymptotic saturability of the quantum Cram\'er-Rao bound, for the estimation of multiple parameters encoded in multimode Gaussian states. We then apply our results to the joint estimation of a phase shift and two parameters characterizing Gaussian phase covariant noise in optical interferometry. In such a scheme, we show that two-mode displaced squeezed input probes with optimally tuned squeezing and displacement fulfill the measurement compatibility condition and enable the simultaneous estimation of all three parameters, with an advantage over individual estimation schemes that quickly rises with increasing mean energy of the probes.

The goal of entanglement distillation is to turn a large number of weakly entangled states into a smaller number of highly entangled ones. Practical entanglement distillation schemes offer a trade-off between the fidelity to the target state and the probability of successful distillation. Exploiting such trade-offs is of interest in the design of quantum repeater protocols. Here, we present a number of methods to assess and optimize entanglement distillation schemes. We start by giving a numerical method to compute upper bounds on the maximum achievable fidelity for a desired probability of success. We show that this method performs well for many known examples by comparing it to well-known distillation protocols. This allows us to show optimality for many well-known distillation protocols for specific states of interest. As an example, we analytically prove optimality of the distillation protocol utilized within the Extreme Photon Loss entanglement generation scheme, even in the asymptotic limit. We proceed to present a numerical method that can improve an existing distillation…

We present a versatile imaging scheme for fermionic $^6$Li atoms with single-particle sensitivity. Our method works for freely propagating particles and completely eliminates the need for confining potentials during the imaging process. We illuminate individual atoms in free space with resonant light and collect their fluorescence on an electron-multiplying CCD camera using a high-numerical-aperture imaging system. We detect approximately \num{20} photons per atom during an exposure of 20 $μ$s and identify individual atoms with a fidelity of $99.4\pm0.3$ % . By addressing different optical transitions during two exposures in rapid succession, we additionally resolve the hyperfine spin state of each particle. The position uncertainty of the imaging scheme is 4.0 $μ$m, given by the diffusive motion of the particles during the imaging pulse. The absence of confining potentials enables readout procedures, such as the measurement of single-particle momenta in time of flight, which we demonstrate here. Our imaging scheme is technically simple and easily adapted to other atomic species.

Optical quantum memories are devices that store and recall quantum light and are vital to the realization of future photonic quantum networks. To date, much effort has been put into improving storage times and efficiencies of such devices to enable long-distance communications. However, less attention has been devoted to building quantum memories which add zero noise to the output. Even small additional noise can render the memory classical by destroying the fragile quantum signatures of the stored light. Therefore, noise performance is a critical parameter for all quantum memories. Here we introduce an intrinsically noise-free quantum memory protocol based on two-photon off-resonant cascaded absorption (ORCA). We demonstrate successful storage of GHz-bandwidth heralded single photons in a warm atomic vapor with no added noise, confirmed by the unaltered photon-number statistics upon recall. Our ORCA memory meets the stringent noise requirements for quantum memories while combining high-speed and room-temperature operation with technical simplicity, and therefore is immediately…

We study what is arguably the most experimentally appealing boson sampling architecture: Gaussian states sampled with threshold detectors. We show that, in this setting, the probability of observing a given outcome is related to a matrix function that we name the Torontonian, which plays an analogous role to the permanent or the Hafnian in other models. We also prove that, provided that the probability of observing two or more photons in a single output mode is sufficiently small, our model remains intractable to simulate classically under standard complexity-theoretic conjectures. Finally, we leverage the mathematical simplicity of the model to introduce a physically motivated, exact sampling algorithm for all boson sampling models that employ Gaussian states and threshold detectors.

The goal of self-testing is to characterize an a priori unknown quantum system based solely on measurement statistics, i.e., using an uncharacterized measurement device. Here we develop self-testing methods for quantum prepare-and-measure experiments, thus not necessarily relying on entanglement and/or violation of a Bell inequality. We present noise-robust techniques for self-testing sets of quantum states and measurements, assuming an upper bound on the Hilbert space dimension. We discuss in detail the case of a $2\ensuremath{\rightarrow}1$ random access code with qubits, for which we provide analytically optimal self-tests. The simplicity and noise robustness of our methods should make them directly applicable to experiments.

We explore theoretically the dynamical properties of a first-order dissipative phase transition in coherently driven Bose-Hubbard systems, describing, e.g., lattices of coupled nonlinear optical cavities. Via stochastic trajectory calculations based on the truncated Wigner approximation, we investigate the dynamical behavior as a function of system size for one-dimensional (1D) and 2D square lattices in the regime where mean-field theory predicts nonlinear bistability. We show that a critical slowing down emerges for increasing number of sites in 2D square lattices, while it is absent in 1D arrays. We characterize the peculiar properties of the collective phases in the critical region.

In the presence of symmetry, entanglement measures of quantum many-body states can be decomposed into contributions from distinct symmetry sectors. Here we investigate the decomposability of negativity, a measure of entanglement between two parts of a generally open system in a mixed state. While the entanglement entropy of a subsystem within a closed system can be resolved according to its total preserved charge, we find that negativity of two subsystems may be decomposed into contributions associated with their charge imbalance. We show that this charge-imbalance decomposition of the negativity may be measured by employing existing techniques based on creation and manipulation of many-body twin or triple states in cold atomic setups. Next, using a geometrical construction in terms of an Aharonov-Bohm-like flux inserted in a Riemann geometry, we compute this decomposed negativity in critical one-dimensional systems described by conformal field theory. We show that it shares the same distribution as the charge-imbalance between the two subsystems. We numerically confirm our field…

The problem of determining whether a given quantum state is entangled lies at the heart of quantum information processing. Despite the many methods---such as the positive partial transpose criterion and the $k$-symmetric extendibility criterion---to tackle this problem, none of them enables a general, practical solution due to the problem's NP-hard complexity. Explicitly, separable states form a high-dimensional convex set of vastly complicated structures. In this work, we build a different separability-entanglement classifier underpinned by machine learning techniques. We use standard tools from machine learning to learn the entanglement feature of arbitrary given quantum states. We perform substantial numerical tests on two-qubit and two-qutrit systems, and the results indicate that our method can outperform the existing methods in generic cases in terms of both speed and accuracy. This opens up avenues to explore quantum entanglement via the machine learning approach.

We propose an efficient strategy to attack a continuous-variable (CV) quantum key distribution (QKD) system, which we call homodyne detector blinding. This attack strategy takes advantage of a generic vulnerability of homodyne receivers: A bright light pulse sent on the signal port can lead to a saturation of the detector electronics. While detector saturation has already been proposed to attack CV QKD, the attack we study in this paper has the additional advantage of not requiring an eavesdropper to be phase locked with the homodyne receiver. We show that under certain conditions, an attacker can use a simple laser, incoherent with the homodyne receiver, to generate bright pulses and bias the excess noise to arbitrary small values, fully comprising CV QKD security. These results highlight the feasibility and the impact of the detector-blinding attack. We finally discuss how to design countermeasures in order to protect against this attack.

The photon blockade based on weak nonlinearities is called unconventional photon blockade. The studies of the unconventional photon blockade in recent decades are all limited to Markovian approximation. In this paper, we propose a scheme to achieve a strong photon antibunching in non-Markovian reservoir. An exact non-Markovian master equation for the optical cavity coupled with a degenerate optical parametric amplifier (DOPA) is derived. We show that this unconventional photon blockade originates from the destructive interference between two paths which are formed by the DOPA pump and a driving field. Unconventional single-photon blockades that exhibit a transition from the non-Markovian to Markovian regime by controlling environmental spectral width regardless of the weakness of DOPA gain and driving field are found. We analytically derive an optimal condition for strong antibunching, which is in good agreement with that obtained by the full numerical simulation. The presented results then are compared with that given by Markovian approximation in the weak-coupling limit. Our…

The efficient simulation of correlated quantum systems is a promising near-term application of quantum computers. Here, we present a measurement of the second R\'enyi entropy of the ground state of the two-site Fermi-Hubbard model on a five-qubit programmable quantum computer based on trapped ions. Our work illustrates the extraction of a nonlinear characteristic of a quantum state using a controlled-swap gate acting on two copies of the state. This scalable measurement of entanglement on a universal quantum computer will, with more qubits, provide insights into many-body quantum systems that are impossible to simulate on classical computers.

We study quantum channels that are close to another channel with weakly additive Holevo information, and we derive upper bounds on their classical capacity. Examples of channels with weakly additive Holevo information are entanglement-breaking channels, unital qubit channels, and Hadamard channels. Related to the method of approximate degradability, we define approximation parameters for each class above, which measure how close an arbitrary channel is to satisfying the respective property. This gives us upper bounds on the classical capacity in terms of functions of the approximation parameters, as well as an outer bound on the dynamic capacity region of a quantum channel. Since these parameters are defined in terms of the diamond distance, the upper bounds can be computed efficiently using semidefinite programming (SDP). We exhibit the usefulness of our method with two example channels: a convex mixture of amplitude damping and depolarizing noise and a composition of amplitude damping and dephasing noise. For both channels, our bounds perform well in certain regimes of the noise…

Reverse annealing is a variant of quantum annealing that starts from a given classical configuration of spins (qubits). In contrast to the conventional formulation, where one starts from a uniform superposition of all possible states (classical configurations), quantum fluctuations are first increased and only then decreased. One then reads out the state as a proposed solution to the given combinatorial optimization problem. We formulate a mean-field theory of reverse annealing using the fully connected ferromagnetic $p$-spin model, with and without random longitudinal fields, and analyze it in order to understand how and when reverse annealing is effective at solving this problem. We find that the difficulty arising from the existence of a first-order quantum phase transition, which leads to an exponentially long computation time in conventional quantum annealing, is circumvented in the context of this particular problem by reverse annealing if the proximity of the initial state to the (known) solution exceeds a threshold. Even when a first-order transition is unavoidable, the…

We study liquid quantum droplets in a mixture of two-component Bose-Einstein condensates under variable confinement introduced along one or two spatial dimensions. Although the atom-atom scattering has a three-dimensional character, discreteness of the available modes in the reduced dimension(s) strongly influences the zero-point energy, which for a weakly interacting three-dimensional system is given by the Lee-Huang-Yang term. Here, we generalize the result of Lee, Huang, and Yang and calculate the higher order corrections to the mean-field energy for a single component Bose-Einstein condensate under condition of a tight confinement in one or two spatial directions. We apply our results to the two-component mixture of bosonic species under conditions favorable for the creation of quantum liquid droplets, which constitute a perfect playground for studies of the beyond mean-field effects. Our findings allow one to analyze the properties of quantum droplets at the dimensional crossover and provide demanding conditions for accessing quasilow dimensions. They also pave a way for…

Quantum manipulation of coupled mechanical resonators has become an important research topic in optomechanics because these systems can be used to study the quantum coherence effects involving multiple mechanical modes. A prerequisite for observing macroscopic mechanical coherence is to cool the mechanical resonators to their ground state. Here we propose a theoretical scheme to cool two coupled mechanical resonators by introducing an optomechanical interface. The final mean phonon numbers in the two mechanical resonators are calculated exactly and the results show that the ground-state cooling is achievable in the resolved-sideband regime and under the optimal driving. By adiabatically eliminating the cavity field in the large-decay regime, we obtain analytical results of the cooling limits, which show the smallest achievable phonon numbers and the parameter conditions under which the optimal cooling is achieved. Finally, the scheme is extended to the cooling of a chain of coupled mechanical resonators.

Recent experiments on a one-dimensional chain of trapped alkali-metal atoms [Bernien et al., Nature (London) 551, 579 (2017)] have observed a quantum transition associated with the onset of period-3 ordering of pumped Rydberg states. This spontaneous ${\mathbb{Z}}_{3}$ symmetry breaking is described by a constrained model of hard-core bosons proposed by Fendley et al. [Phys. Rev. B 69, 075106 (2004)]. By symmetry arguments, the transition is expected to be in the universality class of the ${\mathbb{Z}}_{3}$ chiral clock model with parameters preserving both time-reversal and spatial-inversion symmetries. We study the nature of the order--disorder transition in these models and numerically calculate its critical exponents with exact diagonalization and density-matrix renormalization-group techniques. We use finite-size scaling to determine the dynamical critical exponent $z$ and the correlation length exponent $\ensuremath{\nu}$. Our analysis presents the only known instance of a strongly coupled generic transition between gapped states with $z\ensuremath{\ne}1$, implying an…

While Bohr's complementarity principle constitutes a bedrock of quantum mechanics with profound implications, coherence, as a defining feature of the quantum realm originating from the superposition principle, pervades almost every quantum consideration. By exploiting the algebraic and geometric structure of state-channel interaction, we show that an information-theoretic measure of coherence and a quantitative symmetry-asymmetry complementarity emerge naturally from the formalism of quantum mechanics. This is achieved by decomposing the state-channel interaction into a symmetric part and an asymmetric part, which satisfy a conservation relation. The symmetric part is represented by the symmetric Jordan product, and the asymmetric part is synthesized by the skew-symmetric Lie product. The latter further leads to a significant extension of the celebrated Wigner--Yanase skew information, and has an operational interpretation as quantum coherence of a state with respect to a channel. This not only presents a basic and alternative framework for addressing complementarity, but also puts…

A circuit-QED architecture is proposed to study $\mathcal{P}\phantom{\rule{0}{0ex}}\mathcal{T}$ symmetry and its breaking. In addition to being scalable, the platform is shown to be flexible and versatile concerning the engineering of Hamiltonians and corresponding fabrication on real physical systems.

Over the past decade, the rogue wave debate has stimulated the comparison of predictions and observations among different branches of wave physics, particularly between hydrodynamics and optics, in situations where analogous dynamical behaviors can be identified, thanks to the use of common universal models. Although the scalar nonlinear Schr\"odinger equation (NLSE) has constantly played a central role for rogue wave investigations, moving beyond the standard NLSE model is relevant and needful for describing more general classes of physical systems and applications. In this direction, the coupled NLSEs are known to play a pivotal role for the understanding of the complex wave dynamics in hydrodynamics and optics. Benefiting from the advanced technology of high-speed telecommunication-grade components, and relying on a careful design of the nonlinear propagation of orthogonally polarized optical pump waves in a randomly birefringent telecom fiber, this work explores, both theoretically and experimentally, the rogue wave dynamics governed by such coupled NLSEs. We report, for the…

Quantum Fisher information matrix (QFIM) is a cornerstone of modern quantum metrology and quantum information geometry. Apart from optimal estimation, it finds applications in description of quantum speed limits, quantum criticality, quantum phase transitions, coherence, entanglement, and irreversibility. We derive a surprisingly simple formula for this quantity, which, unlike previously known general expression, does not require diagonalization of the density matrix, and is provably at least as efficient. With a minor modification, this formula can be used to compute QFIM for any finite-dimensional density matrix. Because of its simplicity, it could also shed more light on the quantum information geometry in general.

We present a general framework for the generation of random unitaries based on random quenches in atomic Hubbard and spin models, forming approximate unitary $n$-designs, and their application to the measurement of R\'enyi entropies. We generalize our protocol presented in Elben et al. [Phys. Rev. Lett. 120, 050406 (2018)] to a broad class of atomic and spin-lattice models. We further present an in-depth numerical and analytical study of experimental imperfections, including the effect of decoherence and statistical errors, and discuss connections of our approach with many-body quantum chaos.

We derive a mean-field relativistic formula for the isotope shift of an electronic energy level for arbitrary angular momentum; we then use it to predict the spectra of superheavy metastable neutron-rich isotopes belonging to the hypothetical island of stability. Our results may be applied to the search for superheavy atoms in astrophysical spectra using the known values of the transition frequencies for the neutron-deficient isotopes produced in the laboratory. An example of a relevant astrophysical system may be the spectra of the Przybylski's star where superheavy elements up to $Z=99$ have been possibly identified. In addition, it has been recently suggested to use the measurements of King plot nonlinearity in a search for hypothetical new light bosons. On the other hand, one can find the nonlinear corrections to the King plot arising already in the standard model framework. We investigate contributions to the nonlinearity arising from relativistic effects in the isotope field shift, the nuclear polarizability, and many-body effects. It is found that the nuclear polarizability…

We construct a quantum Markovian master equation for a driven system coupled to a thermal bath. The derivation utilizes an explicit solution of the propagator of the driven system. This enables the validity of the master equation to be extended beyond the adiabatic limit. The nonadiabatic master equation (NAME) is derived employing the weak system-bath coupling limit. The NAME is valid when a separation of timescales exists between the bath dynamics and the external driving. In contrast to the adiabatic master equation, the NAME leads to coupled equations of motion for the population and coherence. We employ the NAME to solve the example of an open driven time-dependent harmonic oscillator. For the harmonic oscillator the NAME predicts the emergence of coherence associated with the dissipation term. As a result of the nonadiabatic driving the thermalization rate is suppressed. The solution is compared with both numerical calculations and the adiabatic master equation.

We present a rigorous security analysis of continuous-variable measurement-device-independent quantum key distribution (CV MDI QKD) in a finite-size scenario. The security proof is obtained in two steps: by first assessing the security against collective Gaussian attacks, and then extending to the most general class of coherent attacks via the Gaussian de Finetti reduction. Our result combines recent state-of-the-art security proofs for CV QKD with findings about min-entropy calculus and parameter estimation. In doing so, we improve the finite-size estimate of the secret key rate. Our conclusions confirm that CV MDI protocols allow for high rates on the metropolitan scale, and may achieve a nonzero secret key rate against the most general class of coherent attacks after ${10}^{7}$--${10}^{9}$ quantum signal transmissions, depending on loss and noise, and on the required level of security.

Topological edge states appear at the interface of two topologically distinct Hermitian insulators. We study the extension of this idea to non-Hermitian systems. We consider $\mathcal{P}T$-symmetric and topologically distinct non-Hermitian insulators with real spectra and study topological edge states at the interface of them. We show that $\mathcal{P}T$ symmetry is spontaneously broken at the interface during the topological phase transition. Therefore, topological edge states with complex energy eigenvalues appear at the interface. We apply our idea to a complex extension of the Su-Schrieffer-Heeger model.

We investigate how the combined effects of strong Ohmic dissipation and monochromatic driving affect the stability of a quantum system with a metastable state. We find that, by increasing the coupling with the environment, the escape time makes a transition from a regime in which it is substantially controlled by the driving, displaying resonant peaks and dips, to a regime of frequency-independent escape time with a peak followed by a steep falloff. The escape time from the metastable state has a nonmonotonic behavior as a function of the thermal-bath coupling, the temperature, and the frequency of the driving. The quantum noise-enhanced stability phenomenon is observed in the investigated system.

We define two ways of quantifying the quantum correlations based on quantum Fisher information (QFI) in order to study the quantum correlations as a resource in quantum metrology. By investigating the hierarchy of measurement-induced Fisher information introduced in Lu et al. [X. M. Lu, S. Luo, and C. H. Oh, Phys. Rev. A 86, 022342 (2012)], we show that the presence of quantum correlation can be confirmed by the difference of the Fisher information induced by the measurements of two hierarchies. In particular, the quantitative quantum correlations based on QFI coincide with the geometric discord for pure quantum states.

We present a security analysis of conference key agreement (CKA) in the most adversarial model of device independence (DI). Our protocol can be implemented by any experimental setup that is capable of performing Bell tests [specifically, the Mermin-Ardehali-Belinskii-Klyshko (MABK) inequality], and security can in principle be obtained for any violation of the MABK inequality that detects genuine multipartite entanglement among the $N$ parties involved in the protocol. As our main tool, we derive a direct physical connection between the $N$-partite MABK inequality and the Clauser-Horne-Shimony-Holt (CHSH) inequality, showing that certain violations of the MABK inequality correspond to a violation of the CHSH inequality between one of the parties and the other $N\ensuremath{-}1$. We compare the asymptotic key rate for device-independent conference key agreement (DICKA) to the case where the parties use $N\ensuremath{-}1$ device-independent quantum key distribution protocols in order to generate a common key. We show that for some regime of noise the DICKA protocol leads to better…

A general framework is developed to assess capabilities and limitations of the Gaussian toolbox in continuous-variable quantum information theory. It is shown that under a few assumptions on the set of free states, no Gaussian quantum resource can be distilled with free Gaussian operations, even when an unlimited supply of the resource state is available.

Ultracold fermionic ${}^{23}$Na${}^{40}$K polar molecules are produced in their ground rovibrational state. A multilevel stimulated Raman adiabatic passage (STIRAP) state-transfer process is employed with an intermediate state having an unresolved hyperfine structure, which can be a situation commonly encountered in performing the state transfer.

We present a detailed beyond-mean-field analysis of a weakly interacting Bose gas in the crossover from three to low dimensions. We find an analytical solution for the energy and provide a clear qualitative picture of the crossover in the case of a box potential with periodic boundary conditions. We show that the leading contribution of the confinement-induced resonance is of beyond-mean-field order and calculate the leading corrections in the three- and low-dimensional limits. We also characterize the crossover for harmonic potentials in a model system with particularly chosen short- and long-range interactions and show the limitations of the local-density approximation. Our analysis is applicable to Bose-Bose mixtures and gives a starting point for developing the beyond-mean-field theory in inhomogeneous systems with long-range interactions such as dipolar particles or Rydberg-dressed atoms.

We investigate heat engines whose working substance is made of two coupled qubits performing a generalized Otto cycle by varying their applied magnetic field or their interaction strength during the compression and expansion strokes. During the heating and cooling strokes, the two qubits are coupled to local and common environments that are not necessarily at equilibrium. We find instances of quantum engines coupled to nonequilibrium common environments exhibiting nontrivial connections to quantum correlations as witnessed by a monotonic dependence of the work produced on quantum discord and entanglement.

We systematically investigate scrambling (or delocalizing) processes of quantum information encoded in quantum many-body systems by using numerical exact diagonalization. As a measure of scrambling, we adopt the tripartite mutual information (TMI) that becomes negative when quantum information is delocalized. We clarify that scrambling is an independent property of the integrability of Hamiltonians; TMI can be negative or positive for both integrable and nonintegrable systems. This implies that scrambling is a separate concept from conventional quantum chaos characterized by nonintegrability. Specifically, we argue that there are a few exceptional initial states that do not exhibit scrambling, and show that such exceptional initial states have small effective dimensions. Furthermore, we calculate TMI in the Sachdev-Ye-Kitaev (SYK) model, a fermionic toy model of quantum gravity. We find that disorder does not make scrambling slower but makes it smoother in the SYK model, in contrast to many-body localization in spin chains.

We investigate tunneling ionization of a single active electron with a strong and short laser pulse, circularly polarized. With the recently proposed backpropagation method, we can compare different criteria for the tunnel exit as well as popular approximations in strong-field physics on the same footing. Thereby, we trace back discrepancies in the literature regarding the tunneling time to inconsistent tunneling exit criteria. The main source of error is the use of a static ionization potential, which is, however, time dependent for a short laser pulse. A vanishing velocity in the instantaneous field direction as tunneling exit criterion offers a consistent alternative, since it does not require the knowledge of the instantaneous binding energy. Finally, we propose a mapping technique that links observables from attoclock experiments to the intrinsic tunneling exit time.

We study the dynamics of a quantum system whose interaction with an environment is described by a collision model, i.e., the open dynamics is modeled through sequences of unitary interactions between the system and the individual constituents of the environment, termed ``ancillas,'' which are subsequently traced out. In this setting, non-Markovianity is introduced by allowing for additional unitary interactions between the ancillas. For this model, we identify the relevant system-environment correlations that lead to a non-Markovian evolution. Through an equivalent picture of the open dynamics, we introduce the notion of ``memory depth'' where these correlations are established between the system and a suitably sized memory rendering the overall system+memory evolution Markovian. We extend our analysis to show that while most system-environment correlations are irrelevant for the dynamical characterization of the process, they generally play an important role in the thermodynamic description. Finally, we show that under an energy-preserving system-environment interaction, a…

Large dynamical fluctuations---atypical realizations of the dynamics sustained over long periods of time---can play a fundamental role in determining the properties of collective behavior of both classical and quantum nonequilibrium systems. Rare dynamical fluctuations, however, occur with a probability that often decays exponentially in their time extent, thus making them difficult to be directly observed and exploited in experiments. Here, using methods from dynamical large deviations, we explain how rare dynamics of a given (Markovian) open quantum system can always be obtained from the typical realizations of an alternative (also Markovian) system. The correspondence between these two sets of realizations can be used to engineer and control open quantum systems with a desired statistics ``on demand.'' We illustrate these ideas by studying the photon emission behavior of a three-qubit system which displays a sharp dynamical crossover between active and inactive dynamical phases.

The photonic router is a key device in optical quantum networks. Conventional routers, however, can only transfer a photon from the input port to the desired port probabilistically. Here, we propose to use chiral photon-atom interactions for targeted routing that can transfer a single photon from the input port to an arbitrarily selected output port deterministically, i.e., with $100%$ probability. The configuration of the proposed router consists of a driven three-level atom which is chirally coupled to two photonic waveguides simultaneously. It is shown that, by properly adjusting the driving field on the atom, a single photon inputting from one port of the first waveguide can be deterministically transferred to one of the selected output ports of the second waveguide. Both resonant and nonresonant photons can be deterministically routed to the desired ports. We also examine how the routing fidelity is influenced by dissipations and imperfections, and investigate the transmission characters of two resonant photons.

Radiative polarization of electrons and positrons through the Sokolov-Ternov effect is important for applications in high-energy physics. Radiative spin polarization is a manifestation of quantum radiation reaction affecting the spin dynamics of electrons. We recently proposed that an analog of the Sokolov-Ternov effect could occur in the strong electromagnetic fields of ultra-high-intensity lasers, which would result in a buildup of spin polarization in femtoseconds. In this paper, we develop a density matrix formalism for describing beam polarization in strong electromagnetic fields. We start by using the density matrix formalism to study spin flips in nonlinear Compton scattering and its dependence on the initial polarization state of the electrons. Numerical calculations show a radial polarization of the scattered electron beam in a circularly polarized laser, and we find azimuthal asymmetries in the polarization patterns for ultrashort laser pulses. A degree of polarization approaching 9% is achieved after emitting just a single photon. We develop the theory by deriving a local…

Building a scalable quantum computer requires developing appropriate models to understand and verify its complex quantum dynamics. We focus on superconducting quantum processors based on transmons for which full numerical simulations are already challenging at the level of qubytes. It is thus highly desirable to develop accurate methods of modeling qubit networks that do not rely solely on numerical computations. Using systematic perturbation theory to large orders in the transmon regime, we derive precise analytic expressions of the transmon parameters. We apply our results to the case of parametrically modulated transmons to study recently implemented, parametrically activated entangling gates.

A generalization of $\mathcal{P}\phantom{\rule{0}{0ex}}\mathcal{T}$-scattering theory to nonstatic systems is developed, unveiling characteristics such as CPA-laser operation and bidirectional invisibility. The results may lead to the creation of novel non-Hermitian devices that exploit the tunability and reconfigurability of time-Floquet systems.

Quantized vortices have been observed in a variety of superfluid systems, from $^{4}\mathrm{He}$ to condensates of alkali-metal bosons and ultracold Fermi gases along the BEC-BCS crossover. In this article we study the stability of singly quantized vortex lines in dilute dipolar self-bound droplets. We first discuss the energetic stability region of dipolar vortex excitations within a variational ansatz in the generalized nonlocal Gross-Pitaevskii functional that includes quantum fluctuation corrections. We find a wide region where stationary solutions corresponding to axially symmetric vortex states exist. However, these singly charged vortex states are shown to be unstable, either by splitting the droplet in two fragments or by vortex-line instabilities developed from Kelvin-wave excitations. These observations are the results of large-scale fully three-dimensional simulations in real time. We conclude with some experimental considerations for the observation of such states and suggest possible extensions of this work.

A famously hard graph problem with a broad range of applications is computing the number of perfect matchings, that is, the number of unique and complete pairings of the vertices of a graph. We propose a method to estimate the number of perfect matchings of undirected graphs based on the relation between Gaussian boson sampling and graph theory. The probability of measuring zero or one photons in each output mode is directly related to the hafnian of the adjacency matrix, and thus to the number of perfect matchings of a graph. We present encodings of the adjacency matrix of a graph into a Gaussian state and show strategies to boost the sampling success probability for the studied graphs. With our method, a Gaussian boson sampling device can be used to estimate the number of perfect matchings significantly faster and with lower-energy consumption compared to a classical computer.

We apply genuine multipartite entanglement concurrence to investigate entanglement properties of Dirac fields in noninertial frames. We present analytical concurrences for bipartite and tripartite entanglements simultaneously, which enriches previous results. We note that the entanglement of the Greenberger-Horne-Zeilinger-like state is degraded by the Unruh effect, but this entangled system always remains entangled to a degree and can be used in quantum teleportation between parties in relatively uniform acceleration. We find that all tripartite subsystems in noninertial frames are monogamous in that they all satisfy Coffmann-Kundu-Wootters monogamous inequality. We also find two useful relations regarding concurrences.

We investigate dissipative extensions of the Su-Schrieffer-Heeger model with regard to different approaches of modeling dissipation. In doing so, we use two distinct frameworks to describe the gain and loss of particles: One uses Lindblad operators within the scope of Lindblad master equations, and the other uses complex potentials as an effective description of dissipation. The reservoirs are chosen in such a way that the non-Hermitian complex potentials are $\mathcal{PT}$-symmetric. From the effective theory we extract a state which has similar properties as the nonequilibrium steady state following from Lindblad master equations with respect to lattice site occupation. We find considerable similarities in the spectra of the effective Hamiltonian and the corresponding Liouvillian. Further, we generalize the concept of the Zak phase to the dissipative scenario in terms of the Lindblad description and relate it to the topological phases of the underlying Hermitian Hamiltonian.

We propose a scheme to exchange optical vortices of slow light using the phenomenon of electromagnetically induced transparency in a four-level double-$\mathrm{\ensuremath{\Lambda}}$ atom-light coupling scheme illuminated by a pair of probe fields as well as two control fields of larger intensity. We study the light-matter interaction under the situation where one control field carries an optical vortex, and another control field has no vortex. We show that the orbital angular momentum (OAM) of the vortex control beam can be transferred to a generated probe field through a four-wave-mixing process and without switching on and off of the control fields. Such a mechanism of OAM transfer is much simpler than in a double-tripod scheme in which the exchange of vortices is possible only when two control fields carry optical vortices of opposite helicity. The losses appearing during such OAM exchange are then calculated. It is found that the one-photon detuning plays an important role in minimizing the losses. An approximate analytical expression is obtained for the optimal one-photon…

The Dicke model is of fundamental importance in quantum mechanics for understanding the collective behavior of atoms coupled to a single electromagnetic mode. Here, we demonstrate a Dicke-model simulation via cavity-assisted Raman transitions in a configuration using counterpropagating laser beams. The observations indicate that motional effects should be included to fully account for the results. These results are contrary to experiments using single-beam and copropagating configurations. We give a theoretical description that accounts for the beam geometries used in the experiments and indicates the potential role of motional effects. In particular, a model is given that highlights the influence of Doppler broadening on the observed phase-transition thresholds.

The interaction among the components of a hybrid quantum system is often neglected when considering the coupling of these components to an environment. However, if the interaction strength is large, this approximation leads to unphysical predictions, as has been shown for cavity-QED and optomechanical systems in the ultrastrong-coupling regime. To deal with these cases, master equations with dissipators retaining the interaction between these components have been derived for the quantum Rabi model and for the standard optomechanical Hamiltonian. In this article, we go beyond these previous derivations and present a general master equation approach for arbitrary hybrid quantum systems interacting with thermal reservoirs. Specifically, our approach can be applied to describe the dynamics of open hybrid systems with harmonic, quasiharmonic, and anharmonic transitions. We apply our approach to study the influence of temperature on multiphoton vacuum Rabi oscillations in circuit QED. We also analyze the influence of temperature on the conversion of mechanical energy into photon pairs in…

Although the three-body Rydberg antiblockade regime (RABR) can produce Rabi oscillation between the Rydberg collective excited state and the collective ground state, it is still hard to use the RABR to construct the three-qubit quantum logic gate in one step since the effective Hamiltonian is always accompanied by undesired Stark shifts. In order to overcome this difficulty, an additional laser is introduced to eliminate the Stark shifts in the ground-state subspace. And the initial RABR condition is modified to eliminate the remaining undesired Stark shifts in the collective-excitation subspace. The modified RABR is then generalized to the $n (n>3)$-qubit case. Based on the proposed regime, one-step schemes to construct three- and $n$-qubit quantum controlled-PHASE gates are proposed without the requirement of atomic addressability. The asymmetric Rydberg-Rydberg interaction, which is more practical for Rydberg atoms, is also discussed and proven to be feasible for the modified RABR and quantum controlled-PHASE gate in theory. A full-Hamiltonian-based master equation is used to…

The decoy-state protocol has been considered to be one of the most important methods to protect the security of quantum key distribution (QKD) with a weak coherent source. Here we test two experimental approaches to generating the decoy states with different intensities: modulation of the pump current of a semiconductor laser diode, and external modulation by an optical intensity modulator. The former approach shows a side channel in the time domain that allows an attacker to distinguish s signal state from a decoy state, breaking a basic assumption in the protocol. We model a photon-number-splitting attack based on our experimental data, and show that it compromises the system's security. Then, based on the work of Tamaki et al. [New J. Phys. 18, 065008 (2016)], we obtain two analytical formulas to estimate the yield and error rate of single-photon pulses when the signal and decoy states are distinguishable. The distinguishability reduces the secure key rate below that of a perfect decoy-state protocol. To mitigate this reduction, we propose to calibrate the transmittance of the…

Level repulsion---the opening of a gap between two degenerate modes due to coupling---is ubiquitous anywhere from solid-state theory to quantum chemistry. In contrast, if one mode has negative energy, the mode frequencies attract instead. They converge and develop imaginary components, leading to an instability; an exceptional point marks the transition. This only occurs if the dissipation rates of the two modes are comparable. Here we expose a theoretical framework for the general phenomenon and realize it experimentally through engineered dissipation in a multimode superconducting microwave optomechanical circuit. Level attraction is observed for a mechanical oscillator and a superconducting microwave cavity, while an auxiliary cavity is used for sideband cooling. Two exceptional points are demonstrated that could be exploited for their topological properties.

Spontaneous symmetry breaking is an important concept in many areas of physics. A fundamentally simple symmetry-breaking mechanism in electrodynamics occurs between counterpropagating electromagnetic waves in ring resonators, mediated by the Kerr nonlinearity. The interaction of counterpropagating light in bidirectionally pumped microresonators finds application in the realization of optical nonreciprocity (for optical diodes), studies of $\mathcal{PT}$-symmetric systems, and the generation of counterpropagating solitons. Here, we present comprehensive analytical and dynamical models for the nonlinear Kerr interaction of counterpropagating light in a dielectric ring resonator. In particular, we study discontinuous behavior in the onset of spontaneous symmetry breaking, indicating divergent sensitivity to small external perturbations. These results can be applied to realize, for example, highly sensitive near-field or rotation sensors. We then generalize to a time-dependent model, which predicts different types of dynamical behavior, including oscillatory regimes that could enable…

We introduce a method for representing the low-energy subspace of a bosonic field theory on the qubit space of digital quantum computers. This discretization leads to an exponentially precise description of the subspace of the continuous theory thanks to the Nyquist-Shannon sampling theorem. The method makes the implementation of quantum algorithms for purely bosonic systems as well as fermion-boson interacting systems feasible. We present algorithmic circuits for computing the time evolution of these systems. The complexity of the algorithms scales polynomially with the system size. The algorithm is a natural extension of the existing quantum algorithms for simulating fermion systems in quantum chemistry and condensed-matter physics to systems involving bosons and fermion-boson interactions and has a broad variety of potential applications in particle physics, condensed matter, etc. Due to the relatively small amount of additional resources required by the inclusion of bosons in our algorithm, the simulation of electron-phonon and similar systems can be placed in the same…

By coupling a $\mathrm{\ensuremath{\Lambda}}$-type quantum emitter to a chiral waveguide, in which the polarization of a photon is locked to its propagation direction, we propose a controllable photon-emitter interface for quantum networks. We show that this chiral system enables the swap gate and a hybrid-entangling gate between the emitter and a flying single photon. It also allows deterministic storage and retrieval of single-photon states with high fidelities and efficiencies. In short, this chirally coupled emitter-photon interface can be a critical building block toward a large-scale quantum network.

The excitation of toroidal multipoles in metamaterials is investigated for a high-$Q$ response at a subwavelength scale. In this paper, we explore the optimization of toroidal excitations in a planar metamaterial comprised of asymmetric split ring resonators (ASRRs). It is found that the scattering power of a toroidal dipole can be remarkably strengthened by adjusting the characteristic parameter of ASRRs: an asymmetric factor. Interestingly, the improvement in toroidal excitation accompanies an increment of the $Q$ factor of the toroidal metamaterial; it is shown that both the scattering power of the toroidal dipole and the $Q$ factor increase more than one order by changing the asymmetric factor of ASRRs. The optimization in the excitation of a toroidal multipole provides an opportunity to further increase the $Q$ factor of the metamaterial and boost light-matter interactions at the subwavelength scale for potential applications in low-power nonlinear processing and sensitive photonic applications.