We investigate both analytically and numerically the dynamics of quantum scrambling, characterized by out-of-time ordered correlators (OTOCs), in a non-Hermitian quantum kicked rotor subject to quantum resonance conditions. Analytical expressions for OTOCs as a function of time are obtained, demonstrating a sudden transition from linear growth to quadratic growth when the non-Hermitian parameter decays to zero. At this critical point, the rates of the linear growth are found to diverge to infinity, indicating the existence of quantum criticality at the boundary of the non-Hermitian regime. The underlying mechanism of this quantum criticality is uncovered, and possible applications in quantum metrology are discussed.

Kochen–Specker contextuality is a fundamental feature of quantum mechanics and a crucial resource for quantum computational advantage and reduction of communication complexity. Its presence is witnessed in empirical data by the violation of noncontextuality inequalities. However, all known noncontextuality inequalities corresponding to facets of noncontextual polytopes are either Bell inequalities or refer to cyclic or state-independent contextuality scenarios. We introduce a general method for lifting noncontextuality inequalities, deriving facets of noncontextual polytopes for more complex scenarios from known facets of simpler subscenarios. Concretely, starting from an arbitrary scenario, the addition of a new measurement or a new outcome preserves the facet-defining nature of any noncontextuality inequality. This extends the results of Pironio [J. Math. Phys. 46, 062112 (2005)] from Bell nonlocality scenarios to contextuality scenarios, unifying liftings of Bell and noncontextuality inequalities. Our method produces facet-defining noncontextuality inequalities in all scenarios with contextual correlations, and we present examples of facet-defining noncontextuality inequalities for scenarios where no examples were known. Our results shed light on the structure of noncontextuality polytopes and the relationship between such polytopes across different scenarios.

Concatenation of a bosonic code with a qubit code is one of the promising ways to achieve fault-tolerant quantum computation. As one of the most important bosonic codes, the Gottesman-Kitaev-Preskill (GKP) code is proposed to correct small displacement errors in phase space. If the noise in phase space is biased, the square-lattice GKP code can be concatenated with the repetition code that promises a high fault-tolerant threshold to suppress the logical error. In this work, we study the performance of GKP repetition codes with finite-energy ancillary GKP qubits in correcting biased noise. We find that there exists a critical value of noise variance for the ancillary GKP qubit such that the logical Pauli error rate decreases when increasing the code size. Furthermore, one round of GKP error correction has to be performed before concatenating with the repetition code. Our study paves the way for practical implementation of error correction by concatenating the GKP code with low-level qubit codes.

We present a fermionic cellular automaton model which describes massless Dirac fermions in $1+1$ dimension coupled with local, number preserving interaction. The diagonalization of the two particle sector shows that specific values of the total momentum and of the coupling constant allow for the formation of bound states. Furthermore, we present a classification of the local number preserving interactions that are invariant under the isotropy group of the cellular automaton which simulates the Weyl equation.

Strong nonlocality, proposed by Halder et al. [Phys. Rev. Lett. 122, 040403 (2019)], is a stronger manifestation than quantum nonlocality. Subsequently, Shi et al. presented the concept of the strongest nonlocality [Quantum 6, 619 (2022)]. Recently, Li and Wang [Quantum 7, 1101 (2023)] posed the conjecture about a lower bound to the cardinality of the strongest nonlocal set $\mathcal{S}$ in ${\otimes }_{i=1}^n{\mathbb{C}}^{d_i}$, i.e., $\left|\mathcal{S}\right|\le {max}_i\{{\prod }_{j=1}^n{d}_j/d_i+1\}$. In this work, we construct the strongest nonlocal set of size $d^2+1$ in ${\mathbb{C}}^d\otimes {\mathbb{C}}^d\otimes {\mathbb{C}}^d$. Furthermore, we obtain the strongest nonlocal set of size $d_2{d}_3+1$ in ${\mathbb{C}}^{d_1}\otimes {\mathbb{C}}^{d_2}\otimes {\mathbb{C}}^{d_3}$. Our construction reaches the lower bound, which provides an affirmative solution to Li and Wang's conjecture. ln particular, the strongest nonlocal sets we present here contain the least number of orthogonal states among the available results.

Quantum computing has a potential to accelerate data processing efficiency, especially in machine learning, by exploiting special features such as the quantum interference. The major challenge in this application is that, in general, the task of loading a classical data vector into a quantum state requires an exponential number of quantum gates. The approximate amplitude encoding (AAE) method, which uses a variational means to approximately load a given real-valued data vector into the amplitude of a quantum state, was recently proposed as a general approach to this problem mainly for near-term devices. However, AAE cannot load a complex-valued data vector, which narrows its application range. In this work, we extend AAE so that it can handle a complex-valued data vector. The key idea is to employ the fidelity distance as a cost function for optimizing a parametrized quantum circuit, where the classical shadow technique is used to efficiently estimate the fidelity and its gradient. We apply this algorithm to realize the complex-valued-kernel binary classifier called the compact Hadamard classifier, and then we present a numerical experiment showing that it enables classification of the Iris dataset and credit card fraud detection.

We introduce a stronger form of quantum nonlocality, termed local subset unidentifiability, that arises from the limitation of spatially separated parties to perfectly identify a subset of mutually orthogonal multipartite quantum states, randomly chosen from a larger known set, using local operations and classical communication (LOCC). We show that this nonlocality is stronger than other existing forms of quantum nonlocality, such as local indistinguishability and local unmarkability. If more than one multipartite states from a locally indistinguishable set are distributed between spatially separated parties in a sequentially ordered fashion, then they may or may not mark which state is which using LOCC. However, we show that even when the parties cannot mark the states, they may still locally identify the particular states given to them, though not their order—i.e., they can identify the elements of the given subset of states. Then we prove the existence of such subsets that are not even locally identifiable, thereby manifesting a stronger nonlocality. We also present the genuine version of this nonlocality—genuine subset unidentifiability—where the provided subset remains unidentifiable unless all the parties come together in a common location and perform global measurements. We anticipate potential applications of this nonlocality for future quantum technologies. We discuss one such application in a certain secret password distribution protocol, where this nonlocality outperforms its predecessors as a resource.

Spin squeezing, as a crucial quantum resource, plays a pivotal role in quantum metrology, enabling us to achieve high-precision parameter estimation schemes. Here, we investigate the spin squeezing and the quantum phase transition in an anisotropic central spin system. We find that this kind of central spin system can be mapped to the anisotropic Lipkin-Meshkov-Glick model in the limit where the ratio of transition frequencies between the central spin and the spin bath tends towards infinity. This property can induce a one-axis twisting interaction and provides another possibility for generating spin squeezing. We consider the generation of spin-squeezed states through the ground state and the dynamical evolution of the central spin model, respectively. The results show that the dynamical approach is more effective, and the spin-squeezing parameter improves as the anisotropy parameter decreases, while its value scales with system size as $N^{-2/3}$. Furthermore, we obtain the critical exponent of the quantum Fisher information around the critical point by numerical simulation, and find its value tends to $4/3$ as the frequency ratio and the system size approach infinity. This paper offers a promising scheme for generating spin-squeezed state and paves the way for potential advancements in quantum sensing.

Ultracold diatomic molecules find application in quantum studies ranging from controlled chemistry and precision measurement physics to quantum many-body simulation and potentially quantum computing. Accurate knowledge of molecular properties is required to guide and explain ongoing experiments. Here, in an extensive and comparative study, we theoretically investigate the electronic properties of the ground-state diatomic molecules composed of alkali-metal (Li, Na, K, Rb, Cs, Fr) and alkaline-earth-metal (Be, Mg, Ca, Sr, Ba, Ra) atoms. We study 78 heteronuclear and homonuclear diatomic combinations, including 21 alkali-metal molecules in the $X^1{\mathrm{\Sigma }}^{+}$ and $a^3{\mathrm{\Sigma }}^{+}$ electronic states, 36 alkali-metal–alkaline-earth-metal molecules in the $X^2{\mathrm{\Sigma }}^{+}$ electronic state, and 21 alkaline-earth-metal molecules in the $X^1{\mathrm{\Sigma }}^{+}$ electronic state. We calculate potential energy curves, permanent electric dipole moments, and polarizabilities using the hierarchy of coupled-cluster methods up to CCSDTQ with large Gaussian basis sets and small-core relativistic energy-consistent pseudopotentials. We collect and analyze corresponding spectroscopic constants. We estimate computational uncertainties and compare the present values with previous experimental and theoretical data to establish a different theoretical benchmark. The presented results should be useful for further application of the studied molecules in modern ultracold physics and chemistry experiments.

In quantum technologies, it is essential to understand and exploit the interplay of light and matter. We introduce an approach creating and maintaining the coherence of four oscillators: a global microwave reference field, a polarization-gradient traveling-wave pattern of light, and the spin and motional states of a single trapped ion. Our method employs a UV light pattern capable of achieving a gigahertz-modulation bandwidth, here demonstrated in the megahertz regime, allowing for stroboscopic tracking of dynamic changes in phase space. We achieve noise floors of $1.8\left(2\right)\text{nm}$ for position and $8\left(2\right)\text{zN}\mu \mathrm{s}$ for momentum observables, superresolving variations on timescales $\lesssim 100$ ns. The implications of our findings contribute to enhancing quantum control and metrological applications.

Dynamical properties of homogeneous Fermi-Fermi mixtures of dipolar and nondipolar atoms are studied at zero temperature, where dipoles are polarized by an external field. We calculate the density-density correlation functions in a ring-diagram approximation and analyze the pole structure to obtain eigenfrequencies of collective excitations. We first determine stability phase diagrams for the mixtures available in experiments:, i.e., ${}^{167}\mathrm{Er}\text{−}{}^{173}\mathrm{Yb}$, ${}^{167}\mathrm{Er}\text{−}{}^6\mathrm{Li}$, ${}^{161}\mathrm{Dy}\text{−}{}^{173}\mathrm{Yb}$, and ${}^{161}\mathrm{Dy}\text{−}{}^6\mathrm{Li}$ systems, and show that the mixtures with larger mass imbalance tend to be more unstable. We then investigate the parameter dependence of an undamped zero sound with an anisotropic real dispersion relation in the stable phase for the ${}^{161}\mathrm{Dy}\text{−}{}^{173}\mathrm{Yb}$ mixture, and the speed of sound exhibits a critical angle of possible propagation with respect to the dipole polarization direction, above which the sound mode disappears in the particle-hole continuum. Since the sound mode is a coherent superposition of density fluctuations of dipolar and nondipolar atoms, the existence of the sound mode, e.g., the value of the critical angle, is significantly affected by the interparticle interaction through the density-density correlation between dipolar and nondipolar atoms. We have also observed such an effect of the interparticle interaction in the study of a linear response of density fluctuations to an external perturbation.

The collective excitation modes in quantum droplets trapped in a two-dimensional harmonic potential in the context of symmetric weakly interacting binary bosonic mixtures are studied. By utilizing the linearization technique, the time-dependent extended Gross–Pitaevskii equation, and a sum-rule approach with a variational approximation, the ground-state properties and collective excitations of such a two-dimensional quantum system are investigated for various system parameters. We present comprehensive analysis and calculations on the effect of the confinement strength and anisotropy of the trapping potential, the number of atoms in the droplet, and the collective excitation modes. The radius of the droplet, as well as the chemical potential, is nonmonotonically related to the number of atoms in the droplet, and the confinement tends to shift the minimum values towards the ideal-gas limit. The excitation frequency peaks, which are prominent in a self-bounded droplet, become less pronounced and smoother when subjected to a strong trapping potential. The sum-rule approach fails to reproduce the breathing mode frequency for a moderate number of atoms in a weak trapping potential, however, works perfectly well in a strong confinement. It was found that the anisotropy in the trap eliminates the degeneracy between the quadrupole and scissors modes that occurs in an isotropic trap, causing the frequencies of these two modes to immediately diverge from each other for any degree of anisotropy. These findings provide valuable insights into the unique characteristics and behavior of quantum droplets, offering potential implications for future research and applications in the dynamic behaviors of intriguing quantum droplets.

We study spin transport in a one-dimensional finite-length wire connected to fermionic leads. The interacting wire is described by the sine-Gordon model while the leads are either noninteracting or interacting Luttinger liquids. We calculate the spin current driven by a spin bias in the nonlinear regime by solving numerically the classical equation of motion, and find that the cosine term in the sine-Gordon model gives rise to an oscillating spin current when the spin bias exceeds its critical value. We discuss the results in connection with transport experiments with ultracold atoms.

Near-electric-field enhancement induced by the nanoscale light-matter interactions has been advancing plasmonics such as plasmon-enhanced spectroscopy, leading to a linear scaling of the observed far-field spectral signals in theory. However, the contributions of an additionally existed chemical effect to the propagated optical signals from near- to far-field are commonly irregular. Here, inspired by the physical origin of surface-enhanced Raman spectroscopy (SERS), we experimentally map the far-field signals on the near-field properties through utilizing the purely electromagnetic coupled plasmon-molecule interactions of particular Raman probe molecules, thereby enabling the precise estimation for the enhanced local electric field in the subwavelength dimension only with the SERS intensity. This work can truly accelerate the translation of SERS into a quantitative analysis tool, but also lays the foundation of an intuitive probing into the plasmonic excited field employing plasmon-enhanced spectroscopic techniques.

We present a work of promoted optical nonreciprocity (ONR) in an asymmetrical cavity containing two asymmetrically arranged two-level atoms with a weak atom-atom interaction. The input-output relation is worked out by using a perturbative approach. Results show that the bistable-monostable-bistable phase transition would exist when the second atom is present, where the optical bistability and nonreciprocity change considerably. Contributions of two types of spatial asymmetries suggest that the ONR originates from the cooperation of the cavity spatial symmetry breaking and the optical nonlinearity, regardless of the atomic spatial symmetry breaking. In addition to the experimentally proved bistable ONR, a type of monostable ONR is proposed, which operates in the monostable phase. Both the ONR optimal regime and the block rate are boosted by adding the other atom in the cavity. Our findings suggest a prospective approach to the generation of a giant ONR by two atoms with unequal atom-cavity coupling strengths.

An unextendible biseparable basis (UBB) is a set of orthogonal pure biseparable states which span a subspace of a given Hilbert space while the complementary subspace contains only genuinely entangled states. These biseparable bases are useful to produce genuinely entangled subspace in a multipartite system. Such a subspace could be more beneficial for information theoretic applications if we were able to extract distillable entanglement across every bipartition from each state of this subspace. In this paper, we have derived a rule for constructing such a class of UBB which exhibits the phenomenon of strong quantum nonlocality. This result positively answers the open problem raised by Agrawal et al. [Agrawal, Halder, and Banik, Genuinely entangled subspace with all-encompassing distillable entanglement across every bipartition, Phys. Rev. A 99, 032335 (2019)], that there exists a UBB which can demonstrate the phenomenon of strong quantum nonlocality in the perspective of the local irreducibility paradigm.

We present an implementation of a recently proposed procedure for defining time, based on the description of the evolving system and its clock as noninteracting, entangled systems, according to the Page and Wootters approach. We study how the quantum dynamics transforms into a classical-like behavior when conditions related to macroscopicity are met by the clock alone, or by both the clock and the evolving system. In the description of this emerging behavior finds its place the classical notion of time, as well as that of phase-space and trajectories on it. This allows us to analyze and discuss the relations that must hold between quantities that characterize the system and clock separately, in order for the resulting overall picture to be that of a physical dynamics as we mean it.

Estimating the eigenvalue or energy gap of a Hamiltonian $H$ is vital for studying quantum many-body systems. Particularly, many of the problems in quantum chemistry, condensed-matter physics, and nuclear physics investigate the energy gap between two eigenstates. Hence, how to efficiently solve the energy gap becomes an important motive for researching new quantum algorithms. In this work, we propose a hybrid nonvariational quantum algorithm that uses the Monte Carlo method and real-time Hamiltonian simulation to evaluate the energy gap of a general quantum many-body system. Compared to conventional approaches, our algorithm does not require controlled real-time evolution, thus making its implementation much more experimental friendly for near-term quantum devices and early fault-tolerant quantum computers. To verify the efficiency of our algorithm, we conduct numerical simulations for the Heisenberg model and molecule systems on a classical emulator.

Quantum error correction (QEC) exploits redundancy by encoding logical information into multiple physical qubits. In current implementations of QEC, sequences of nonperfect two-qubit entangling gates are used to codify the information redundantly into multipartite entangled states. Also, to extract the error syndrome, a series of two-qubit gates are used to build parity-check readout circuits. In the case of noisy gates, both steps cannot be performed perfectly, and an error model needs to be provided to assess the performance of QEC. We present a detailed microscopic error model to estimate the average gate infidelity of two-qubit light-shift gates used in trapped-ion platforms. We analytically derive leading-error contributions in terms of microscopic parameters and present effective error models that connect the error rates typically used in phenomenological accounts to the microscopic gate infidelities hereby derived. We then apply this realistic error model to quantify the multipartite entanglement generated by circuits that act as QEC building blocks. We do so by using entanglement witnesses, complementing in this way the recent studies in Ref. [Phys. Rev. X 12, 011032 (2022); PRX Quantum 2, 020304 (2021)] by exploring the effects of a more realistic microscopic noise.