Protecting quantum batteries from environmental noise remains a challenge. Using exact Burshtein-Kubo equations, we study a two-spin quantum battery with Dzyaloshinskii-Moriya (DM) coupling under independent local longitudinal random telegraph noise (RTN). At a fixed effective noise scale, the DM-assisted slow-switching protocol yields a superadditive transient ergotropy gain and near-maximal ergotropy during the initial charging stage, while the no-DM slow-switching control reaches comparable ergotropy only in a later revival. A finite superadditive region persists at fixed RTN amplitude, with protocol-dependent location and gain. In the Ising model, the enhancement is nonmonotonic in DM strength, with intermediate coupling giving near-optimal performance. Dressed-channel analysis associates this enhancement with changes in transition frequencies and longitudinal-noise matrix elements that reduce slow-RTN spectral weight. Superadditivity also persists in the tested anisotropic XY model.

The Boolean satisfiability (SAT) problem is a central benchmark for quantum optimization, but conventional encodings typically require one qubit per active variable, limiting their use on near-term quantum hardware. Here we introduce a space-efficient framework for one-in-three SAT based on the decisive chain reduction algorithm (DCRA), which exploits clause-induced dependences. For an instance generated with $n$ variables and $m$ clauses, let $\tilde{n}$ be the number of active variables appearing in the clauses. The DCRA identifies $s$ initial variables and expresses the remaining $\tilde{n}-s$ active variables as linear combinations of them, reducing the effective search space from $2^{\tilde{n}}$ to $2^s$. For positive random instances near the critical regime, we empirically find $s$ close to $\tilde{n}-m$, yielding substantial qubit savings. In the reduced space, we derive a compact quadratic unconstrained binary optimization formulation whose problem Hamiltonian provides a common input for quantum annealing (QA), the quantum adiabatic algorithm (QAA), and the quantum approximate optimization algorithm (QAOA). Numerical simulations validate the framework on instances with up to 150 variables for QA-based solvers and up to 50 variables for QAA- and QAOA-based implementations. For QA-based solvers, finite-size scaling on satisfiable positive random instances with up to 200 variables shows an approximately exponential decay of the mean success probability and reveals a clause-density-dependent tradeoff between qubit reduction and annealing hardness. On a superconducting processor, the six-qubit QAOA solves a 25-variable instance with $\tilde{n}=21$ active variables, achieving $12.62\%$ success above the $4.69\%$ uniform-sampling baseline. For a 13-variable instance, the DCRA achieves a measured success probability of $3.37\%$, compared to $0.05\%$ with the direct encoding at equal shot budgets. These results demonstrate that structure-exploiting reductions offer a practical route to qubit-efficient quantum formulations of satisfiability problems on near-term hardware.

Entanglement is a cornerstone in quantum information science, yet detecting it efficiently remains a challenging task. Focusing on states with nonpositive partial transpose, we establish a hierarchy among entropy-based, majorization, realignment, and reduction criteria for Haar uniformly generated random states in finite dimensions, analyzing their performance based on rank and subsystem dimension. We prove lower bounds on the rank of mixed quantum states beyond which the realignment and entropic criteria fail to detect entanglement. We evaluate the relative effectiveness of the considered detection methods using three key indicators—fraction of detected states, mean detectable entanglement, and minimum required entanglement. Our results provide insights into the entanglement thresholds needed for reliable detection, showing that, beyond a certain level of entanglement, all criteria become equally powerful for low-rank states, while a hierarchy emerges among the various criteria for moderate to high ranks. Intriguingly, the proposed ordering among the considered criteria in qubit-qudit systems is different from that in higher dimensions. Additionally, we establish that the detection efficiency is influenced by the asymmetry in the subsystem dimensions by illustrating how the realignment criterion behaves more efficiently than other detection methods when the difference between the subsystem dimensions is small.

To investigate gauge theories with near-term quantum computers warrants exploration of nontraditional quantum simulators to find resource-efficient simulation protocols and ultimately access exotic features of different field theories, including unexplored regimes of the QCD phase diagram. In this work, using superconducting transmon qutrit processors, we formulate and implement a pulse-based, three-level, hybrid analog-digital simulation protocol of the ($1+1$)-dimensional Abelian Higgs model (AHM) on two sites. Alongside this approach, we experimentally realize a gate-based implementation of the same model. Using the natural mapping of the three-level truncation of the transmon Hilbert space to the spin-1 truncated AHM, we observe real-time dynamics of AHM field observables, which are analogous to electric field operators, with both protocols. For the analog-digital protocol, we engineer a Floquet simulation with a combination of local analog drives, driven modification of the natural interaction Hamiltonian of the two transmons, and dynamical decoupling pulses. For the digital protocol, we use a state-of-the-art qutrit processor to implement a Trotterized simulation of the model incorporating advanced error mitigation techniques. We further discuss the scalability of the two approaches, and their potential to be extended to the simulation of other model Hamiltonians. Our experiments demonstrate a viable platform for future studies of spin-1- and SU(3)-based gauge theory models on current and near-term transmon qutrit processors.

The rotational excitation of the three asymmetric-top molecular ion isotopologues ${\mathrm{H}}_2{\mathrm{O}}^{+}$, ${\mathrm{HDO}}^{+}$, and ${\mathrm{D}}_2{\mathrm{O}}^{+}$ is studied theoretically using a combined framework of electron-molecule R matrix scattering theory, multichannel quantum-defect theory, frame transformation theory, and the Coulomb-Born approximation. The latter two have been adapted here for asymmetric-top rotors. State-resolved cross sections and kinetic rate coefficients for transitions from the rotational ground state of the ions are presented.

In this work, we theoretically investigate a tandem crossed twisted nematic liquid crystal architecture for the generation of broadband (“white”) optical vortices. Operating in transmission, the system consists of two twisted nematic cells cascaded such that the liquid crystal director at the output of the first cell is strictly orthogonal to the director at the input of the second. Unlike conventional $q$-plates, this crossed configuration preserves the handedness of incident circularly polarized light. By rotating the entire polarization state by a target angle, the architecture imparts a corresponding spatial phase shift directly to the circular polarization. To evaluate its performance under realistic physical conditions, we develop a rigorous Jones matrix model. We systematically analyze the impact of deviations from the ideal waveguiding regime, manufacturing thickness mismatches, oblique incidence, and structural misalignments. By utilizing the modal overlap integral, we establish strict analytical figures of merit that provide a universal lower bound for the global mode purity. To mitigate the inherent amplitude and phase distortions, we propose three distinct operational strategies, ranging from parameter optimization to active phase correction. We demonstrate that active compensation effectively decouples the amplitude transmission efficiency from fabrication thickness tolerances, ensuring high optical throughput and superior phase fidelity. Ultimately, the direct structural compatibility of this architecture with emerging in-plane switching technologies establishes the tandem twisted nematic cell as a highly versatile blueprint for next-generation, fully dynamic broadband spatial light modulators.

Energy conservation is ubiquitous in the understanding of the process of high-harmonic generation. Yet a complete quantum-optical description of the photon-number-resolved structure implied by exact energy conservation remained elusive. Here, we solve this problem by introducing an information-theoretic perspective that separates the microscopic dynamics from the constraints imposed by energy conservation and only considers the imposed symmetry structure of the underlying state space. This leads to a decomposition into invariant eigenspace sectors of fixed energy, which we refer to as the energy-conserving subspaces of high-harmonic generation. The resulting weighted-photon-number sector structure is the Fock-space counterpart of the familiar harmonic energy-conservation condition and makes the photon-number correlations required by exact energy exchange between the participating field modes explicit. Energy conservation fixes the allowed support of the optical state, whereas the microscopic electron dynamics determine the amplitudes within this support. Coherent population of several allowed photon partitions can consequently generate intermode entanglement and nonclassical reduced states. More generally, the construction provides an information-theoretic description of symmetry constraints in strong-field processes without requiring a complete solution of the microscopic dynamics.

We propose a theoretical model of a fully functional nonreciprocal quantum battery inspired by the architecture of bacterial light-harvesting complexes. We assign functional roles to collective quantum optical subradiant and superradiant states and introduce a unimodal cavity to assist storage. The collective bright- and dark-state energies and total effective decay rates are obtained from an effective non-Hermitian Hamiltonian calculated using electromagnetic dyadic Green tensors. Upon varying the ring size, we find that work, flux, and power attain coincident maxima at the same intermediate ring size, whereas ergotropy reaches its maximum at a slightly larger ring size. The battery capacity is governed primarily by the ring size and depends weakly on the ring-central system coupling. Large coupling produces a pronounced finite-size optimum in ergotropy, whereas under weaker coupling the ergotropy increases monotonically with the battery capacity.

Finite-energy electron Airy beams in a uniform magnetic field are investigated by reducing the transverse dynamics to a shifted one-dimensional harmonic oscillator. For an exponentially truncated Airy beam, an exact Airy-function representation of the propagated wave function is derived, and its asymptotic behavior at the characteristic moments of the magnetic period is examined. Near odd quarter periods, the Airy argument is driven toward the oscillatory sector, and direct evaluation of the Airy representation is therefore numerically delicate. To avoid this numerical difficulty, we further derive an exact Wigner representation, in which the dynamics appears as a rigid harmonic rotation in phase space and the position and momentum marginals remain stable throughout the magnetic period. For obstructed beams, the phase-space formulation is combined with a phase-sensitive similarity measure in a finite window. The analysis separates the Gaussian-amplitude transition, in which the state acquires a Gaussian envelope differing from the initial Airy state, from exact oscillator recurrence and uses Wigner regularization as a stable phase-space diagnostic; as an application, local self-healing is demonstrated for obstructed beams. The results show that the obstruction is not globally erased by the unitary evolution, but the surviving Airy components can locally reconstruct the beam profile within selected observation windows. This work provides a phase-space framework for evaluating structured electron beams in magnetic fields and offers a quantitative diagnostic for local self-healing in magnetically guided Airy beams.

Quantum batteries can exploit quantum resources to enhance energy storage and work extraction, and recent experimental progress has brought their implementation closer to reality. In realistic settings, however, environmental dissipation is unavoidable, making dissipative charging a physically relevant operating regime. Here, we investigate ergotropy in dissipatively charged quantum batteries, focusing on interaction-induced work extraction. For two coupled two-level systems (TLSs), we derive exact analytical expressions for the total, coherent, and incoherent ergotropy in both resonant and detuned configurations. We show that in the resonant case, ergotropy is activated only above a critical coupling associated with an interaction-induced energy-level crossing, whereas detuning enables ergotropy already in the weak-coupling regime. Moreover, quantum coherence, although necessary for coherent work extraction, is not by itself sufficient to guarantee nonzero coherent ergotropy. In the strong-coupling regime, the resonant setup reaches the maximum ergotropy at a finite coupling strength, whereas the detuned setup approaches the same limit only asymptotically. Extending the analysis to a periodic $\mathit{XX}$ spin chain of $N$ TLSs, we analytically derive the finite-temperature coupling threshold for ergotropy activation and show that it scales as $1/N$ in the large-$N$ limit. These results identify frequency detuning, interaction strength, and system size as key control parameters for ergotropy generation in open quantum batteries.

Positive but not completely positive maps provide one of the most direct ways to detect entanglement beyond the positive-partial-transpose (PPT) criterion. We introduce and analyze an exactly solvable two-parameter family of sparse bistochastic positive maps on qutrits, in which two coherence channels are independently tuned by parameters $w$ and $z$. The sparse structure makes the full phase diagram analytic: positivity holds exactly on the square $0\le w,z\le 2/3$, complete positivity holds on the smaller square $0\le w,z\le 1/3$, and decomposability is lost precisely outside a quarter circle in the corner $w,z\ge 1/3$. The indecomposable region is certified by explicit PPT entangled states adapted to the same witness geometry. At the end point $W_{*}=W(2/3,2/3)$ we construct a four-parameter family of PPT edge states of rank type (5,5), derive their analytic detection region, and show that the corresponding rays are exposed faces of the PPT cone. Finally, although $W_{*}$ is not optimal, we give an explicit optimal refinement whose detection region on this family is strictly larger. The result is an analytically tractable qutrit setting in which positivity, indecomposability, PPT entanglement, optimality, and exposed convex geometry can be studied in a single framework.

Certifying the fidelity of a prepared state to a target stabilizer state is a fundamental task in quantum information processing. The reference [Phys. Rev. A 99, 042337 (2019)] gave the optimal worst-case lower bound from one fixed stabilizer generator gauge, but gauge dependence can leave a large fidelity ambiguity. We develop an adaptive extension that reports the full certified fidelity interval. First, for a single gauge, we derive the complementary optimal worst-case upper bound. We then formulate gauge selection as an adaptive design problem in which each round solves endpoint linear programs and chooses a new gauge by a witness elimination policy. We prove monotonic tightening, simultaneous finite-shot coverage with an explicit uncertainty floor, exact recovery once all nontrivial stabilizers are covered, and the worst-case necessity of full coverage. Finally, we identify affine-subspace-supported syndrome distributions for which adaptivity can beat this exponential benchmark, and we numerically confirm faster concentration.

For reliable large-scale quantum computation, quantum error correction (QEC) is essential to protect logical information distributed across multiple physical qubits. Taking advantage of recent advances in deep learning, neural network-based decoders have emerged as a promising approach to improve the reliability of QEC. We propose the qubit-centric transformer (QCT), a QEC decoder for stabilizer codes based on a transformer architecture with a qubit-centric attention mechanism. Our decoder transforms input syndromes from the stabilizer domain into qubit-centric tokens via a specialized embedding strategy. These qubit-centric tokens are processed through attention layers to effectively identify the underlying logical error. Furthermore, we introduce a graph-based masking method that incorporates the topological structure of quantum codes, enforcing attention toward relevant qubit interactions. Across various code distances for surface codes, QCT achieves strong decoding performance, significantly outperforming existing neural decoders and the belief propagation (BP) with ordered statistics decoding (OSD) baseline. Notably, QCT achieves a high threshold of 18.1% under the code-capacity noise model, which closely approaches the theoretical bound of $18.9\%$ and surpasses both the BP+OSD and the minimum-weight perfect matching (MWPM) thresholds, while also exhibiting a substantially higher error suppression factor $\mathrm{\Lambda }$. Furthermore, we extend QCT to the circuit-level noise model by incorporating temporal convolution blocks to process repeated syndrome measurements. Under realistic circuit-level noise conditions, QCT demonstrates scalable error suppression across the evaluated code distances, consistently outperforming advanced decoders including the correlated MWPM and BP+OSD. This qubit-centric approach provides a scalable and robust framework for surface code decoding, advancing the path toward fault-tolerant quantum computing.

We apply Hoeffding's inequality directly to weighted estimators of Pauli-expanded witnesses to obtain finite-sample tests for mixed-state nonstabilizerness. With witnesses and shot allocations fixed in advance, the tests control false positives under independent sampling. We also derive sufficient shot counts for a specified positive violation margin and target detection probability. A separate plug-in Gaussian diagnostic is used for comparison. Examples include the single-qubit stabilizer-octahedron criterion, a fixed two-qubit Pauli-correlation Triangle witness, and a previously proposed two-copy Clifford circuit with postselection. For this circuit, we construct eight linear contrasts of the four-qubit input state for each prescribed output threshold. When the postselection probability is positive, the threshold is exceeded if and only if at least one contrast is positive. These contrasts involve 31 nonidentity Pauli observables covered by 15 local product-Pauli bases. Using independent measurement batches, we obtain ratio-free threshold tests and explicit sufficient bounds on shots and input copies. For two identical, independent copies of a two-qubit state, we establish a sharp upper bound on the unnormalized contrast margin at the thresholds considered. An explicit state family attains every positive margin up to this bound. Finite-shot simulations assess detection probabilities for a bound-attaining input and its noisy extension. Separate null checks cover boundary and interior states, as well as inputs with zero postselection probability.

Quantum reservoir computers (QRCs) have emerged as a promising approach to quantum machine learning, since they utilize the natural dynamics of quantum systems for data processing and are simple to train. Here we consider $n$-qubit quantum extreme learning machines (QELMs) with initial-state encoding and continuous-time reservoir dynamics. Applying the Pauli transfer matrix (PTM) formalism reveals the encoding-generated features and their linear transformation by quantum channels and thereby provides a nonlinear vector autoregression model as an interpretable classical representation of a QELM. We show that the nonlinear information processing capacity of a QELM factorizes into the ability of the encoding to represent a given target function and the decodability of the relevant Pauli features after the effective PTM. Comparing geometric and statistical decodability reveals features that are algebraically hidden yet recoverable through data correlations. We relate the decodability of Pauli features to the spreading of measurement operators under Heisenberg evolution (Krylov growth). Focusing on the unitary channel, we discuss how structured Hamiltonians, when paired with certain observables, can impair model performance, as reflected in a low rank of the readout and the effective PTMs. We trace this effect to Hamiltonian symmetries and derive asymptotic rank estimates for symmetry-resolved observable families. Our decodability analysis disentangles the contributions of encoding, reservoir dynamics, and measurement observables and thus provides interpretable diagnostics that can inform the design of QELMs and reduce reliance on exhaustive hyperparameter search. As a specific application, we consider forecasting nonlinear dynamical systems and show that the readout of a trained QELM closely matches the expression of the underlying flow map at leading orders.

Here we report atomic structure calculations and experimental observations of the two-photon $6s^2{}^{1}S_0\to 6s23s{}^{1}S_0$ transition in Yb. The unique level structure of Yb places the $6s6p{}^{1}P_1$ state's energy at $\approx 49.7\%$ of the ionization energy, which facilitates two-photon Doppler-free excitation of the $6s23s{}^{1}S_0$ Rydberg state from the $6s^2{}^{1}S_0$ ground state at a relatively low optical intensity. This $J=0\to J=0$ transition is immune to first-order Zeeman and electric quadrupole shifts, has reduced sensitivity to higher-order Zeeman shifts, and is further predicted to have relatively low sensitivity to density shifts. Using configuration interaction theory, we compute relevant properties of the $6s23s{}^{1}S_0$ Rydberg state for sensing, including the $C_6$ coefficient, dc polarizability, blackbody radiation (BBR) shift, and BBR depopulation rate. As a first experimental step, we demonstrate two-photon Doppler-free spectroscopy of the $6s^2{}^{1}S_0\to 6s23s{}^{1}S_0$ transition. From our experimental spectra, we estimate the natural linewidth (lifetime) of the $6s23s{}^{1}S_0$ state to be 90 kHz (1.8 $\mu \mathrm{s}$). We believe this transition, or other $6s^2{}^{1}S_0\to 6sns{}^{1}S_0$ transitions in Yb with $n\approx 23$, may find use in a variety of sensing applications, potentially including a two-photon clock, electrometer, or BBR thermometer.

We present a state-of-the-art theoretical approach for computing bound-state energies in muonic atoms, incorporating improved quantum electrodynamics effects and nuclear polarization corrections with a systematic assessment of theoretical uncertainties. Our approach is based on a combination of the $Z\alpha$ expansion and the all-order formalism (Furry picture) optimized for the medium-mass range $(3\le Z\lesssim 30)$ and guided by the accuracy requirements of modern muonic spectroscopy experiments. These calculations are directly relevant to ongoing and forthcoming measurements aimed at extracting nuclear structure parameters, particularly nuclear-charge radii, with unprecedented precision.

Counterrotating, circularly polarized, time-delayed pulses generate electron wave packets that interfere in momentum space and form spiral-shaped free-electron vortices. By numerically solving the time-dependent Schrödinger equation beyond the Born-Oppenheimer approximation for one-photon single ionization of ${\mathrm{H}}_2$, we show that these spirals rotate within the polarization plane as a function of the nuclear energy. A kinematical model, based on the instantaneous sharing of photon energy between the freed electron and the parent molecular ion, predicts this rotation and agrees quantitatively with the simulations. We further demonstrate that integrating over vibrational energies diminishes the visibility of the interference structure. Results from fixed-nuclei and atomlike reference calculations resemble single vibrational channels, whereas incoherent summation over multiple vibrational states leads to blurring and noticeable shifts of the apparent rotation. The joint-energy spectrum exhibits pronounced electron-nuclear correlation lines. In the case of corotating pulses, these lines are related to the interference rings in the momentum distribution. Conversely, for counterrotating pulses, they originate from a dipolar modulation of the spiral pattern, caused by the nonisotropic molecular orbital.

We solve the two-body problem of ultracold heteronuclear atoms in a quasi-two-dimensional (quasi-2D) geometry. The quasi-2D confinement is realized by a harmonic trap along the longitudinal ($z$) direction, with different trap frequencies for the two atoms, as in many current experiments on ultracold heteronuclear gases. As a consequence, the longitudinal center-of-mass (c.m.) motion is coupled to the relative motion, which significantly complicates the two-body problem. We solve this problem exactly and derive the 2D scattering length $a_{2\mathrm{D}}$, the 2D effective range parameter $R_{2\mathrm{D}}$, and the bound-state energies, as functions of the $s$-wave scattering length and effective range of the two atoms in free 3D space. We show that multiple 2D scattering resonances can be induced by the coupling between the longitudinal c.m. and relative motion. Around these resonances, $a_{2\mathrm{D}}$ varies rapidly with the 3D scattering parameters, while $R_{2\mathrm{D}}$ is strongly enhanced. Since the effective pairwise interaction in quasi-2D ultracold gases is determined by the two-body scattering amplitudes and bound-state energies, our results can be used for manipulating the effective 2D interatomic interaction in quasi-2D ultracold heteronuclear gases by tuning the confinement frequencies and the 3D scattering parameters.