Periodic waves expressed in terms of Jacobi elliptic functions serve as canonical coherent backgrounds in integrable systems, providing a natural interpolation between the plane-wave background and soliton limit in appropriate parameter regimes. For vector (two-component) fields, however, the corresponding periodic-background theory is far less developed, the usual analysis being confined to quasi-single-component periodic states with linearly coupled components, which prevents the energy exchange between the components and polarization-resolved spectral features. To overcome the constraint, we construct a tractable class of elliptic-function periodic backgrounds for the Manakov system, whose linear stability is addressed by means of the Floquet-Fourier-Hill method. In parallel, the nonlinear spectral structure of the background is investigated through the spectrum of the spatial Lax operator. Guided by these spectral scenarios, the Darboux transform yields explicit families of vector localized excitations riding on top of the periodic background, including bright-dark solitons, Akhmediev breathers, and collisions between counterpropagating localized modes. In the Fourier domain, wave-number spectra exhibit pronounced asymmetry and energy redistribution between the components, leading to a “semi-Fermi-Pasta-Ulam-Tsingou recurrence,” different from the plane-wave case. Numerical simulations, initialized with the exact solutions, show that the dominant localized structures remain identifiable in the course of the propagation.

We present a scheme to realize simultaneous nonreciprocal unconventional photon blockades in a system of two coupled spinning resonators (modes $a$ and $b$), each embedded with a degenerate optical parametric amplifier (DOPA). The rotation of the resonators induces opposite Sagnac-Fizeau shifts for input light from opposing directions, leading to the appearance or suppression of destructive quantum interference in two-photon excitation processes. When such interference occurs, photons from one input direction are simultaneously blocked in both resonators, whereas its absence lifts the blockade for the opposite direction. We analytically derive the optimal conditions for achieving strong photon antibunching in both modes under parametric amplification. The two-DOPA configuration offers two key advantages: (i) the optimization of simultaneous unconventional photon blockades in both resonators relies on four independent parameters (two strengths and two phases for two DOPAs), enabling greater control, and (ii) the system allows tunability in transition pathways to simultaneously access two-photon states in both resonators. By tuning the Sagnac-Fizeau shifts, we demonstrate that mode $a$ exhibits a nonreciprocal photon blockade, while mode $b$ maintains a blockade in both directions. Furthermore, we show the robustness of this nonreciprocal photon blockade against memory effects by deriving a non-Markovian master equation. This work provides a theoretical foundation for multimode nonreciprocal single-photon devices, with potential applications in quantum optics.

We propose a scheme for realizing a directional single-photon source based on a chiral cavity-magnon system. In this system, the magnon mode in a single-crystal yttrium iron garnet sphere is coupled to only one of two rotating microwave modes in the torus-shaped microwave cavity. When two-photon driving fields are applied to both ports of the waveguide, the chiral cavity-magnon coupling leads to an unconventional photon blockade in one propagation direction, resulting in directional single-photon emission. The emission direction of the single-photon source can be controlled by reversing the bias magnetic field. Furthermore, we examine the effects of imperfect chiral cavity-magnon coupling and the coupling between the two cavity modes on the photon-blockade behavior. The results show that the system remains robust in the presence of these nonideal factors, and the unidirectional photon-blockade effect remains clearly preserved. Our approach may offer a different perspective for the design of unidirectional single-photon devices.

We propose to use the antisqueezing-enhanced non-Gaussian Schrödinger cat quantum states of the probing light for the task of detection of a given phase shift in optical interferometers. We show that the antisqueezing allows to increase the robustness of the setup to optical losses. We find the optimal degrees of the antisqueezing for experimentally achievable values of the Schrödinger cat amplitude and the optical losses and compare the resulting sensitivity with the one provided by the Gaussian squeezed states.

We examine a quantum absorption refrigerator that comprises three qubits, each of which is connected with a separate spin-star environment, with the three qubit-bath units coupled through an effective six-body interaction. The refrigerator exhibits the feature of transient cooling, i.e., lowering of the temperature of the first qubit in sufficiently small timescales, rather than steady-state refrigeration. A key advantage of our model is that the symmetries of the Hamiltonian enable a semianalytic solution of the reduced density matrices of the refrigerator qubits, even in the presence of a large number of environmental spins. We derive the condition for autonomous refrigeration and analyze how the optimal cold-qubit temperature scales with the number of bath spins. We find a power-law scaling toward a constant asymptotic value. We also find the scaling of the minimum time required for optimal cooling as a function of the number of bath spins. Furthermore, we quantify the non-Markovianity of the cold-qubit dynamics using a restricted Breuer-Laine-Piilo information-backflow measure and observe that stronger backflow correlates with lower transient minimum temperatures across the sampled parameter regime. The transient-cooling performance is found to be robust under broad parameter variations. Compared to a conventional Markovian three-qubit refrigerator, the central-spin quantum absorption refrigerator achieves lower cold-qubit temperatures on shorter timescales. We further analyze the heat currents associated with the three qubits and their respective baths.

Gaussian boson sampling is an important protocol for testing the performance of photonic quantum simulators. As such, various noise sources have been investigated that degrade the operation of such devices. In this paper we examine a situation with phase noise between different modes of the input state leading to dephasing of the system. This models the phase fluctuations, which remain even when the mean phase is controlled. We aim to determine whether these phase-noisy input states still form a computationally difficult problem. To do this, we use matrix product operators to model the system, a technique recently used to model boson sampling scenarios. Our investigation finds that the entanglement entropy grows linearly with the number of input states even for noisy input states. This implies that, unlike boson loss, this form of experimentally relevant noise remains difficult to simulate with tensor networks and may allow for the demonstration of quantum advantage without the need for implementing the challenging task of input-state phase stabilization.

Understanding the fundamental limits of state convertibility is crucial for establishing the boundaries of quantum information processing and thermodynamic efficiency. While auxiliary systems—catalysts—can facilitate otherwise impossible transformations, standard catalysis rigidly requires the auxiliary system to return to its exact initial state. In this work, we investigate the power of flexible catalysis, where the catalyst evolves through a cycle of states, restoring its initial configuration only after a finite number of steps. Focusing on the regime of fixed, finite dimensions, we analyze the capabilities of flexible catalysis within the resource theories of entanglement and quantum thermodynamics. In the context of entanglement, we derive conditions limiting flexible catalysts, yet show that flexible catalysis can be strictly more powerful than same-dimensional standard catalysis: it enables deterministic transformations achievable by no standard catalyst of the same dimension, and it strictly increases the success probability of stochastic local operations and classical communication. A similar deterministic advantage arises in quantum thermodynamics, where flexible catalysis enables state transformations that are impossible with any standard catalyst of fixed dimension and Hamiltonian but become achievable via flexible catalysis.

We present analytical results toward the Wigner entropy conjecture, which posits that among all physical Wigner non-negative states, the Wigner entropy is minimized by pure Gaussian states for which it attains the value $1+ln\pi$. Working under a minimal set of constraints on the Wigner function, namely, non-negativity, normalization, and the pointwise bound $\pi W\le 1$, we construct an explicit hierarchy of lower bounds $B_n$ on $S\left[W\right]$ by combining a truncated series lower bound for $-lnx$ with moment identities of the Wigner function. This yields closed-form sufficient conditions, expressed in terms of the state purity $\mu :=Tr\left({\rho }^2\right)=2\pi \int dqdpW{(q,p)}^2$, ensuring $S\left[W\right]\ge 1+ln\pi$. In particular, we first prove that all physical Wigner non-negative states with $\mu \le 4-2\sqrt{3}$ satisfy the Wigner entropy conjecture. We further obtain a systematic purity-only relaxation of the hierarchy, whose limiting sufficient condition is $\mu \le 2/e$. Finally, we show that the threshold $2/e$ is sharp under the relaxed constraints considered here, thereby identifying the need for additional quantum-realizability information in the remaining high-purity regime.

Fault-tolerant quantum computation (FTQC) requires fast and accurate decoding of quantum errors, which is often formulated as a minimum-weight perfect-matching (MWPM) problem. A determinant-based approach has been proposed as a novel method to surpass the conventional polynomial runtime of MWPM decoding via the blossom algorithm, asymptotically achieving polylogarithmic parallel runtime. However, the existing approach requires an impractically large bit length to represent intermediate values during the computation of the matrix determinant; moreover, when implemented on a finite-bit machine, the algorithm cannot detect overflow and, therefore, the mathematical correctness of such algorithms cannot be guaranteed. In this work, we address these issues by presenting a polylog-time MWPM decoder that treats finite-precision truncation naturally by employing an algebraic framework over a truncated polynomial ring. Within this framework, all arithmetic operations are implemented using bitwise XOR and shift operations. Furthermore, with algorithmic optimizations tailored to the structure of the determinant-based approach, we reduce the arithmetic bit length required to represent intermediate values in the determinant computation by more than $99.9\%$, reducing the required arithmetic bit length to the 512-bit scale while preserving the decoder's polylog runtime scaling. These results provide a theoretical and numerical basis for future proof-of-principle demonstrations of the polylog-time MWPM decoding in the early FTQC regime.

We discuss a conceptually simple scheme for cooling a one-dimensional gas of microwave photons in a superconducting transmission line. By shunting one end of the transmission line by a nonlinear Josephson element, we show how a cooling mechanism can be engineered that transfers photons from high- into low-frequency modes, while preserving their total number. We evaluate the resulting nonequilibrium steady state of the photon gas, which arises from a competition between this engineered cooling process and the natural, number nonconserving thermalization with the surrounding bath. Our analysis predicts that for realistic experimental parameters, this mechanism can be used to prepare photonic gases at submillikelvin temperatures, considerably below the typical base temperature of a dilution refrigerator. In addition, the system exhibits a new type of condensation transition that does not occur in the corresponding equilibrium scenario. As an outlook, we discuss potential applications of this cooling approach for quantum simulation schemes with interacting microwave photons.

We consider a Hamiltonian $\widehat{H}$ with a (partially) continuous spectrum and examine the zero-overlap condition which involves the projection onto exact continuum eigenstates of a set of pseudostates obtained from the diagonalization of $\widehat{H}$ in a finite basis of square-integrable functions. For each projected pseudostate the condition implies the occurrence of zeros at all energies that correspond to the pseudocontinuum matrix eigenvalues, except for the eigenenergy associated with that pseudostate. This feature was observed for the Coulomb continuum represented in a Laguerre basis [M. McGovern et al., Phys. Rev. A 79, 042707 (2009)] and later explained using special properties of the Laguerre functions [I. B. Abdurakhmanov et al., J. Phys. B 44, 075204 (2011)]. We establish that a sufficient condition for the zero-overlap condition to occur is that the image space of the operator $\widehat{Q}\widehat{H}\widehat{P}$, where $\widehat{P}$ is the projection operator onto the subspace spanned by the basis and $\widehat{Q}=\widehat{1}-\widehat{P}$ its complement, has dimension one. We show that the condition is met for the one-dimensional free-particle problem by a basis of harmonic-oscillator eigenstates and by a minimal set of simple momentum-space wave functions, and for the Coulomb problem by a Laguerre basis, thus offering an alternative proof for the latter case. The zero-overlap condition ensures that in, e.g., an ionizing collision or laser-atom interaction process, transition probabilities obtained from the projection of a time-propagated pseudostate-expanded system wave function onto eigenstates of $\widehat{H}$ are asymptotically stable.

We calculate parity nonconservation (PNC) amplitudes for all magnetic dipole ($M1$) transitions within the ground $5p^2$configuration of Sn, including the standard model interaction and contribution of a hypothetical additional $Z^{\prime }$ boson. Among the transitions considered, the ${}^1{S}_0{\text{−}}^3{P}_1$ transition has the largest PNC amplitude and appears to be the most promising candidate for an experiment. We also discuss a measurement method capable of achieving unprecedentedly high precision in a measurement of PNC in this transition. We argue that the most robust test should be based on ratios of PNC amplitudes for different isotopes, since the atomic-structure factor largely cancels in such ratios. We study the effect of the neutron skin on these isotope ratios using available nuclear data for Sn and show that the uncertainty associated with the neutron skin can be reduced to the ${10}^{-4}$ level relative to the isotopic variation of the PNC effect. Our results indicate that PNC measurements along a chain of Sn isotopes offer a realistic and sensitive probe of new physics.

A promising route to testing quantum gravity in the laboratory is to look for gravitationally induced entanglement (GIE) between two or more quantum matter systems. To date, proposed tests have primarily focused on microsolid platforms prepared in highly nonclassical states, such as N00N states or strongly squeezed states. Here, we instead consider measuring GIE in atom interferometry as evidence of quantum gravity. We propose placing two atom interferometers next to each other in parallel and looking for correlations in the atom-number statistics at their output ports. Importantly, GIE is possible without challenging macroscopic superposition states, such as N00N or Schrödinger-cat states. Instead, GIE can arise using coherent, near-classical atomic states, substantially reducing the experimental complexity. Observing the effect in this regime would require the total mass of the atom interferometers to be near the Planck mass scale. However, we show that state-of-the-art quantum squeezing techniques in cold-atom systems can significantly lower this mass requirement, and outline realistic pathways by which the necessary mass scales could be achieved in the near future, placing laboratory tests of GIE with atom interferometers within reach.

Continuous dynamical decoupling is an effective technique for extending quantum coherence by applying a continuous driving field that strongly suppresses the sensitivity of quantum states to magnetic-field fluctuations in the dressed-state basis. We experimentally measure the dressed-state spectrum of a spin-1 Bose-Einstein condensate under continuous rf driving and investigate the properties of the resulting sidebands from a Floquet-theory perspective. It is found that under resonant rf driving, two of the three dressed states exhibit markedly enhanced coherence times, and both the coherence time and the coherence coupling strength are symmetric for the two conjugate Floquet sidebands. In contrast, under off-resonant rf driving, although the coherence times are symmetrically reduced for the two conjugate Floquet sidebands, the coherence coupling strength exhibits a completely asymmetric behavior. Our study demonstrates the feasibility of implementing continuous dynamical decoupling for coherent quantum control in ultracold atomic systems and provides both experimental and theoretical foundations for dressed-state-based quantum control and precision measurement.

Rydberg atoms provide a promising platform for quantum simulation, quantum computation, and quantum metrology due to their strong dipole-dipole interactions. In metrology, frequency or time is the most critical quantity to be measured with the highest possible precision. In this paper, we systematically study three different scenarios for generating entanglement to enhance frequency metrology beyond the standard quantum limit. The first scenario involves adiabatically preparing the entangled state via stimulated Raman adiabatic passage. The second scenario analogously quenches the system by leveraging effective interactions within the ground-state manifold. The third scenario digitally drives the system by employing parallel quantum gate operations. To further improve robustness in the measurement process, we also study various efficient echo methods. Our proposal offers a practical approach to enhancing frequency-measurement precision in quantum metrology using Rydberg atoms, with potential applications in high-precision timekeeping and related technologies.

Recent theoretical studies have predicted the existence of caustics in many-body quantum dynamics, where they manifest as extended regions of enhanced probability density that obey temporal and spatial scaling relations. Focusing on the transverse-field Ising model, we investigate the dynamics initiated by a local quench in a spin chain, resulting in outward-propagating excitations that create a distinct caustic pattern. We calculate the scaling of the first two maxima of the interference fringes dressing the caustic, finding a universal exponent of 2/3, associated with an Airy-function catastrophe. We demonstrate that this property is universal over the entire paramagnetic phase of the model and starts varying at the quantum phase transition (QPT). This robust scaling persists even under perturbations that break the integrability of the model. We additionally explore the effect of boundary conditions and find that open boundaries introduce significant edge effects, leading to complex interference patterns. These findings highlight the potential of quantum caustics to act as powerful diagnostic tools for QPTs in the dynamics of interacting many-body quantum systems.

In this paper, we investigate the non-Hermitian skin effect in a semi-infinite Fock-state lattice, where the inherent coupling between neighboring Fock states scales as $\sqrt{n}$ with $n$ denoting the phonon number or lattice site index. By analytically solving a nonuniform, nonreciprocal Su-Schrieffer-Heeger model, we demonstrate that the intrinsic inhomogeneous coupling, in combination with nonreciprocity, fundamentally modifies the conventional skin effect. Instead of accumulating at the physical boundary, all eigenmodes become compressed and skewed within a finite spatial range determined by the inhomogeneous profile. Consequently, the evolution of the probability distribution on the lattice starting from a single site is doubly confined: it is spatially bounded to a finite range by the inhomogeneous coupling, and further restricted to a one-sided trajectory at the edge of this range by the nonreciprocity. Moreover, a feasible experimental scheme based on a single trapped ion is also proposed. This work reveals how engineered coupling profiles in synthetic dimensions can reshape non-Hermitian properties and enable protocols for quantum state manipulation.

Too often, quantum computer scientists seek to create new algorithms entirely fresh from new cloth when there are extensive and optimized classical algorithms that can be generalized wholesale. At the same time, one may seek to maintain classical advantages of performance and runtime bounds, while enabling potential quantum improvement. Hybrid quantum algorithms tap into this potential, and here we explore a class of hybrid quantum algorithms called iterative quantum algorithms (IQA) that are closely related to classical greedy or local search algorithms, employing a structure where the quantum computer provides information that leads to a simplified problem for future iterations. Specifically, we extend these algorithms beyond past results that considered primarily quadratic problems to arbitrary $k$-local Hamiltonians, proposing a general framework that fundamentally incorporates logical inference. As an application, we develop a hybrid quantum version of the well-known classical Davis-Putnam-Logemann-Loveland (DPLL) algorithm for satisfiability problems, which embeds IQAs within a complete backtracking-based tree search framework. Our results also provide a general framework for handling problems with hard constraints in IQAs. We further show limiting cases of the algorithms where they reduce to classical algorithms, and provide evidence for regimes of quantum improvement.

Characterizing time-periodic Hamiltonians is important for validating and controlling driven quantum platforms, yet generic time-domain reconstruction methods, when applied directly, can require dense temporal sampling and overparametrized time-slice descriptions. Informed by the Floquet theorem, we study Hamiltonian learning for time-periodic Hamiltonians under a structured Fourier Ansatz and show that, when the Hamiltonian is well captured by a small number of harmonics and a local operator basis, the unknown parameters can be recovered from a linear inverse problem in the Floquet-band representation. In this formulation, the resource requirements of the assembled inverse problem are governed by the retained Fourier modes, sampled times, and local operator coefficients rather than directly by the Hilbert-space dimension. We also analyze the access assumptions, resource estimates, and a conditional stability statement for the assembled regression problem. Numerical experiments on driven Ising and Heisenberg models, together with waveform-dependent tests and a naive time-slice baseline, identify when the Fourier-informed description is accurate and when it fails because of truncation or model mismatch. These results provide a structured route to characterizing driven platforms whose dynamics admit a compact Fourier description.

Understanding the structure and stability of open quantum dynamics is increasingly important for both fundamental studies of nonequilibrium quantum systems and the development of quantum simulation algorithms. In this work, we introduce a structural framework for Markovian open quantum systems that characterizes Lindbladian generators in terms of two scalar quantities: the dissipative strength and the non-normality. We show that normal generators admit an exact decoupling between dissipative and norm-preserving dynamics, leading to purely exponential behavior governed by the dissipative scale. In contrast, non-normality is an intrinsically dissipative feature: it vanishes in the absence of dissipation but is not implied by it. Moreover, it is structurally constrained by the interplay between the Hermitian and anti-Hermitian components of the generator. For generic Markovian open quantum systems, we identify scaling regimes controlled by a dimensionless ratio between non-normality and dissipative strength, governing the onset of transient amplification. These structural features have direct implications for quantum simulation. While Hamiltonian and normal dissipative dynamics exhibit stable evolution with standard scaling behavior, non-normal generators can induce transient growth that amplifies numerical errors and increases simulation cost. Our results provide a unified generator-level perspective on irreversibility, stability, and quantum simulation of open quantum systems.