Papers

Parity-time ($\mathcal{PT}$) symmetric systems exhibit long-lived excitations by balancing gain and loss in coupled resonators, driving extensive theoretical interest and diverse experimental realizations. Realistic physical implementations, however, inevitably introduce nonlinearities and noise. This mandates a rigorous reevaluation of their global long-time dynamics. In this work, we show that Hamiltonian Duffing nonlinearity restricts the $\mathcal{PT}$-unbroken phase to a finite, nonattracting region of phase space. Consequently, unavoidable fluctuations drive first-passage escape into runaway trajectories. This renders the linearly $\mathcal{PT}$-unbroken phase a purely transient phenomenon. We then recover global stochastic stability by introducing two-photon loss on the gain oscillator. This nonlinear damping explicitly breaks exact $\mathcal{PT}$ symmetry while supplying genuine phase-space attraction, generating a bistable regime where a low-amplitude orbit mimicking the original linear state coexists with a high-amplitude limit cycle. Thus, we establish a revised origin for stability in non-Hermitian experiments: the observed long-time stochastic stability is governed by inherent restoring dissipation rather than the spectral $\mathcal{PT}$ symmetry itself.

Measuring the angular displacement of a mechanical oscillator is a ubiquitous task; however, the multimode nature of angular optomechanical coupling makes coherent signal enhancement challenging. Here we demonstrate coherently enhanced angular displacement readout with an integrated guided mode resonance (GMR) structure, applying it to precision readout of a nanomechanical oscillator. Specifically, we fabricate subwavelength gratings into 100-nm-thick Si$_3$N$_4$ membranes and record their vibration by direct transmission measurements. The narrow linewidth $\approx 2.5\;\text{mrad}$ of the GMR enables a shot-noise-limited displacement imprecision of $ 10^{-9}\;\text{rad}/\sqrt{\text{Hz}}$ with nanowatts of optical power, sufficient to resolve the thermal motion of a $Q\approx 10^6$ torsion mode with a signal-to-noise ratio of 47 dB. Control experiments based on polarization and wavelength detuning confirm that the measured signal arises from GMR-mediated transduction. These results establish guided-mode resonance as an on-chip approach to angular displacement readout in quantum optomechanical sensors.

Quantum functional programming has been developed through two distinct paradigms in the last few years: Quantum Signal Processing (QSP)-based methods, including the Quantum Singular Value Transformation (QSVT), and methods based on higher-order quantum transformations, such as the Universal Hamiltonian Eigenvalue Transformation (UHET). While UHET performs functional transformations of Hamiltonian dynamics, its relationship to QSP-based techniques has remained unclear despite evident structural similarities. In this work, we resolve this gap by establishing a connection between UHET and QSP-based frameworks; specifically, we show that UHET can be interpreted as a (randomised) linearisation of Generalised QSP (GQSP). Building on this result, we introduce a linearised variant of (Hamiltonian-based) QSVT, which we call Universal Hamiltonian Singular Value Transformation (UHSVT), that enables the efficient transformation of the singular values of any arbitrary matrix $A$ encoded in a block of a Hamiltonian, whose dynamics is accessible as a black box, by any sufficiently differentiable complex-valued function $f$. Our algorithm requires the sole condition that $f$ vanishes at the origin, in contrast to previous QSVT-based approaches that assumed either a lower bound on the singular values of $A$ or the ability to perform $X$-rotation gates on the induced two-dimensional 'qubitised' subspace.

Quantum processors with native multi-qubit gates may offer very efficient implementations of near-term quantum algorithms on noisy hardware. Here, we introduce the multiunimon, a superconducting multimode circuit that encodes multiple qubits and enables native multi-qubit gates in a device consisting of a single Josephson junction embedded in a coplanar waveguide structure. Closely related to the unimon qubit, it inherits properties such as high anharmonicity, full protection against low-frequency charge noise, and partial protection against flux noise. By designing such a three-qubit device with Josephson-to-inductive energy ratio above unity and using a leakage-aware encoding scheme for the computational states, we simulate all twelve different controlled-controlled-NOT gates with a mean fidelity of 99.5% with simple sine-squared pulses of comparable length to single-qubit gates. The performance is limited by incoherent errors dominated by dielectric loss. With improvements in noise protection, design, and pulse shaping, the simulations suggest that fidelities approaching 99.99% are within reach. Our results demonstrate the potential of the multiunimon as a highly connected multi-qubit unit for larger superconducting quantum processors.

Orbital angular momentum (OAM) transport in solids, prominently manifested in the orbital Hall effect, has emerged as a fundamental phenomenon that can decisively exceed its spin-based counterparts. However, the microscopic mechanisms governing OAM dynamics remain only partially understood. In particular, the role of band geometry in orbital transport is still largely unresolved. Here we address this question in the TaAs family of Weyl semimetals, TaAs, TaP, NbAs, and NbP, whose well-established topology and associated OAM textures make them an ideal platform in this context. Using ab initio density functional theory, complemented by a minimal Weyl model based on adiabatic perturbation theory, we establish — both numerically and analytically — a direct link between OAM transport, band geometry, and topological electronic structure.

Cavity-mediated collective-spin interactions are commonly described by a quadratic one-axis twisting Hamiltonian. However, the underlying atom-light interaction naturally generates nonlinearities to arbitrary order. Here, we derive a closed-form analytical expression for the complete hierarchy of cavity-mediated collective-spin interactions. We show that the nonlinear coefficients $\chi_k$ are governed by Chebyshev polynomials, with $k$ the order of nonlinearity. This yields a universal scaling $\chi_k\propto\eta^k$ with the single-atom cooperativity $\eta$ and a description of their dependence on cavity detuning. The result provides a systematic framework for determining when higher-order nonlinearities become relevant and when the quadratic approximation breaks down. We identify experimentally relevant regimes in which higher-order terms substantially modify collective-spin dynamics, accelerating the generation of quantum correlations and quantum Fisher information, and demonstrate that finite-order expansions can accurately reproduce the full cavity-mediated evolution. Our results establish a general framework for understanding higher-order nonlinearities in cavity quantum electrodynamics and their role in collective entanglement and quantum-enhanced sensing.

The relationship between cryptography and learning theory has long been a central theme in the foundations of theoretical computer science: cryptographic primitives can imply hardness of learning, while hardness of learning can in turn be used to construct cryptographic schemes. Recent works have begun exploring analogous connections in the quantum setting, relating the average-case hardness of learning quantum states (AHL) to cryptographic primitives such as one-way state generators (OWSG). Despite recent progress exploring this for pure states, the relationship for mixed states has remained an open question. In this work, we prove that the existence of AHL for mixed quantum states is equivalent to the existence of inefficiently verifiable one-way state generators (IV-OWSGs). As a consequence, this relates mixed-state AHL to EFI pairs. Moreover, as a corollary of existing results, we obtain a separation between IV-OWSGs and OWSGs relative to the SWAP oracle.

A projective measurement of a many-body state produces a microscopic snapshot, usually viewed as random classical data. We show that partial occupation snapshots of the critical XX chain contain a universal angle with a precise conformal meaning. Dividing the ring into two measured and two unmeasured arcs, we assign geometry-dependent conformal side weights to the observed occupations and obtain a compact variable $\delta_L$. At every finite size, $\delta_L$ is fixed by the measured sites alone; the particular complete-configuration lift $X_L$ used in the proof additionally depends on unobserved particles. This angle is an exact microscopic compact coordinate whose scaling-limit law is that of the relative Dirichlet phase of the associated conformal quadrilateral—the boundary coordinate conjugate to charge in continuum post-measurement descriptions. Exact free-fermion determinants yield all of its Fourier moments. We prove that the lift becomes Gaussian with variance $2h(\zeta)$, where $h(\zeta)$ is the rectangle modulus, and hence $\langle e^{\ii q\delta_L}\rangle\to e^{-h(\zeta)q^2}$. Thus raw quantum snapshots realize the heat kernel on a circle and provide an outcome-level microscopic foundation for the compact zero-mode sector of Born averages over fluctuating conformal boundary conditions.

We show that geometric phases accumulated during adiabatic evolution can be converted into observable interference in Krylov space, leading to a geometric-phase-dependent Krylov oscillation. Adiabatic dynamics force Krylov complexity to vanish if the initial Krylov basis is an instantaneous eigenstate of the Hamiltonian; Nevertheless, we demonstrate that the Krylov complexity will be non-vanishing if the initial Krylov basis is a superposition state rather than an eigenstate. Consequently, Krylov complexity is found to depend on the difference of dynamical phases in the Krylov space, which is deeply related to the Berry connections in the original Hilbert space. In particular, for a single qubit system with constant Lanczos coefficients, Krylov complexity oscillates harmonically at a frequency given by the strength of the external field and the geometric Berry phase. Therefore, our work may provide a novel avenue to probe the geometric phase from the Krylov complexity.

We study quantum multi-armed bandits (QMAB) and quantum linear bandits (QLB), where the learner queries each arm or action through a quantum reward oracle or its inverse. Prior work gives algorithms over horizon $T$ with regret $O(K\log T)$ for QMAB with $K$ arms and $O(d^2\operatorname{polylog} T)$ for $d$-dimensional QLB. This leaves open the optimal dependence on $K$ and $T$ and whether the dependence on $d$ can be further improved. In this work, we prove the first tight minimax regret bound of $\Theta(K\log(1+T/K))$ for QMAB and the first lower bound of $\Omega(d\log(1+T/d))$ for finite-action QLB, ruling out regret independent of $T$. Our lower bounds rely on a high-confidence single-arm quantum testing lower bound for distinguishing a fixed reward mean from an interval of alternatives. A bandit-to-testing reduction then lifts it to the QMAB lower bound, while a linear embedding gives the finite-action QLB lower bound. The matching QMAB upper bound is obtained using a tail bound for the Quantum Monte Carlo (QMC) estimator. For finite-action QLB, we propose a phased elimination algorithm that combines a low-bias low-variance quantum mean estimator with a small-support $G$-optimal design through a query allocation matched to the design weights. When the action set has size $\operatorname{poly}(d)$, its regret is nearly linear in $d$ and matches our lower bound up to polylogarithmic factors.

Entanglement spectra in gauge theories can encode both symmetry breaking and the organization of gauge sectors. In the two-flavor Schwinger model at vacuum angle $\theta=\pi$, we find that the joint Schmidt distribution $p_{Q_A,F_A}$, labeled by the subsystem gauge charge $Q_A$ and flavor imbalance $F_A$, reveals a cut-dependent gauge-sector hierarchy and a mass-induced flavor asymmetry: changing the staggered cut reorganizes the gauge-charge distribution $p_{Q_A}$, while mass imbalance breaks the $F_A\leftrightarrow-F_A$ symmetry of the conditional flavor distribution $p_{F_A|Q_A}$. Defining the combined weight $W_F^{(q)}=p_{q,+1}+p_{q,-1}$ and conditional polarization $\mathcal P_F^{(q)}=(p_{q,+1}-p_{q,-1})/W_F^{(q)}$, we find that changing the cut reverses the weight hierarchy, $W_F^{(-1)}>W_F^{(+1)}$ at unit-cell boundaries but $W_F^{(+1)}>W_F^{(-1)}$ at intra-cell cuts, while mass imbalance drives $\mathcal P_F^{(q)}$ away from zero with a $q$-dependent cut response. Symmetry resolution therefore separates gauge-sector ordering, sector weight, and flavor polarization that are mixed in the globally ordered entanglement spectrum.

Quantum circuits are fundamental components of quantum computing, and state-vector-based quantum circuit simulation is a widely used technique for tracking qubit behavior throughout circuit evolution. However, simulating a circuit with $n$ qubits requires $2^{n+4}$ bytes of memory, making simulations of more than 40 qubits feasible only on supercomputers. To address this limitation, we propose the Qu-Trefoil, a system designed for large-scale quantum circuit simulations on an FPGA-based platform called Trefoil. Trefoil is a multi-FPGA system connected to eight storage subsystems, each equipped with 32 SATA disks. Qu-Trefoil integrates a suite of HLS-based universal quantum gates, including Clifford gates (Hadamard (H), Pauli-Z (Z), Phase (S), Controlled-NOT (CNOT)), the T gate, and unitary matrix computation, along with HDL-designed modules for system-wide integration. Our extensive evaluation demonstrates the system's robustness and flexibility, covering quantum gate performance, chunk size, disk extensibility, and efficiency across different SATA generations. We successfully simulated quantum circuits with over 43 qubits, which required more than 128 TB of memory, in approximately 3.72 to 13.06 hours on a single storage subsystem equipped with one FPGA. This achievement represents a significant milestone in the advancement of quantum computing simulations. Furthermore, thanks to its unique architecture, Qu-Trefoil is more accessible, flexible, and cost-efficient than other existing simulators for large-scale quantum circuit simulations, making it a viable option for researchers with limited access to supercomputers.

We present SymQuPS, a SymPy-based algebra system in Python mainly aimed toward the phase space representation of quantum mechanics within the Cahill-Glauber formalism (including the Glauber-Sudarshan $P$, Wigner, and Husimi $Q$ representations). By extension, the package serves as an algebraic venue for canonical quantization. A key feature is the phase space representation of an arbitrary Lindblad master equation, which gives the phase space equation of motion of the quantum system. We describe the core functionalities of the package, consisting of $s$-ordered operators, the star products, and the phase space representation. Some examples of use are given to illustrate the application of the package, and the package's performance in typical use cases is discussed.

Hybrid approaches that combine different spin qubit encodings offer promising advantages. In particular, the additional degrees of freedom available in exchange-only qubits and their extensions enable enhanced spin lifetimes and facilitate error detection through the use of auxiliary spins. We show that integrating Loss-DiVincenzo with exchange-only qubits provides a practical route to realizing these benefits while remaining compatible with spin-shuttling architectures. We further demonstrate how the singlet-only exchange-only qubit can be employed for error detection, and we present a fault-tolerant $\pi$-rotation about each of the three control axes of the (singlet-only) exchange-only qubit. By enabling error detection at the lowest encoding level, our approach effectively converts charge and nuclear noise into erasures, thereby suppressing error propagation and potentially enhancing the performance of quantum error-correction schemes. More broadly, our work establishes a new perspective on the singlet-only exchange-only qubit as a logical encoding, opening the door to fault-tolerant gate constructions and spin-tailored quantum error-correction protocols for semiconductor-based quantum computing.

Simulating strongly correlated quantum materials often involves not a single Hamiltonian, but a family of Hamiltonians whose ground states evolve across experimentally tunable couplings. Foundation neural quantum states (FNQS) offer a promising route to amortizing many-body calculations across such families, but can lose accuracy near phase transitions and still incur non-negligible sampling costs that grow with the number of target couplings. We introduce the Foundation Neural Effective Hamiltonian (FNEH), which projects a Hamiltonian family onto a compact subspace spanned by FNQS sampled at selected couplings. By variationally combining FNQS across parameter space, FNEH systematically improves their ground-state approximation and can recover phase boundaries that the foundation model misidentifies. Once the required operator matrix elements are sampled, FNEH enables sweeps over couplings, observables, and phase boundaries at a cost governed by the small effective-Hamiltonian dimension, without repeated neural-network sampling at every target coupling. We demonstrate FNEH in strongly correlated moiré materials, where it accurately resolves competing phases, enables high-resolution multidimensional phase scans, and substantially reduces the computational cost of exploring many target Hamiltonians. The results open a new avenue for studying strongly correlated quantum materials with foundation models.

Corner states in higher-order topological insulators are typically confined to geometric corners, limiting their flexibility for scalable quantum information processing. We propose a scheme to synthesize topological corner states at arbitrary positions within the bulk of a two-dimensional Su-Schrieffer-Heeger (SSH) lattice by coupling it to giant atoms. By engineering an L-shaped multi-point coupling that satisfies the vacancy-like dressed state (VDS) condition, where the photonic wavefunction vanishes at the coupling sites to form an artificial bulk boundary, we derive the conditions for synthesizing a zero-energy corner state at any target position. We demonstrate that the engineered corner state exhibits high fidelity and spatial localization, remaining robust against realistic disorder. Extending to multi-atom networks, we realize a versatile quantum switch via a giant superatom, enabling multi-channel control over 0D corner states and 1D edge states through the dual-resonance condition. Furthermore, we demonstrate the coherent interactions between two giant atoms mediated by VDS-engineered corner states. Governed by a sublattice selection rule, the coupling activates exclusively in intersecting configurations and decays exponentially with distance. Our work establishes a highly reconfigurable platform for embedding topological boundary modes within the bulk, offering a robust pathway for scalable topological quantum networks.

Suppose that $F_E$ is the face of the convex set of all $m\otimes n$ bi-partite states which consists of states with ranges contained in a subspace $E$. For generic subspaces $E$ with a specific dimension, we use the result in [Phys. Rev. A 112 (2025), 032426] to see that there exists a number $\kappa$, depending only on the dimension of $E$, such that there exist Schmidt number $\ell$ witnesses outside of $F_{E^\perp}$ if and only if $\ell\le\kappa$. In this generic case, we show in this paper that there exist Schmidt number $\ell$ witnesses for $\ell>\kappa$ around the projection states located at the center of $F_{E^\perp}$.

For an open quantum reservoir, how the system forgets is part of how it computes. Quantum reservoir computing processes input streams with fixed quantum dynamics and trains only a linear readout. Dissipation can make old inputs fade, but prior studies commonly fix the environmental process and tune only its strength. Here we show numerically that the coupling pattern, meaning whether transitions connect to separate or shared environmental channels, changes which parts of the input history remain accessible. Paired simulations of finite spin reservoirs keep the Hamiltonian, inputs, measurements, and readout fixed. The tested patterns produce distinct task profiles, with no universal winner. Shared relaxation preserves more recent input history than independent local loss, and the retained memory changes when the qubits contribute with different relative phases to the shared decay channel. This ordering recurs across system sizes, Hamiltonians, input protocols, and targeted controls. Environmental coupling is therefore more than a damping parameter: it is a design layer that shapes not only how quickly information fades, but which input history remains available for computation.

Spectral filtering has been proposed as a route to regularization in quantum generative models: the quantum Fourier transform exposes the amplitude spectrum of a quantum circuit Born machine, and a diagonal filter suppresses the high frequencies associated with finite-sample noise, an operation whose classical counterpart seemingly requires manipulating an exponentially long amplitude vector. We examine whether this coherent operation produces anything that classical post-processing of samples from the unfiltered model cannot match. Measuring the filter against convolution with a symmetric probability kernel at matched sampling cost, which accounts for the post-selection overhead of attenuation, we derive necessary and sufficient conditions for the gap between the two to vanish. Magnitude (attenuating) filters obey a dichotomy: at a fixed affordability threshold, the filtered output is either a constant-size Fourier object with an efficient classical sampler, or the passband must widen until no fixed frequency is attenuated and the filter no longer smooths. In neither case does the filter create a quantum-classical separation. Whatever separation survives is inherited from the spectral phase of the input state. Numerical experiments on trained circuit Born machines confirm the classification and show that the deciding phases are invisible to the Born-rule training loss and set by the initialization. Within the diagonal family, pure phase filters remain the only spectral operations exempt from these constraints.

The authors present a rigorous empirical evaluation of three distinct optimization paradigms for institutional factor portfolio construction: an entropy-based photonic quantum annealer (Dirac-3, Quantum Computing Inc.), a commercial mixed-integer programming solver (Gurobi), and a model-free deep reinforcement learning agent (SAC). Evaluating these pipelines on the Jensen-Kelly-Pedersen 13-factor equity library across 164 months test window, we implement a full factorial penalty sweep comprising 48 hyperparameter configurations that govern return, volatility, and skewness trade-offs. Our findings demonstrate that while photonic hardware can locate superior risk-return topologies within a narrow operating range, classical mixed-integer programming remains superior for risk-constrained mandates requiring tight tail-risk control and cross-seed stability. Furthermore, we document structural failure modes in reinforcement learning factor allocators under unanchored higher-moment shaping. We translate these empirical results into actionable, mandate-specific guidelines for quantitative portfolio managers deploying advanced optimization engines.

We develop the kinematical and operator-algebraic foundations of a groupoid-based relational quantum field theory (RQFT) on curved spacetimes. Indeed, the usual group-based quantum reference frame (QRF) formalism is not directly suited to generic curved Lorentzian backgrounds as global symmetry groups are typically absent or too small. We formulate a notion of QRF for a continuous groupoid. This yields a groupoid relativization map and relational observables. We show that a localization limit recovers the ordinary non-relational description. We construct canonical sharp groupoid QRFs, which form the groupoidal counterpart of the ideal group QRFs based on $L^2(G)$. We further prove that the groupoid QRF construction reduces to the standard operational QRF formalism for locally compact groups. The action groupoid QRFs are torsor QRFs only for specific classes of fields of positive operator-valued measures (POVMs), and the torsor relativization map only applies to constant operator fields of system observables. We review the foundations of RQFT in Minkowski spacetime. We prove new results that further link RQFT to Wightman QFT. We show that covariant POVMs are $\mu$-continuous with respect to quasi-invariant $\sigma$-finite positive Borel measures $\mu$. Thus, relational quantum fields can be understood as the smearing of pointwise-defined kernels with respect to the QRF's statistics. We develop RQFT in curved spacetime, where we argue that the correct replacement for the Poincaré group is the Poincaré groupoid of the spacetime. We also indicate how the framework extends further to internal gauge symmetry and relational gauge-covariant quantum field theory via Atiyah groupoids, providing a first step towards formulating a relational quantum Yang-Mills field theory.

Entanglement certification is often performed on states that have already undergone noisy transmission or processing. Noise can reduce the surviving entanglement and can also cause a given criterion to fail even when entanglement remains. In this context, the quantum switch, a paradigmatic realization of indefinite causal order (ICO), coherently controls the orders in which two channels act and has been shown to offer advantages across a range of quantum information-processing tasks. Here we ask whether this coherent control enlarges the noise-parameter region in which entanglement remains certifiable. We regard the two order branches as the arms of a causal-order interferometer and insert a local unitary between the channel uses to tune their interference. For stochastic Pauli noise, a postselected ICO output can exhibit greater entanglement negativity than any classical mixture of the two definite orders; in particular, we identify regimes where its negativity remains nonzero while that of every classical mixture vanishes. A suitable local Pauli unitary substantially enlarges this ICO-only region, while an input-dependent path-difference indicator qualitatively links operator noncommutativity to the postselected negativity gain. Numerical examples extend the advantage to local amplitude-damping noise and two-qutrit Weyl noise. At a representative Weyl-noise point for the $3\times 3$ positive-partial-transpose (PPT) Tiles bound-entangled state, a nondecomposable witness detects the postselected ICO output, whereas an analytic bound excludes detection of the definite-order outputs and their mixtures by the entire locally rotated witness family. These results identify causal-order interferometry as a strategy for enhancing entanglement certification across distinct noise models and dimensions.

Quantum diffusion models typically parameterize forward corruption by raw channel strength, even though this parameter does not directly quantify how much ensemble information is erased or how difficult the corresponding reverse problem is. We introduce the classical–quantum information decrement $\Delta_t=I(X{:}Q_{t-1})-I(X{:}Q_t)$ as an intrinsic diffusion coordinate that links forward noise allocation to reverse recoverability. Along depolarization, equalizing $\Delta_t$ yields the unique minimax discretization of the forward information loss, while universal recoverability gives the same quantity an operational interpretation as a physically attainable local recovery budget. We further show that such local calibration is not sufficient for stochastic generation: models can satisfy the same recovery criterion while producing substantially different state distributions. This motivates a stochastic learner that combines information-calibrated recovery constraints with distribution matching. We establish finite-sample calibration and compositional trace-Wasserstein control for the resulting learner. Controlled quantum experiments validate the predicted information–recovery alignment, show that the recovery constraints improve local inversion, and confirm the complementary role of distribution matching in endpoint generation. The resulting framework also achieves stronger endpoint trace-Wasserstein performance than an official QuDDPM implementation with fewer trainable parameters. Overall, our work provides a unified information-theoretic principle for designing forward schedules, calibrating reverse steps, and separating physical recovery from generative coverage in quantum diffusion.

Cylindrical Dirac modes underlie constructions in rotating QCD matter, boost-invariant Dirac-field quantization in heavy-ion physics, and high-energy twisted-particle scattering. The corresponding complete spinor frames can be regarded as alternative bases, but their equivalence does not determine the global behavior of eigenlines selected by conserved observables. Within the positive-energy doublet of the free massive Dirac Hamiltonian, we compare three conserved resolutions: $K$, which couples spin to transverse momentum; $K_m$, a mass-dependent operator derived from the transverse Dirac Hamiltonian; and helicity. On the common regular domain away from the momentum axis, explicit smooth, single-valued $SU(2)$ transformations relate all three splittings. Although globally $SU(2)$-equivalent on this common domain, they exhibit three distinct global extension behaviors. The $K$ projectors have azimuth-dependent polar limits and do not extend continuously to the axis. For nonzero mass, the $K_m$ projectors extend smoothly over the enclosed momentum ball and define Chern-trivial eigenlines. The helicity projectors are smooth on every nonzero momentum sphere, but their eigenlines carry opposite unit Chern numbers and cannot extend through the enclosed origin. The parent positive-energy Dirac connection Abelianizes exactly in the $K$ eigenlines on fixed-azimuth meridians, whereas its full three-dimensional curvature has noncommuting components. We obtain the azimuthal Wilson loop in closed form and derive the exact conversion probability between the two $K$ branches under purely geometric positive-energy transport.

We show that quantum phase estimation (QPE) circuits can be significantly compressed in depth by preprocessing the input operator with a sigmoid spectral filter before estimation. For systems with small spectral gaps Delta_lambda, standard QPE requires m = ceil(log2(1/Delta_lambda)) precision qubits and depth Theta(2^m). Applying a soft-step transformation f(lambda; tau,w) amplifies the effective gap to Delta_f > Delta_lambda (for w < 1/4), reducing the required precision to m_f = ceil(log2(1/Delta_f)) and compressing circuit depth by 2^(alpha Delta_m), where alpha = 1 for the LMR density-matrix exponentiation framework and alpha is in [0.11,0.42] for controlled-phase-gate circuits. We prove that this compression is exact, bounded above by log2(1/(4w Delta_lambda)) + 1, and impossible for exactly degenerate spectra. We further show that the threshold parameter tau requires only O(w) accuracy, so classical preprocessing such as covariance diagonalisation or CASSCF avoids circularity. A net resource advantage occurs when 4w^2(2^Delta_m - 1) > Delta_lambda log(1/epsilon). Validation on LiH and BeH2 bond-stretch calculations, classical covariance datasets, and synthetic near-degenerate cases demonstrates depth reductions of up to 27x and CX-gate reductions of up to 21x. For LiH, QPE output fidelity improves from 0.66 to 0.98 at a 1% hardware error rate. The method preserves the principal subspace to machine precision, requires no modification of QPE, and can be combined with readout-stage and state-preparation filtering. Negative-control tests establish the benefit condition: m_raw >= 2 and Delta_lambda > 0.

Quantum illumination exploits entanglement between a transmitted signal and a retained idler to improve the error-probability exponent of target detection by roughly a factor of four (6 dB) over that with a coherent state of the same transmitted energy. This advantage presumes a known return phase. In practice, the phase is set by the range to the target and the condition of its surface, and is difficult to know in advance. Whether the advantage survives when this phase is unknown is not obvious. Here, we cast target detection as a composite hypothesis test in which the return phase is an unknown constant common to all trials, and we restrict the receiver to independent and identical measurements on each copy. We bound the worst-case error exponent at low reflectivity for every such measurement and every input state of a single signal mode and an idler of any dimension. We then show that unentangled coherent light with heterodyne detection already saturates this bound, for every value of the phase. Entanglement therefore confers no advantage in this setting. The class of independent and identical measurements contains many implementable quantum-illumination receivers, including the optical parametric amplifier and phase-conjugate receivers. Our result shows that none of them can offer a quantum advantage in the worst case over the phase, to leading order in the reflectivity.

To maximize the potential of quantum error-correcting codes, it is essential to develop high-performance decoders. The subsystem many-hypercube (MHC) codes have been developed to achieve both high encoding rates and low-weight syndrome-measurements, but the introduction of gauge degrees of freedom makes decoding more challenging. In this work, we develop neural-network-based decoders for the subsystem MHC codes in a circuit-level noise model. We demonstrate that even the gauge-measurement information can be utilized for decoding by carefully arranging the syndrome-measurement sequence, improving the decoding performance. We further show that recurrent neural decoders outperform simple fully connected neural decoders, and can decode syndrome-measurement sequences longer than those used during training.

For testing quantum mechanics in the macroscopic domain, a major challenge is to devise effective means for enhancing the observable nonclassical signatures despite the ubiquitous presence of environmental decoherence. Toward this goal, we invoke the Quantum Zeno Effect (QZE) for achieving a tunable amplification of an inherently nonclassical quantum disturbance induced by any measurement. Such an enhancement of otherwise small and decoherence-suppressed nonclassicality can arise from the cumulative quantum disturbances generated by repetitive measurements, with the tunability of amplification controlled by the number of measurements. To evidence this, we formulate a testable loophole-free scheme using a massive oscillator, where the system preparation requires trapping and ground-state cooling of a massive object. The required measurements can be realized through a beam-splitter-type interaction between the mechanical oscillator and an optical field, followed by photon detection. Our analysis shows that such amplification, suitably quantified in terms of a testable witness, remains appreciably observable even in the realistic regimes of optomechanical damping, and for sufficiently large masses, thus enabling the demonstration of QZE in the macroscopic domain.

Atomic spin-based comagnetometers are powerful tools for precision sensing and tests of fundamental physics. Compared with the widely used gas-cell comagnetometer systems, cold-atom systems offer access to much shorter distance scales and allow implementation of {optical} quantum control techniques. However, in order to realize long spin coherence times with cold atoms, it is necessary to employ diamagnetic atoms and overcome decoherence induced by light shifts. Here we demonstrate a cold-atom comagnetometer based on the nuclear spins of $^{171}$Yb (spin-1/2) and $^{173}$Yb (spin-5/2), jointly trapped in an optical lattice. Vector light shifts are suppressed by enforcing linear polarization of the lattice, while tensor shifts in $^{173}$Yb are suppressed via the use of a Schrödinger cat state. This enables simultaneous Ramsey interferometry on both isotopes with a spin coherence time of 60 s. We achieve a magnetic noise suppression factor exceeding $3\times10^4$, and determine the ratio of nuclear magnetic moments to 4 ppm precision. Our results establish a new cold-atom platform for spin-based sensing and open pathways toward quantum-enhanced searches for physics beyond the Standard Model.

Electrocardiogram (ECG) recordings are sensitive biomedical data, limiting the ability of hospitals and wearable devices to share raw signals for centralized model training. Federated learning addresses this practical privacy constraint by enabling collaborative model training while keeping raw biosignal data at their respective sources. However, federated ECG classification remains challenging due to limited client-side samples, imbalanced arrhythmia labels, and non-independent and identically distributed (non-IID) data across clients. These constraints require classifiers that are both communication-efficient and robust to cross-client distribution shifts. In this work, we evaluate a hybrid quantum-inspired Kolmogorov-Arnold network (HQKAN) against a multilayer perceptron (MLP) for five-class arrhythmia classification on the MIT-BIH dataset and three-class classification on the INCART dataset under federated averaging (FedAvg). Across multiple client configurations, HQKAN improves most aggregate and minority-class metrics while using 37.35% fewer trainable parameters and reducing communication cost by 24.89% on MIT-BIH; on INCART, it achieves corresponding reductions of 44.81% and 36.41%. These results indicate that HQKAN offers a compact, communication-efficient and robust alternative to the MLP baseline for privacy-aware federated learning on biosignal data.