Quantum Physics Paper Analysis

Projective snapshots are a standard readout tool for quantum simulators, but they directly probe only observables that are diagonal in the measurement basis. We show how local equilibration and an independently calibrated equilibrium equation of state can reveal otherwise hidden conserved-density profiles. We demonstrate numerically that such ``quantum snapshot thermometry'' can recover energy fronts and a diffusion constant, distinguish spin transport from energy spreading, and reveal conserved-charge profiles invisible in the initial measurements. We also identify symmetry-imposed ambiguities in the readout and show how prior knowledge of the spatial structure can resolve them. Fixed-basis snapshot thermometry thus provides quantitative hydrodynamic information beyond transport exponents, bypassing additional measurement bases and quantum state tomography.

Local error correction can preserve classical information against noise, but protection under synchronized updates need not survive when sites evolve at independent random times. Establishing stability is particularly challenging when protection relies on the collective action of competing local rules. Here we develop a spacetime renormalization framework that reveals how independently acting local updates can collectively stabilize memory. We identify sufficient conditions under which the geometry of stable interfaces and suppression of defect propagation produce reliable erosion at large scales. Applying this framework, we prove stability of the asynchronous \textsf{R} squeezing code and introduce robust processes in two and three dimensions. In these systems, both encoded phases persist under sufficiently weak noise, even when the noise favors one phase. Our results provide a criterion for designing autonomous memories sustained by competing local stochastic dynamics.

Trapped-ion quantum computers are promising as a platform for realizing quantum computational advantage. They promise long coherence times, near all-to-all connectivity, and potential multiqubit gates as distinguishing advantages compared to competing platforms. Regarding these advantages, it is crucial to understand the trade-offs between increasing engineering complexity and actual improvements in running quantum algorithms with a more flexible gate set. In this work, we investigate this question and develop a versatile toolset to evaluate the performance of gate sets composed of native Mølmer--Sørensen multiqubit gates. To this end, we employ unitary synthesis as an application-agnostic benchmark target and identify specific hardware requirements for multiqubit gates to be advantageous.

Stochastic resetting drives quantum systems into nonequilibrium stationary states unreachable under uninterrupted unitary evolution, and their entanglement depends on whether the reset history is resolved or averaged over. We study this interplay in the transverse-field Ising chain, deriving closed-form results for two qubits and evaluating chains of up to 12 qubits exactly. In the two-qubit system, these closed-form results show that phase matching between energy eigenstates produces resonances, and their visibility in the stationary state is determined by the symmetry of the reset state. Measurements on an IBM superconducting processor show the entropies evaluated before and after the reset average closely following noiseless predictions with no fitted parameter, while concurrence lies below prediction across most of the hardware measurements. The two diagnostics respond differently because they read different components of the same reconstructed state, and a depolarizing model captures the concurrence suppression with one fitted parameter. The difference between the two entropies, i. e., the Jensen gap of entanglement entropy, equals the Holevo information that a subsystem retains about the time since the last reset. With a Bell-state reset, this information grows with chain length across a half-chain cut over the sizes studied, without visible saturation at the smaller reset probabilities. Since reset times are sampled and recorded classically, the trajectory-averaged entropy, and with it the Jensen gap, is obtained without postselection, in contrast to monitored circuits, where trajectory-resolved entanglement requires sampling exponentially rare measurement records.

Can the ground state of a local Hamiltonian be prepared by local dissipation? We address this question for free-fermion Hamiltonians, using a quadratic Lindbladian with linear jump operators for the dissipative ground-state preparation. For translation-invariant targets, Fourier correspondence relates spatial locality to momentum-space analyticity, allowing us to derive a complete spectral criterion for the existence of exponentially local linear jump operators that prepare the ground state. This criterion leads to a no-go theorem that, sign-changing Fermi-level crossings exclude exponentially local linear jump operators for preparing the ground state. While these crossings are the complete obstruction in one dimension, additional obstructions generally arise in higher dimensions. We illustrate these additional obstructions using two quadratic-band-touching models with algebraically decaying ground-state correlations. We further show that short-range ground-state correlations, although not necessary, are sufficient for local dissipative preparation even without translation invariance. Our results establish how the spectral structure of the target Hamiltonian governs the locality of dissipative ground-state preparation.

Left-handed (LH) superconducting transmission lines, built with series capacitors and shunt inductors instead of the series inductors and shunt capacitors of a conventional right-handed (RH) line, have a spectrum with a nonzero lower band edge and modes that become sparse at high frequencies. We study the dynamical Casimir effect in a LH line terminated by a flux-modulated SQUID and compare it with an RH line built from the same elements and with a long coplanar waveguide terminated by the same SQUID. We derive the quantum Hamiltonian and show that the coupling between two modes factorizes into their amplitudes at the SQUID. Together, the LH spectrum and the mode dependence of this coupling determine which modes are populated and how fast. With equal elements, the LH coupling grows with frequency and exceeds the RH one above a crossover pump frequency set by the cell inductance and capacitance, and only the LH line has resonances above the RH band edge. Pumping two modes at once lets a weakly coupled mode borrow coupling from a strongly coupled one, while crossings of resonance lines populate three or four modes without increasing the growth rate. Compared with the coplanar waveguide, the LH line has a similar coupling but keeps the created particles in the target mode, whereas the nearly equidistant waveguide spreads them over many pairs and needs more pump energy.

The diamond distance between two quantum channels determines the optimal probability of distinguishing them from a single use. We give a quantum algorithm that estimates the diamond distance between two unknown $d$-dimensional unitary channels to within additive error $\varepsilon$, using $O(\sqrt{d}/\varepsilon)$ queries to the unitary channels and their inverses. The query complexity is optimal, as it matches the lower bound due to Jeon and Oh (npj Quantum Inf. 2026).

Efficient control of quantum devices requires the knowledge of their environmental noise, yet the commonly measured power spectrum does not fully characterize non-Gaussian fluctuations of realistic environments. Here we show that exceptional points (EPs) in the noise-averaged dephasing response can expose observable signatures of non-Gaussian statistics, distinguishing environments with identical lower-order statistics. We also introduce a theoretical model that describes dephasing environments in terms of identical independent noise sources while preserving the power spectrum. Given a calibrated single-source model, the largest EP order extracted from the measured dephasing response determines the number of sources and predicts the higher-order statistics of the combined noise. We illustrate an atomtronic readout that maps distinct EP signatures onto an evolving ensemble-averaged atomic interference pattern. Our results connect non-Hermitian dynamics to environmental noise statistics, providing a route to characterize noise in quantum devices used in computing, metrology, and precision measurement.

We develop an algebraic theory of fusion, mobility, and statistics in abelian gapped fracton orders and topological phases. The framework generalizes the algebraic description of abelian anyons to systems with restricted-mobility and spatially extended excitations. We consider translation-invariant bosonic systems whose pointlike and extended excitations have finite fusion order. The basic objects are braided fusion complexes (BFCs): chain complexes encoding fusion and mobility, equipped with a braiding chain map encoding statistics. Their equivalence classes define braided fusion theories (BFTs). Our framework encompasses arbitrary translation-invariant Pauli codes, as well as all abelian anyon theories in two spatial dimensions, including chiral theories. We give evidence for the conjecture that every nondegenerate BFT can be realized as the excitation theory of a gapped phase and that the BFT describing such a phase is a phase invariant. We derive constraints on pointlike fusion and mobility, showing, for example, that neither the Pauli X nor Z sectors of the X-cube and anisotropic models can occur alone in a nondegenerate BFT. For nondegenerate theories with only pointlike excitations, we extract a simpler theory of mutual statistics, consisting of a fusion module and a map to its statistical dual. This theory of mutual statistics is an invariant of the BFT and, at odd fusion order, gives an equivalent description of the full braided fusion theory. We interpret remote detection as the generalization of mutual statistics to fracton orders. In the BFC setting, we give a precise formulation of the excitation-detector principle: every nontrivial excitation can be detected by an operator supported at spatial infinity, and every nontrivial detector detects some excitation. Assuming a unique infinite-space ground state, we prove that this principle is equivalent to nondegeneracy.

Single-qubit quantum gates are implemented as the time-controlled unitary evolution of a two-level system under harmonic driving. The rotating-wave approximation (RWA) provides closed-form gate parameters for weak coupling. Larger amplitudes, desirable to speed up the dynamics, make the RWA-designed gates inaccurate because of the neglected counter-rotating term, which also shifts the resonance (Bloch-Siegert shift). Here we study theoretically the infidelity of gates beyond the RWA, using the effective Magnus-Taylor Hamiltonian through second order in the inverse of the driving frequency. By detuning the driving frequency by an amplitude-dependent shift of Bloch-Siegert type and rescaling the operation time, the RWA gate conditions are recovered with corrected parameters. Numerical solutions of the Schrodinger equation show that these corrections lower the gate infidelity by several orders of magnitude, extending the range of usable amplitudes

Electrically spin-injected ensembles of InGaAs/GaAs quantum dots emit circularly polarized single photons, with the emission helicity determined by the spin polarization of the injected electrons. A ferromagnetic CoFeB spin-injection layer with perpendicular magnetic anisotropy, combined with an MgO tunnel barrier, enables spin-polarized electron injection into the quantum-dot active region, resulting in circularly polarized photon emission at zero applied magnetic field. These devices realize direct spin-charge-photon conversion in an electrically driven, microelectronics-compatible quantum light source that operates without an external pump laser. Using an extended Hanbury Brown-Twiss interferometer with four detectors and time-tagged readout, we measure time-resolved photon-number statistics that resolve up to $|2\rangle$ Fock states within a single excitation cycle. While single-photon ($n=|1\rangle$) emission tracks the electrical excitation pulse as expected, the two-photon ($n=|2\rangle$) statistics exhibit pronounced fluctuations at multiple temporal positions within the pulse. These fluctuations vanish upon demagnetization of the spin-injection layer, establishing a direct link between the multi-photon emission dynamics and the spin polarization of the injected carriers. The observations indicate that spin injection controls not only the helicity of the emitted photons but also higher-order temporal correlations of the emission. The behavior is phenomenologically captured by inserting both a variable excitation mechanism and a set of multi-emitter collapse operators within a stochastic wave function evolution. The platform thus opens a route to electrically driven, spin-controlled single and multi-photon Fock-state sources and provides a testbed for spin-conditioned multi-emitter dynamics in solid-state quantum light sources.

Topological Calderbank-Shor-Steane (CSS) codes in more than two spatial dimensions offer features useful for fault-tolerant quantum computation, such as transversal non-Clifford gates and single-shot decoding, but a systematic understanding of them is still lacking. One approach is to decouple a code: map it to a stack of higher-form toric codes by a finite-depth local CSS-preserving Clifford circuit, possibly after adding ancillas. For translation-invariant $p$-ary CSS codes, where $p$ is prime ($p=2$ for qubits), we require the circuit to commute with the translations of a superlattice. In two dimensions, such a decoupling exists once these translations act trivially on every anyon type. In higher dimensions, excitations are sorted by their dimension into superselection layers, which can remain glued together even when translations act trivially on each layer. We show that this gluing is the only remaining obstruction: a code can be decoupled on a superlattice exactly when, after coarse-graining to it, translations act trivially on every layer and the gluing vanishes. Moreover, for a code with finitely many excitation types in each layer and $m$ nonzero layers, once translations act trivially on every layer, further coarse-graining by a factor of $p^{m-1}$ in every direction removes the aforementioned gluing. Physically, the same criterion determines when the code encodes the maximal number of logical qudits on a finite torus. Finally, we give an explicit algorithm that constructs the decoupling as a circuit of SUM (qudit CNOT) and SWAP gates.

An autonomous research laboratory could conduct an entire study, from formulating questions to preparing manuscripts. Artificial intelligence (AI) offers one route towards this goal. Recent AI systems take on several research roles, but may draw conclusions that the evidence does not support. Here, we present an autonomous research laboratory in which agents based on large language models assess one another's work and can stop or redirect investigations. They can generate and reject research questions, require separate theoretical checks and conduct experiments designed to challenge their claims. We demonstrate these capabilities by investigating ensembles of quantum spins in diamond. The agents derived the minimum number of calibration settings needed to predict responses to a defined family of microwave pulse sequences. They checked the result computationally and designed experiments to distinguish competing predictions. An initial experiment agreed with the theoretical predictions, but repeated reference measurements showed that the signal was drifting during data collection. The agents therefore treated the result as inconclusive and revised the measurement protocol without relaxing the acceptance criteria. The revised experiment met those criteria and supported the theoretical predictions. This study demonstrates that collaborating AI agents can select research questions, derive theoretical results and test their predictions experimentally.

Can entangling codewords across independent uses of a quantum channel improve the rate of classical communication? An old conjecture states that there is no such entanglement advantage for all channels. Although Hastings's result and follow-up works disproved this conjecture, it turns out that enormous dimension is required to construct a channel where entanglement enhances classical communication. This indicates that there might be no entanglement advantage for many physical channels, or for all low dimensional channels. Motivated by recent progress on (generalized) amplitude damping channels, we propose a general Schur-weighted block entropy inequality, and show that there is no entanglement advantage for all phase-covariant channels including multi-level amplitude damping channels, generalized dephasing channels, and damping-dephasing channels. As a by-product, we also recover the recently established result that there is no entanglement advantage for all qubit channels.

Can quantum computation become more powerful when operations do not need to follow a definite causal order? We study this question in the process matrix formalism of Oreshkov et al. (Nature Communications, 2012), which allows quantum operations to be connected without a fixed global order. In the computational model, a quantum circuit succinctly describes a process matrix, and the algorithm is given access to its generated channel, with computational cost measured by the size of the generating circuit. We give polynomial-time algorithms in two settings. First, general process matrix computation suffices to solve every problem in $\textbf{NP}$. The valid processes used by our algorithm satisfy the purification postulate of Araújo et al. (Quantum, 2017), and their generated channels are unitary, although their generating circuits are not. Second, requiring the process matrices themselves to be pure, we give a polynomial-time algorithm for unique-sink orientation, a general problem capturing several longstanding computational problems in optimization. Our unitary generators are constructed explicitly and efficiently. Assuming that unique-sink orientation has no quantum polynomial-time algorithm, our result shows that indefinite causal order can provide computational power beyond $\textbf{BQP}$ within the process matrix formalism, even while preserving unitarity.

We confirm a conjecture of the first author [SODA'26] on a strong form of pseudo-telepathy for Khot's $d$-to-$1$ games: for every $d\geq 4$, every $ε>0$, and every $k\in\mathbb N$, there is a $d$-to-$1$ label-cover game of classical value less than $ε$ that admits a perfect quantum strategy using finite-dimensional shared entanglement with measurement contexts of radius at least $k$. As a consequence, there exist graphs whose quantum chromatic number $χ_q$ is $3$ and whose classical chromatic number $χ$ is arbitrarily large. This is the first improvement on the quantum chromatic gap since the work of Brassard, Cleve, and Tapp [Phys. Rev. Lett.'99], which produced graphs for which $χ$ grows exponentially in $χ_q$. To prove the conjecture, we proceed as follows. We start with a ``stretched'' version of the Mermin--Peres magic square, obtained by spacing out its equations and linking them with additional long equation wires. This operation increases the radius of the initial measurement contexts of a perfect quantum strategy for the game, while preserving classical unsatisfiability. We then apply parallel repetition to make the classical value small, and we turn the system into a pseudo-telepathic multi-layered Kneser hypergraph via a PCP construction of Dinur, Guruswami, Khot, and Regev [STOC'03]. Finally, we feed the resulting hypergraph into the reduction of Fei, Minzer, and Wang from hypergraph colouring to $4$-to-$1$ games, we establish quantum completeness of this reduction, and we show that it preserves context radius.

Coherent noise can give rise to unconventional regimes of quantum information recovery and mixed-state order. We study these phenomena in two settings related by Wegner duality: the triangular-lattice surface code subject to single-qubit Pauli-$Z$ rotations followed by syndrome measurements, and a $\mathbb{Z}_2$ paramagnet subject to strongly symmetric decoherence. Increasing the rotation angle drives a transition from a decodable phase to a \emph{partially decodable} critical phase in the code, and from a strongly symmetric phase to a phase with \emph{algebraic} $\mathbb{Z}_2$ strong-to-weak spontaneous symmetry breaking (SWSSB) in the dual paramagnet. We develop a common description of these phenomena in terms of a weakly coupled $\mathrm{SO}(n)$ nonlinear sigma model in the replica limit $n\to1$. Taking this replica limit analytically, we derive universal signatures of the critical phase: an optimal Pauli decoding fidelity that approaches a universal function of the system's aspect ratio in the thermodynamic limit, and a dual fidelity correlator that decays as a universal power law. These observables relate to correlations of twist operators in the sigma model description. Large-scale numerical simulations confirm these analytical predictions. We also argue that the algebraic SWSSB phase cannot be realized by any Pauli dephasing channel acting on the $\mathbb{Z}_{2}$ paramagnet. We probe this "non-classical" character through the output state's sensitivity to well-separated $\mathbb{Z}_{2}$ fluxes inserted in the initial state, which reveals persistent coherence between distinct $\mathbb{Z}_{2}$ charge trajectories at long distances.

While Variational Quantum Eigensolver (VQE) variants are among leading candidates for electronic structure calculations on quantum computers, gradient-based operator selection limits their scalability. To solve this, we introduce the Hamiltonian-gradient-free VULCAN (Variational Upbuilding, Layered Compression, Adaptive N-body perturbation) layered VQE framework. Our method dynamically generates ansatz operators using Variational Double Bracket Flow (VDBF) equations. Combined with a linearly scaling minimal complete pool, it creates a pool 4-12 times smaller than QEB (Qubit-Excitation-Based) pools. By appending entire layers simultaneously, Hamiltonian gradient measurements are completely eliminated. Circuit depth is managed via a grow-then-compress scheme using efficient state-overlap measurements, and qubit requirements are reduced by projecting the Hamiltonian onto a dominant-determinant subspace. Using high-performance emulation up to 32 logical qubits, we achieve chemical accuracy at just 5-20% of the measurement cost of batched ADAPT-VQE for hydrogen chains, BeH2 and H2O. For the 32-qubit C3H6, where batched ADAPT-VQE does not reach chemical accuracy, a single VULCAN layer combined with a GPU-accelerated stochastic Epstein-Nesbet (ENPT2) correction does. This stochastic ENPT2 post-processing step enables early termination at chemical accuracy.

Within quantum many-body phase diagrams, continuous transition lines can appear and then terminate. However, it has remained unclear whether the neighboring regimes can be meaningfully described as distinct phases, akin to water and vapour, since any sharp characterization would have to go beyond the usual notion of phases of matter. We answer this in the affirmative by introducing quasi-phases: gapped regimes near a critical point that are connected in the broader phase diagram, but not by any gapped path accessible from small perturbations of the critical theory. The physical consequences include interface modes between regimes in the same phase of matter. More striking still, describing both the extended critical line and the gapped path connecting the regimes requires a bigger multicritical parent theory. In spin-chain examples with continuous terminating lines with central charge $c=1$, we find multicritical $c=3/2$ and $c=9/5$ orbifolds describing so-called 'quotient symmetry protected' and 'representation symmetry protected' topological phenomena. While one-dimensional symmetry-protected topological phases are labeled by projective representation classes, these quasi-phases can have interface modes carrying higher-dimensional linear representations. We turn this into a constructive principle through a weakening of the Lieb-Schultz-Mattis anomaly. Supporting distinct quasi-phases makes an unnecessary critical point infrared-necessary, even if it is unnecessary at the ultraviolet scale. This condition is more restrictive than simply having a codimension-one critical line, revealing richer structure within phases of matter than their conventional classification suggests.

In this paper we present a gauge-invariant formalism for describing the spin and orbital angular momenta of scalar and vector optical vortices. The correction term, arising from consistent incorporation of the transverse vector potential's nonlocality, restores gauge invariance and makes it possible to separate the total angular momentum into spin and orbital components. We propose a method for calculating the orbital and spin angular momenta of multimode vector vortex fields and show that the orbital angular momentum of such beams contains two qualitatively different components. The polarization-independent contribution to the orbital angular momentum is related to the topological charge that determines the order of the phase singularity, while the polarization-dependent one is proportional to the helical topological charge that determines the spatial inhomogeneity of the polarization. We also discuss the quantization procedure for fields with spatially inhomogeneous polarization in terms of modes with a helical topological charge, and examine the limits of applicability of the proposed formalism.

We consider the distribution of domain walls arising in ground states of frustrated 1-dimensional Ising spin chains with anti-parallel boundary spins. For ideal chains, a sine-squared particle-in-a-box distribution of domain walls is expected in the quantum setting, and a uniform distribution expected classically. However, for chains with random imperfections, prior work [Chancellor et al., npj Quantum Inf. 8, 73, 2022] found that the distribution in a physical implementation corresponded to neither. Instead, the domain wall distribution forms a U-shaped profile arising from a classical model with random fields, where the combination of averaging over these fields and thermal averaging produces the characteristic U-shape. With D-Wave's newer fast anneal feature, we access anneal times shorter than the coherence time and observe the expected coherent quantum behavior in the form of a sine-squared distribution. For the shortest available anneal time, the dynamics have not yet reached the sine-squared shape and instead display a different U-shape in the middle of the chains. This motivates using the extent of the domain wall distribution tail in this regime as a platform independent metric that provides a signature of both coherence time and noise levels.

Quantum error correction is essential for fault-tolerant quantum computing. High-rate quantum low-density parity-check (qLDPC) codes have emerged as a promising approach to reducing the substantial physical qubit overhead of quantum error correction, enabling encoding rates exceeding $1/2$ in blocks of approximately one thousand physical data qubits. However, their practical implementation requires decoders that combine high accuracy with low latency to keep pace with quantum hardware. Existing decoders of high-rate qLDPC codes can achieve high accuracy but often incur substantial computational latency, whereas neural network decoders have yet to be demonstrated for high-rate qLDPC codes. Here, we introduce \emph{neural triage decoding}, a framework that uses syndrome consistency to adaptively allocate neural computation. A local neural message-passing network rapidly predicts error corrections, additional iterations reduce residual syndrome violations, and a rarely invoked diversification stage searches for consistent corrections to the remaining shots. We demonstrate that the \texttt{Triage} decoder can decode ultra-high-rate qLDPC codes encoding a few hundred logical qubits, including lifted-product and Kasai codes, achieving state-of-the-art accuracy comparable to the near optimal algorithmic decoders while reducing decoding latency by approximately one to two orders of magnitude. Our framework is inspired by a rigorous analysis of the exact bitwise marginal decoder, revealing a distance-independent syndrome-inconsistent error floor. In addition, we show the robustness of neural network decoders to mismatched error priors. Our results establish adaptive neural decoding as a promising route towards fast, accurate, and scalable quantum error correction in the near term.

We show that the ensemble of unimodular Gottesman$-$Kitaev$-$Preskill distributions fails to form a rigged quantum $3$-design and quantify the replica defect that determines this failure. This is established by rederiving a second moment formula for symplectic lattices in a self-contained manner.

The celebrated Evans--Searles, respectively Gallavotti--Cohen, fluctuation theorem concerns certain universal statistical features of the entropy production rate of a classical system in a transient, respectively steady, state. In this paper, we review and compare several possible extensions of these fluctuation theorems to quantum systems. We present, in an introductory way, the approach proposed in a recent series of works [Lett. Math. Phys. 114, 32 (2024): doi:10.1007/s11005-024-01777-0], [Rev. Math. Phys 38, 2461006 (2026): doi:10.1142/S0129055X24610063], [Commun. Math. Phys. 406, 201 (2025): 10.1007/s00220-025-05360-z] and [J. Math. Phys. 67, 022101 (2026): doi:10.1063/5.0311182] including a previously missing extension of the Gallavotti--Cohen (steady state) version of the FT to two-time measurement entropy production in the algebraic setting of quantum dynamical systems. We focus on the open quantum systems, where a small system interacts with several (infinitely extended) reservoirs, and discuss the following approaches: naive, two-time measurement, phase space contraction and ancilla state tomography. We review the connection with modular theory. The latter provides a way to extend the classical notions to the quantum domain. We discuss the quantum version of the principle of regular entropic fluctuations, introduced in the classical context in [Nonlinearity 24, 699 (2011): doi:10.1088/0951-7715/24/3/003]. Finally, we relate the statistical properties of these various notions of entropy production to spectral resonances of quantum transfer operators and apply this approach to a paradigmatic model of non-equilibrium statistical mechanics: the spin-fermion model. The results presented here shed a new light on the nature of entropic fluctuations in quantum statistical mechanics.

We consider a static dipolar impurity immersed in a Fermi gas and show how dipolar interactions shape both the few-body scattering properties and the resulting polaron physics. Using Fumi's theorem, we connect the anisotropic phase shifts directly to the ground-state energy, and compute the exact impurity spectrum via the functional determinant approach. The resulting spectrum is a convolution of independent even- and odd-wave contributions, giving rise to a ground state with simultaneously occupied even- and odd-wave bound states whose separation is tunable via the dipole length. A variational ansatz limited to one particle-hole excitation fails to capture this doubly occupied ground state. We further find that long-range dipolar interactions weaken Anderson's orthogonality catastrophe, reducing the power-law decay of the quasiparticle weight. These effects can be tested with ultracold polar molecules, where microwave shielding and independent tunability of interactions enable experimental access to the predicted regimes.

QAOA mixers play an important role in enabling exploration of the exponentially large solution space of binary optimization problems. However, the choice of mixer Hamiltonian is typically guided by convention and implementation or circuit constraints, rather than by a graph-topology-aware criterion. In this work, inspired by quantum-walk mixing theory, we propose two complementary spectral heuristics for characterizing QAOA mixer topologies. The first is the normalized minimum eigenvalue separation of the mixer Hamiltonian $H_M$, while the second is the long-time averaged minimum eigenvalue separation of the mixer unitary $U_M(β)=e^{-iβH_M}$. Both quantities are invariant under any positive rescaling of the mixer Hamiltonian and provide Hamiltonian- and unitary-level characterizations of the mixer's spectral structure. We use them as heuristic indicators of the mixer dynamics relevant to amplitude redistribution during QAOA evolution. We derive exact expressions and asymptotic bounds for the complete graph, hypercube, cycle, and balanced 2-D torus, revealing a broad spectral separation between the studied topology classes. We then compare these separations with empirical QAOA performance. For random permutation-invariant cost Hamiltonians, the observed performance ordering is broadly consistent with the spectral characterization. In contrast, for structured 1-D and 2-D Ising QUBOs, this ordering breaks down, indicating that mixer-cost alignment can become important. These results illustrate both the usefulness and the limitations of topology-level, cost-agnostic spectral heuristics for QAOA mixer selection.

Quantum reference frame (QRF) transformations relate the description of a physical system to different quantum observers, but their connection to concrete experimental phenomena remains largely unclear. Here we show that the trajectory-sharpening effect obtained by correlating a probed system with an effective negative-mass reference admits a natural interpretation as a QRF transformation to the frame of a negative-mass system. Using a minimal toy model of free particles with signed masses, we identify the Einstein-Podolsky-Rosen-type observables responsible for this effect with a pair of commuting relational observables that, under the instantaneous QRF transformation, are mapped to operators local to distinct subsystems. We then show that the corresponding relational trajectory is reproduced by the dynamical QRF transformation, where the transformed relational position acquires an explicit time dependence. We introduce QRF-invariant sharpness measures for relational trajectories and derive monogamy relations showing that a trajectory cannot be made simultaneously arbitrarily sharp with respect to two distinct negative-mass frames. We further show that trajectory sharpness can instead reside in a collective reference mode encoded across two physical systems, even when neither constituent alone provides an arbitrarily sharp reference, so that sharpness can be distributed rather than localized in a single constituent frame. These results provide an operational, experimentally relevant interpretation of QRF transformations for continuous-variable systems.

We extend the process-matrix framework for defining indefinite causal orders to a broad class of generalised physical theories. We give a simple re-axiomatisation of spacetime contexts in terms of naturality over classical probes, which precisely captures non-contextual assignment together with compatibility with convexity and coarse-graining within local laboratories. Using this compositional perspective, we give a clean characterisation of theories in which abstract spacetime contexts admit a process-matrix representation, and we pin down the precise conditions (satisfied by classical theory, quantum theory, and a Boxworld-like theory) under which the supermap and process-matrix perspectives on higher-order processes coincide.

After truncating the matter Hilbert space of a single-mode light-matter model, gauge transformations leave the spectrum invariant whereas the ground-state photon number is gauge dependent, hence, its meaning remains disputed. We show that this gauge dependence obeys an exact algebraic law whenever the gauge transformation acts as a displacement of the field coupled to a matter operator $G$. Namely, the ground-state photon number is a quadratic polynomial in the gauge parameter $λ$, $\langle a^{\dagger} a\rangle_λ$ $=$ $\langle a^{\dagger} a\rangle_{0}$ $+$ $Cλ$ $+$ $Qλ^2$. Here the coefficients are the correlator $C=\langle G\,p\rangle$ of $G$ and the field momentum $p$, and $Q=\langle G^2\rangle$. Its minimum over all gauges is naturally gauge-invariant, and for the quantum Rabi model it is determined by the ground-state energy alone. We show that it is strictly positive for the quantum Rabi and Dicke models with level splitting, so that a residual photon content survives in every gauge. At weak coupling the gauge of minimal photon number is the Jaynes-Cummings gauge, and for the Dicke model it remains so at all couplings in the thermodynamic limit.

The choice of mixer is a central design decision in the Quantum Approximate Optimization Algorithm (QAOA), yet different structural limitations of a mixer need not be captured by a single metric. We identify two complementary structural bottlenecks for shallow QAOA: configuration-space transport, which limits how strongly probability can concentrate on high-quality solutions, and finite-depth causal reach, which limits which parts of a problem instance can influence a local objective term. In Part I, we derive first-order mixer-dependent objective bounds in complementary small-$β$ and small-$γ$ regimes. For connected regular mixer graphs, the two leading-order expressions are exactly equivalent through a graph-Laplacian identity and reduce to the same cost-weighted Dirichlet energy. We then derive a non-perturbative upper envelope from the layer-wise $\ell_1$ spreading of the mixer unitary, yielding a cost-distribution-dependent necessary spreading condition for attaining a target approximation ratio. In Part II, we study the locality bottleneck for MaxCut by augmenting the transverse-field mixer with problem-graph-aligned two-local interactions. The resulting $k$-hop construction has causal radius at most $(k+1)p$ at depth $p$; for the $k=1$ architectures studied numerically, this gives radius $2p$. Across cycles, circular ladders, and high-girth regular bipartite graphs, $X{+}XX$ and $X{+}YY$ improve the best-found approximation ratios over the standard $X$ mixer at equal depth, while $X{+}YY$ at depth $p$ comes within about one approximation-ratio point of plain $X$ at depth $2p$ in the reach-matched cases examined. The unequal performance of the equal-reach $XX$ and $YY$ augmentations shows that satisfying a structural capability does not by itself guarantee performance. Together, the results provide complementary structural insights for mixer design.

Layered A-type antiferromagnetic (AFM) semiconductors offer a unique platform for spintronic devices by combining robust magnetism with gate-tunable semiconducting properties. We present a dual-gate field-effect transistor based on CrSBr, a layered A-type AFM with pronounced transport anisotropy and complex spin dynamics. Our device provides independent control over carrier density and displacement field. Systematic transport measurements reveal that the displacement field, rather than doping, predominantly governs the sign and magnitude of magnetoresistance ratio (MRR). We identify the origins of both negative and positive MRR components and connect them to interlayer and intralayer spin-dependent transport mechanisms. We interpret these findings with ab initio calculations and an effective spin-circuit model that reproduces the anisotropic magnetotransport. Our results identify the displacement field as an efficient electrical control parameter of spin transport in CrSBr and suggest that multi-gate architectures could provide similar control in other layered antiferromagnetic semiconductors.

We investigate magnon-photon interactions in a resonant cavity starting from the coupled Maxwell and Landau-Lifshitz equations linearized about an arbitrary micromagnetic ground state. By introducing an electric vector potential and a suitable interaction Lagrangian, the formulation avoids the cancellation of large magnetostatic contributions that arises in the conventional magnetic-vector-potential description and becomes inaccurate under modal truncation. The magnetization and cavity fields are expanded in the normal modes of the uncoupled magnetic and electromagnetic subsystems, with coupling coefficients given by overlap integrals of the corresponding eigenfunctions. The resulting multimode Lagrangian has a noncanonical structure due to the gyrotropic terms, and the corresponding Hamiltonian formulation is obtained using the Faddeev-Jackiw approach. The radiative magnon-photon interaction is encoded in the resulting Poisson-bracket structure, while the cavity-induced modification of the magnetostatic field enters explicitly in the Hamiltonian. The coupled system is diagonalized through a generalized Bogoliubov transformation, yielding canonical polariton variables that provide a natural basis for quantization. Application to a perpendicularly magnetized YIG disk in a rectangular microwave cavity shows hybridization between the cavity mode and several magnetostatic modes, together with appreciable cavity-wall-induced frequency shifts when the sample is placed close to the conducting walls.

Quantum sensors have been shown to enable more precise measurements than classical sensors. By using entanglement and coherent evolution, the estimation error can be made to scale better in interrogation time, photon count, and other resources, achieving Heisenberg-limited scaling. However, environmental noise and hardware errors typically destroy the coherence of the sensitive quantum states. This motivates the use of fault-tolerant techniques to create more robust quantum sensing protocols. Such fault-tolerant quantum sensing approaches have been shown to enhance sensitivity for qubit systems, but many practical sensors require bosonic probes. In this paper, we propose a fault-tolerant protocol using bosons to estimate displacements in the presence of dephasing noise. We construct an optimal error-correcting code under a mean photon-number constraint. Controlled displacements couple the probe to a repetition-encoded qubit register, while repeated boson-parity measurements and resets remove probe noise without erasing the stored logical phase. Under circuit-level bit-flip noise, a distance-$d$ code suppresses logical failures to order $p^{(d+1)/2}$. We show that, for a decay rate $γ_A$, a total sensing time $T$ and a mean photon number budget $N$, and for sufficiently small residual signals, the Fisher information scales as $NT^2$ over interrogation times of order $γ_A^{-(d+1)/2}$. This is a significant improvement over the non-fault-tolerant approach that achieves Heisenberg scaling only for a total time $\mathcal O(γ_A^{-1})$.

Polaritonic chemistry holds the promise of controlling chemical reactivity through confined light-matter interactions, yet how reactions respond inside optical cavities remains debated. Here, we take a more zoomed-out view, inspired by electrostatic catalysis. We extend nonempirical linear free-energy relationships to cavity-modified reactions and show that their behavior falls into four distinct reaction types set by simple response-crossing rules. Reactions can follow conventional Bell-Evans-Polanyi (BEP) or counterintuitive Opposite-BEP behavior regardless of cavity tuning, or switch between the two as the cavity frequency is varied. We establish this picture analytically and demonstrate it in the Shin Metiu model and in four molecular reactions treated with ab initio electronic-structure methods. Even at this deliberately coarse-grained level, cavity-modified reactivity already shows qualitatively different and strongly counterintuitive behavior, including reactions that switch character with cavity frequency. Yet this complexity can still be reduced to a simple competition between permanent-dipole and polarizability responses. This reaction-type classification therefore provides a new route to organize and anticipate cavity-modified reactivity.

An algebraic correspondence between an imaging model and a quantum state does not specify a computational method: input access, measurement and decoding determine what can be returned. This exposition develops four distinctions for computational-imaging and engineering readers. It separates amplitude encodings of input values from encodings of complete candidate labelings, explaining why amplitude storage does not provide full-array readout. Complex-field interference motivates unknown-phase inference: complementary measurements resolve ambiguities that local Fisher information alone does not detect. Reshaping joint amplitudes into a matrix connects singular-value decomposition to pure-state entanglement, while distinguishing Schmidt rank from conditions for efficient classical simulation. In a four-pixel segmentation, an objective becomes a cost operator and a sampling circuit. One layer of the quantum approximate optimization algorithm (QAOA) lowers mean energy from $1.675$ to $0.686$ relative to uniform sampling, yet makes a nonoptimal labeling more probable than the optimum 0.484 versus 0.365. Archived IBM and IQM measurements illustrate a separate six-variable local boundary decision. Low-rank state reconstruction and selected quantum algorithms connect these distinctions to an end-to-end resource account. The derivations and reproducible numerical references assume complex linear algebra and probability, without prior quantum mechanics. The accompanying Seeing Amplitudes browser laboratory supports interactive exploration; the article remains self-contained and connects each representation to the estimate or decision it permits and the resources that output requires.

Understanding when quantum many-body systems rapidly converge to thermal equilibrium is a central problem in quantum statistical mechanics. While spatial locality provides powerful tools for systems with an underlying geometry, fully connected models require estimates that accommodate interactions between every pair of spins. We study Gibbs-state preparation for two-local quantum Hamiltonians on arbitrary interaction graphs, including fully connected systems, via Lindblad dynamics that satisfies Kubo--Martin--Schwinger (KMS) detailed balance. Our approach is based on a quantum analogue of the classical Dobrushin condition, which controls the influence of local perturbations on the rest of the system. Using the quantum Wasserstein distance of order $1$, we quantify how these perturbations propagate under the dynamics and derive contraction estimates in a high-temperature regime controlled by the maximum total interaction strength per site. These estimates require no assumptions on spatial geometry or graph growth and yield mixing times logarithmic in the system size and the inverse error tolerance, uniformly over all initial states.

We develop a state discrimination approach to unassisted quantum communication through a noisy quantum channel. Starting from the operational duality between entanglement recovery and state discrimination, we construct entanglement-generation codes with explicit decoders constructed from Petz recovery maps. The resulting error bounds hold for every number of channel uses and are expressed in terms of Petz-Rényi coherent information. For product sources, they yield exponential error decay at rates below coherent information.

Quantum error-correcting codes provide a powerful framework for analyzing and designing fault-tolerant Clifford circuits. In this work, we construct the subsystem spacetime code and use it to characterize the distances of Clifford circuits. We show that its gauge group can be explicitly constructed and classified using the masking properties of the instantaneous stabilizer groups and consists precisely of faults that are harmless to the circuit. We use this framework to identify where a dynamical code loses distance and to analyze how the fault distance changes when circuits are composed from smaller components. Our results provide a versatile tool for analyzing and designing fault-tolerant circuits, with potential applications to the construction of new dynamical codes.

The collapse and revival of localized states in many-body systems is a quintessential example of a quantum interference phenomenon that cannot be explained purely within mean-field theories. Historically, the majority of previous work on quantum revivals has been in a Schrödinger mechanics context, typically for effectively 1D systems with a focus on the autocorrelation function as the key detection observable. The general revival subject acquires a far greater complexity in the bosonic many-body context that offers a larger variety of observables and intrinsically implies high dimensionality. Here, the focus is on the simplest nontrivial (i.e., not 1D) bosonic many-body system, namely a symmetric two-site Bose-Hubbard model. The non-equilibrium situation of a coherent initial state prepared on one of the two sites of this integrable 2D system in the strongly self-trapping regime is considered. The revival behaviors emerging from the resulting dynamics within expectation values, coherences, and the autocorrelation function are theoretically derived, and the entanglement behavior is illustrated. Several new features, unknown so far in the Schrödinger context and identified here in terms of five ``puzzles'', are encountered and discussed, among them, a synchronized resurgence behavior, differing revivals times depending on the specific observable, and a manifestation of a precession that appears in the underlying mean field dynamics. These new phenomena can be entirely understood through a comprehensive semiclassical theory, building upon the underlying classical (mean-field) phase-space structure. A quantitative comparison of the latter with semiclassical predictions and quantum perturbative calculations yields an overall excellent agreement and confirms that a full semiclassical theory is pivotal for the understanding of these genuinely quantum many-body interference phenomena.

We consider bulk-gapped fermion systems whose infinite-volume bulk is obtained by adding sufficiently weak even many-body interactions to a free Hamiltonian with spectral gap $g>0$, allowing polynomial spatial decay of both parts. We prove quantitative local determination of low-energy states: whenever another interaction agrees with the bulk interaction inside a finite or infinite region $U$, with bulk terms crossing its boundary unchanged or removed, all its states with excitation energies in $[0,3g/4]$ have local expectations close to those of the bulk ground state deep inside $U$. The error decays with the distance to the complement of $U$, independently of the interaction terms supported outside $U$ and of the chosen low-energy state. Quantitative local determination has strong consequences. (i) The bulk interaction has a unique algebraic ground state. (ii) A strong "local perturbations perturb locally" (LPPL) principle holds: arbitrary distant defects change local ground-state expectations only by a spatially decaying error. (iii) Low-energy excitations in finite samples remain localized near the boundary for all times, up to spatially decaying tails, uniformly over arbitrary even boundary terms. (iv) Correlations from deep inside $U$ to outside $U$ are small, with quantitative bounds in terms of spatial separation and distance to $U^c$. To prove local determination of low-energy states, we combine quasi-adiabatic transport of the free ground state to the interacting bulk ground state with a new condition, local excitation detectability (LED). A companion paper establishes gap stability and constructs the transport for weak interactions, while we prove LED at sufficiently weak coupling. The abstract theorem is nonperturbative and applies whenever the transport and LED hypotheses hold.

Neutral atoms in optical tweezer arrays have emerged as a leading platform for quantum information processing. The fidelity of entangling gates mediated by Rydberg interactions has improved rapidly and is increasingly constrained by blackbody-radiation-induced transitions, which shorten Rydberg lifetimes and create contaminant states that can cause correlated errors. Cryogenic environments can suppress these transition rates by more than an order of magnitude. However, realizing a universal gate set in such an environment has remained an outstanding challenge. Here, we demonstrate a universal quantum gate set in a cryogenic $^{133}$Cs atom array, with a single-qubit gate fidelity of 99.970(2)% and a raw two-qubit entangling-gate fidelity of 99.76(8)%, within the range of leading room-temperature implementations. The entangling gate uses direct single-photon coupling between the electronic ground state and a Rydberg $P$ state, avoiding scattering and light shifts associated with two-photon coupling. The gate operates at a modest Rabi frequency of $2π\times4.3$ MHz. The measured fidelity agrees with our error model dominated by atomic motion, indicating a straightforward route to higher fidelity through improved cooling, while the fundamental error contribution from Rydberg decay is below $3\times10^{-4}$. These results establish a path to entangling-gate fidelities substantially beyond the current state of the art through cryogenic suppression of Rydberg decay, reducing the overhead for fault-tolerant computation.

Locating the minimum of a nuclear collective landscape can require many interacting many-body calculations. QDMin (Quantum Deformation Minimum Finding) searches a parameterized Hamiltonian family with a coherent collective-coordinate register and an on-demand ground-energy threshold oracle. The oracle supplies the predicate required for quantum minimum-finding without first constructing the energy landscape point by point. We implement it for a schematic pairing-plus-multipole model using circuit-generated energy estimates during the search. In a four-point calculation, one Grover round raises the probability of the true minimum from 0.25 to 0.921. A $4\times4$ quadrupole--octupole-field calculation extends the complete circuit to two coordinates, although its minimum is first sampled in a round with zero Grover iterations. Its worst-case branch-preparation fidelity of 0.744 falls below the declared target, identifying coherent ground-state access as the current bottleneck. QDMin inherits expected $O(\sqrt{N_q})$ candidate-query scaling in the unstructured model; total advantage depends on the many-body oracle cost and remains unestablished.

We extend the generalized transfer-matrix method introduced in [H. Ghaemi-Dizicheh, Phys.\ Rev.\ B \textbf{107}, 125155 (2023)] to one-dimensional spinful non-Hermitian tight-binding lattices with matrix-valued Abelian and non-Abelian gauge couplings. We derive a minimal channel-resolved transfer matrix and identify its eigenvalues with the generalized Bloch factors. The same transfer matrix determines the periodic- and open-boundary spectra, generalized Brillouin zone, skin localization, and finite-sample scattering conditions. In the Abelian limit, the model separates into fixed spin sectors, yielding exact spectral results and closed finite-length transport expressions in terms of Chebyshev polynomials. These results reveal bipolar spin-dependent skin localization and distinguish the reciprocal hopping scale, which governs poles, zeros, and reflectionlessness, from the directed-amplification factor controlling transmission asymmetry, transparency, and invisibility. For non-Abelian gauge fields, noncommuting link matrices coherently mix the spin sectors, such that four transfer eigenmodes jointly determine the non-Bloch spectrum and transport eigenchannels. We show that this mixing produces spin-hybridized lasing and coherent-perfect-absorption channels, Zeeman-tunable lasing thresholds, and direction-dependent reflectionless transport accompanied by pronounced spin conversion. The resulting boundary-condition criteria describe lasing, coherent perfect absorption, reflectionlessness, transparency, and invisibility, while identifying spin polarization and conversion as experimentally accessible signatures that distinguish Abelian from non-Abelian non-Hermitian transport.

We prove that weak long-range many-body interactions preserve the bulk gap of a free fermion system and that a quasi-local spectral flow transports the free ground state to ground states of the interacting system. Let $Φ_h$ be a free fermionic interaction, possibly including pairing terms, whose infinite-volume Majorana coefficient operator $h$ has no spectrum in $(-g,g)$, and let $\mathcal V$ be an even self-adjoint many-body interaction. For sufficiently small $|λ|$, we construct pure ground states $ω_λ$ of the interacting bulk system $Φ_λ=Φ_h+λ\mathcal V$ and quasi-local automorphisms $β_{0,λ}$ such that $ω_λ=ω_0\circβ_{0,λ}$, where $ω_0$ is the free ground state of $Φ_h$. Each $ω_λ$ has a GNS Hamiltonian with gap at least $g-C_*|λ| \|\mathcal V\|_*$, where $\|\cdot\|_*$ is the relevant interaction norm. Our result allows polynomial decay of both the free coefficients and the many-body interaction. For two-site interactions on a uniformly discrete point set $Γ\subset\mathbb{R}^d$, a sufficient condition is decay as $(1+|x-y|)^{-\varpi}$ with $\varpi>2d$, for both the hopping and pairing coefficients and the interaction terms. The spectral-flow generator preserves the spatial exponent of the polynomial interaction norm, and its automorphisms satisfy locality bounds at that exponent. If $h$ and $\mathcal V$ have stretched-exponential decay, so does the spectral-flow generator. The proof constructs the spectral flow and establishes the gap through an excitation-number comparison, using polynomial propagation bounds for evolved interactions proved in a companion paper.

We study general $(r,δ)$-quantum locally recoverable codes (qLRCs) without assuming purity or a stabilizer structure, and with arbitrarily overlapping recovery blocks. Using a selection lemma for multiple-erasure recovery, we establish a Singleton-like upper bound for general quantum subspaces. When $δ=2$, this bound reduces to the general single-erasure bound of Golowich and Guruswami. An integer optimization yields an explicit remainder correction that tightens the bound by up to $δ-2$. For pure codes, local decoupling and entropy arguments extend the parameter bound of Galindo et al., originally obtained for pure stabilizer codes constructed from Euclidean or Hermitian dual-containing classical codes, to arbitrary pure quantum subspaces. We also remove the partition assumption from several existing pure-code bounds for disjoint recovery blocks and obtain a further remainder correction by optimizing the budget. Finally, we analyze three families attaining these bounds: pure codes with overlapping recovery blocks and $d=δ$, which exhibit both a strict improvement of the pure-code bound and simultaneous equality in the pure-code and general bounds; impure codes with disjoint recovery blocks attaining the general bound; and an existing family of pure codes with overlapping recovery blocks and $d>δ$, which simultaneously attains all these bounds.

We prove that the three-dimensional chiral $\Z_p$ Clifford quantum cellular automata of Haah and of Sun--Yang--Wang--Tantivasadakarn--Chen are, for every odd prime $p$, not finite-depth quantum circuits, even after tensoring with arbitrary ancillary degrees of freedom and composing with translations. Previously such statements were known only inside the Clifford category. As a consequence, the group of three-dimensional QCA modulo stabilized circuits and translations is not finitely generated. The key ingredient is a new invariant of invertible subalgebras, which we conjecture to be the square of the total quantum dimension of the hosted anyon theory, modulo rational squares.

Coupling quantum materials to electromagnetic cavities or resonators without external driving has gained prominence as a new control mechanism. Here we develop an equilibrium theory of a mesoscopic, disordered two-dimensional superconductor coupled to a subwavelength terahertz resonator, focusing on the interplay between superconducting phase fluctuations in the sample and electromagnetic fluctuations of the resonator. Modeling the resonator as a lumped-element circuit, we show that the coupling enhances, rather than suppresses, the superconducting transition temperature $T_c$. When the sample is smaller than the Pearl length, phase fluctuations near the Berezinskii--Kosterlitz--Thouless (BKT) transition strongly amplify this enhancement. Crucially, the resistive quasiparticle response of the sample must be included in the analysis: at low frequencies the superfluid shunts the normal-fluid channel, reducing the total sample impedance. For representative parameters, a $1 \,μ\mathrm{m} \times 1 \,μ\mathrm{m}$, $8 $nm-thick disordered film, we find a relative $T_c$ enhancement of about $1\%$, an order of magnitude larger than the $0.1\% $ obtained when phase fluctuations are neglected. These results identify superconductors with soft phase fluctuations as promising platforms for equilibrium control with terahertz resonators.

Cavity-enhanced spectroscopy is a widely used experimental technique. We show that detuning the cavity frequency from the transition of interest can enhance the precision for dipole moment estimation by up to two orders of magnitude beyond the improvement when the cavity is resonant with the transition. We show this for both classical continuous-wave (CW) and pulsed single-photon probes, even in the presence of losses. We trace this enhancement to a detuning-controlled redistribution of information between the light- and matter-like polaritons, with losses determining the optimal branch. We show that this enhancement remains accessible using conventional photodetection and time-correlated single-photon counting.

These notes provide an introduction to Haagerup noncommutative $L^p$ spaces for quantum field theorists. The aim is to explain how the familiar calculus of density matrices, fractional powers, and Schatten norms extends to local observable algebras of type~III, where an intrinsic trace is unavailable. We develop the construction first for a matrix algebra, making the crossed product, its trace, and the dual action explicit, before passing to general von Neumann algebras. Particular attention is paid to the representation of normal states by Haagerup densities and to the distinction between the crossed-product trace and the canonical Haagerup functional used to compute expectation values. As a concrete application, we calculate the sandwiched Rényi divergence for a coherent excitation of a chiral current, verifying monotonicity under restriction and the Rényi quantum null energy condition at every real order $α>1$. The presentation assumes familiarity with quantum mechanics and elementary quantum field theory, while introducing the operator-algebraic concepts needed for the construction and calculation.

Bayes' rule is central to classical statistical inference: given a prior and a stochastic model, it determines the corresponding retrodictive conditional probabilities. In quantum theory, however, the question of whether an equally general rule of retrodiction exists and, if so, whether it is uniquely determined remains nontrivial. Here we prove that a retrodiction assignment defined for all priors and channels, which takes each predicted output state back to its prior, must coincide with the Petz transpose map if it is involutive, respects sequential and parallel composition, and agrees with unitary inversion. The theorem holds for channels between finite-dimensional full matrix algebras, with the input and output spaces restricted to the supports of the corresponding reference states. In particular, affinity under probabilistic mixtures and the characteristic square-root dependence on the reference states follow from these requirements rather than being postulated. Without involutivity, the remaining requirements characterize a family of doubly rotated Petz maps. Our result thus explains why the Petz transpose map arises in seemingly different areas of quantum theory: it is the unique quantum analogue of Bayes' rule compatible with these consistency requirements.

We study the dynamics of an ensemble of $N$ two-level emitters undergoing collective decay at rate $Γ$ and collective incoherent pumping at rate $R$, confined to the fully symmetric Dicke ladder. Although the population dynamics are confined to a finite set of rate equations, their quantum-trajectory representation involves infinitely many pump-decay histories. We derive an exact finite continued fraction for the Laplace-transformed Dicke-state populations by resumming the infinitely many quantum trajectories generated by competing pump and decay processes. Our construction provides a physically transparent interpretation of the tridiagonal resolvent and extends to arbitrary permutationally symmetric initial states. In the strong- and weak-pumping regimes, we obtain perturbative transient solutions. We also identify exact relaxation eigenvalues and emission observables at balanced pump and decay strengths. Our solution provides a starting point for extending trajectory-based analytical methods to more general driven-dissipative collective systems.

Central to non-Hermitian sensing is the question of whether exceptional points (EPs) can make weak perturbations easier to detect. We show that despite enhanced spectral response, in finite-dimensional Lindblad systems with a unique stationary state and a nonzero relaxation gap, EPs offer no fundamental advantage in how the observation time required for reliable detection of a weak perturbation scales with the perturbation strength. We nevertheless demonstrate that by selectively choosing perturbations that enhance the quantum Fisher information rate, EPs can shorten the observation time needed to reach a predefined detection accuracy relative to a comparable non-EP reference at the same decay rate. As an illustration, we show using an optomechanical model at an EP that we can detect a weak force through the cavity output at the same reliability in less time than a non-EP reference. Our results establish fundamental limits on perturbation detection at EPs and can guide the design of faster non-Hermitian sensors based on optomechanical resonators, superconducting qubits, and trapped ions.

Mediated interactions between quasiparticles lie at the heart of Landau Fermi-liquid theory, yet their behavior in the strongly correlated regime is not fully understood. Motivated by recent experiments [Nat. Phys. 20, 68--73 (2024)], we investigate mediated interactions between quasiparticles emerging from a Fermi sea---Fermi polarons---using zero-temperature quantum Monte Carlo methods. Our main result is that the Landau interaction between polarons remains repulsive in the strongly interacting regime for any coupling strength in the polaronic branch, in contrast to the downward trend observed experimentally near resonance. Deep in the short-range universal regime, our results are insensitive to the microscopic details of the interaction potential, providing robust evidence for the sign of the ground-state induced interaction. In addition, we determine the real-space interaction between static impurities, recovering a Ruderman-Kittel-Kasuya-Yosida (RKKY)-like behavior at weak coupling and the nonperturbative Born-Oppenheimer result at strong coupling. More broadly, our results establish a microscopic benchmark for how Landau quasiparticle interactions survive beyond the perturbative regime of strongly correlated quantum matter.

It is not known whether a classical polynomial-time verifier can verify arbitrary polynomial-time quantum computations with an efficient quantum honest prover without computational assumptions. We show that, relative to a classical oracle, such verification is possible for a language beyond the polynomial hierarchy that is decided exactly in quantum polynomial time. The protocol is public-coin, with perfect completeness and soundness error at most 1/4. To our knowledge, no language with such a proof system was previously proved to lie outside AM relative to an oracle. For every unbounded polynomial-time computable function, the oracle can be chosen so that the message count and the oracle query counts of the quantum algorithm, verifier, and honest prover are bounded by this function of the input length. The message count is optimal up to a constant factor, since for a suitable oracle every interactive proof system for the language uses at least a constant fraction of the messages of our protocol on infinitely many lengths, with a constant depending on its verifier. The language is a variant of recursive Fourier sampling in which code tables encode secrets that address data tables. The tables are evaluated recursively, and the oracle stores only the leaves. The quantum algorithm recovers every secret exactly, and the verifier checks the prover's secrets recursively against random code entries. The recursion restricts the input in a correlated way, as the same secret fixes the code bits and chooses the free coordinate, so Håstad's switching lemma does not apply. We prove a switching theorem for these restrictions, which may be of independent interest. For instances of sufficient height, no constant-depth circuit of size $2^{\mathrm{poly}(n)}$ changes its output with probability above $2^{-Ω(n)}$ when the answer of a random instance is flipped by changing a single leaf.

Dynamical quantum simulations are commonly designed to access a particular response function or correlation function. Yet the underlying protocol prepares a family of many-body states that contains information well beyond the observable for which the simulation was originally designed. In this work, we explore the idea of using these states as laboratories for quantum information. As a case study, we consider the local-pulse protocols used to compute Green functions in finite XX and XXX spin chains, and we interpret opposite source rotations as encoding a classical bit into the many-body system. This allows us to follow how the resulting record propagates, how it is encoded across local subsystems, and how readily it can be accessed with different measurements. We also find a clear separation between representation and readout. While fermionic covariance data exactly reconstruct the signed response in the XX chain, simple spin measurements recover a larger fraction of the locally available information in the XXX chain. This reversed ordering persists when we move from finite-pulse discrimination to local source-angle estimation. Going beyond the source record, the same reduced states also allow us to reinterpret results in terms of Bell state recovery and quantum communication rates, as well as providing direct access to the evolving bipartite and genuine multipartite entanglement of the system. Our results show that dynamical quantum simulations developed for response calculations can naturally be used to ask a much broader set of quantum-information questions about the many-body states they already prepare.

Compilation of two-qubit Fibonacci anyon gates is complicated by leakage ($\ell$) from the four-dimensional computational sector to the fifth state of the fusion space. We construct a GPU pipeline to find low-leakage representatives of the $[\text{CNOT}]$ class on different subsets of the braid group. We exhaustively explore the full positive five-generator alphabet up to $L=21$ with minimal leakage $\ell\sim10^{-3}$ and error $d_{[\text{CNOT}]}\sim 10^{-8}$ on it. To reach larger lengths, the search space is successively narrowed to three-generator, boundary-$σ_3$, and palindromic braids, and by considering only the Garside left normal form. These optimizations allow us to reach $L=72$. For $L=69$, a braid with $\ell\sim10^{-10}$ and $d_{[\text{CNOT}]}\sim 10^{-10}$ is found. In addition to directly enumerating optimal braids, we proved that $\ell\in\mathbb Z[\varphi]$, and any nonzero leakage obeys an exponential lower bound in the braid length, and obtained the limit laws $F_{3,\infty}(\ell)=\ell^2$ and $F_{5,\infty}(\ell)=\ell^4$ for our sets. Using asymptotics for the distribution function $F$, we showed that for sufficiently long braids, the asymptotics of exhaustive search are better than the asymptotics of random sampling for finding low-leakage braids.

Exact normalizable solutions of quantum constraints form a symplectic submanifold of the space of rays, whereas classical first-class constraints define a surface on which the symplectic form is degenerate. We ask how the degenerate directions can be recovered when quantum theory is regarded as fundamental and the constraints are imposed through a single positive master operator. For a nonnegative master function whose zero set is a Morse--Bott critical manifold, the image of the linearized Hamiltonian vector field is the symplectic orthogonal of the zero set, and coisotropy is equivalent to this linearization having square zero. The image is fixed by the zero set, but the theorem identifies it with the response of the master dynamics, which makes it accessible to quantum states. Three realizations follow. The exact quantum physical space is the opposite, rotational case of the same dichotomy. For quadratic masters, the bottom of the spectrum is $(\hbar/2)\Tr_+L$, so first-class zero sets carry no offset of order $\hbar$; within the harmonic approximation this explains the $\hbar$ versus $\hbar^2$ offsets observed in tests of the master-constraint programme. Finally, the second time derivative of the limiting covariance of a semiclassical packet, which can be determined by bounded probes, has the gauge distribution as its image. Two oscillators at fixed total energy give exact master evolution, an exact realization of this covariance shear, and the reduced symplectic limit. For the non-Abelian SL(2,$\R$) model we compute the coherent and Weyl master symbols, prove essential self-adjointness and a finite-time propagation estimate, and derive the spectral bottom $\hbar^2/2$.

The "Rayleigh limit" is not an intrinsic property of light, but a consequence of sub-optimal measurement of collected photons by the imaging instrument. To overcome this limitation, we present Adaptive Information Mining, a framework that achieves super-resolution by using sequentially refined measurements for incoming photons. Our approach employs a reconfigurable imaging system that dynamically reshapes the instrument measurement responses to maximize the Fisher information and guide scene estimation toward the fundamental quantum limit, even in deep sub-Rayleigh regimes. We demonstrate that this approach achieves an estimation error 2-5 times closer to the fundamental quantum limit than traditional direct imaging when imaging point sources, without requiring any prior knowledge of their positions and brightnesses. Importantly, we demonstrate that AIM can be extended to fully blind multi-parameter estimation in scenarios involving an unknown number of sources or turbulence-induced wavefront distortions. Our approach addresses the limitations of conventional fixed imaging, offering a practical path toward quantum-limited super-resolution imaging.

We derive an alternative formulation of the stochastic master equation describing the evolution of quantum systems continuously measured via homodyne detection in a squeezed-thermal environment. This formulation allows us to identify two distinct collapse operators, corresponding respectively to the monitored and unmonitored channels, and to express the quantum state evolution directly in terms of Kraus-like operators. As a consequence, it facilitates the application of advanced numerical methods that account for higher-order corrections and discrete-time monitoring, and it also enables the efficient numerical evaluation of Cramér-Rao bounds in parameter estimation problems. To demonstrate the latter, we evaluate the Fisher information of the continuous homodyne monitoring for qubit frequency estimation in the presence of a squeezed-thermal bath. Our results show that exponential scaling of the steady-state Fisher information rate with squeezing is retained even at non-zero temperature.

We construct a rank-one minimal informationally complete measurement (MIC) with an invertible dual operator and prove that, for arbitrary finite input and output dimensions, a channel universally preserves measurement incompatibility if and only if its input space contains a noiseless code subspace of the full output dimension. Preserving the compatibility threshold of a finite family of binary measurements already guarantees such a code. Furthermore, for every $d\ge2$, there exists a family of binary measurements that is incompatible on the full space but compatible after compression to any proper subspace. These results resolve the conjecture of Chitambar and Zhang and the existence question posed by Uola and coauthors. We also give an explicit construction of exact encodings and show that, for a sufficiently small shift in the compatibility threshold, the transmission error of an approximate encoding is bounded by a constant times the square of the shift. These results establish a connection between measurement compatibility, quantum steering, and quantum error correction.

We analyze the security of an Ekert type bipartite key distribution protocol coming under cloning attacks by an untrusted observer. Precisely, an eavesdropper is assumed to intercept and apply an asymmetric, phase-variant cloner on one or both qubits which are transmitted over public channel from an authenticated source to the trusted parties. We partially characterize two-qubit states from the perspective of designing a QKD protocol that can generate a distillable secret key among the trusted users even under such cloning attacks. We rely upon Devetak Winter framework for computing key rate so as to identify states, which when used in the protocol, secret-key can be distilled. Utility of an entangled state, for designing a successful QKD protocol, changes from single-qubit to double-qubits cloning attacks. Interestingly, we can distinguish some useful families of two-qubit entangled states when only one of the transmitted qubits is cloned by a malicious third party.

Every quantum key distribution (QKD) protocol must limit the information available outside the users' laboratories. In device-independent QKD this is essentially the only assumption made on the devices. In a prepare-and-measure setting it cannot be imposed strictly, since the sender's device must emit a signal that depends on her private input. The natural replacement, and a minimal one, is a leakage bound: a bound on how much information about the input leaves the sender's laboratory, through the intended signal or through any side channel. We ask how far this unavoidable requirement can replace a detailed model of the source. We show that this single bound, quantified by the probability of guessing the input from everything the source emits, suffices to prove security against collective attacks. In our analysis, nothing is assumed about the precise form of the emitted states, their dimension, energy or purity, nor about the receiver's measurement device, beyond the standard requirement that it does not leak Bob's data. The standard B92 and BB84 protocols do not certify any key under this minimal leakage bound assumption. But closely related protocols can and, in the ideal limit, achieve one secret bit per key round. For noisy implementations, we compute key rates using semidefinite programming relaxations. Our best protocols tolerate visibilities down to 0.84, corresponding to an 8% quantum bit error rate, compared with the 11% threshold of standard device-dependent BB84.

Feynman once remarked that the double-slit experiment has in its heart the only mystery of quantum mechanics. Arguably, the scientific significance of double-slit experiments lies in motional decoherence and the mechanism behind it. Decoherence of motional states underpins our understanding of quantum-to-classical transition. It is also central to the operation of miniaturized quantum electron devices and poses a resolution limit for electron microscopes. In this work, we provide experimental evidence for the critical role of quantum Brownian motion in electron motional decoherence. We demonstrate, for the first time, clear signatures of electron-metal decoherence and its continuous tunability. Our experiment concludes a two-decade long search for experimental realization of the Anglin-Paz-Zurek proposal, establishing electron-microchannel systems as viable open quantum platforms for free-electron quantum optics. The quantitative agreement between experiment and theory further paves the way for testing the Caldeira-Leggett quantum dissipation theory with free electrons.

Establishing secure communication is an important requirement in existing and future networks. Although current solutions rely on classical approaches, quantum mechanics offers the possibility of moving from computational to information-theoretic security. Quantum key distribution (QKD) has been extensively studied as a means of achieving such security. Recently, epitaxial quantum dots started to be studied and employed in quantum cryptography, because of their rapid development that made them one of the brightest sources of quantum light to date. In particular, they are known to be excellent sources of polarization-entangled photon pairs, especially droplet-etched dots operating at $\sim$780 nm. Here, we employ such a quantum dot to generate entangled photon pairs under 1 GHz excitation rate. Using quantum frequency conversion, we interface the emitted photons with the telecommunication wavelength range while preserving their polarization entanglement. This enables quantum key distribution over a 1.59 km field-deployed fibre link across the University of Stuttgart - campus Vaihingen, using the BBM92 protocol: we achieve a secure key rate of 206 Hz over 19 h of stable operation, resulting in a total secure key length of 14.2 Mbit. This key enables the safe encryption and decryption of a colour image with further implementation of error correction and privacy amplification. These results demonstrate important steps towards hybrid quantum networks by combining high-quality entangled-photon sources operated at high excitation rates, efficient frequency conversion module, and picosecond-level time synchronization in a realistic deployed network.

Classical and quantum computers have achieved collaborative computation and completed applications across numerous fields. Nevertheless, the absence of a unified hybrid computation model has led to issues such as non-standardized engineering architecture design, ambiguous task partitioning criteria and so on. To address these issues, this research proposes a hybrid classical-quantum computation model (HTM). By constructing unified state sets and transition function representations, HTM clarifies hybrid control logic and implements a control-sharing mechanism. Simultaneously, a comprehensive complexity calculation method based on entanglement and superposition was proposed, supporting computation task partitioning and resource scheduling. The HTM fills a theoretical gap in the classical-quantum hybrid computation area and implements the joint promotion and development of computing models and hardware.

We construct explicit quantum circuits for the velocity-stress formulation of elastic wave equations in homogeneous media using Schrödingerisation. After rewriting the equations in symmetric matrix form(SMF), we use Fourier spectral discretization for source-driven periodic problems and staggered-grid finite differences for Dirichlet, Neumann, and impedance boundary conditions. The Schrödingerisation method transforms any linear PDEs into a system of Schrödinger-type PDEs -with unitary evolution- using the warped phase transformation that maps the equations in one higher dimension. For periodic problems, we develop circuits by combining controlled Fourier-mode rotations. For physical boundaries, interleaved encoding swaps the spatial and field-component registers, enabling a more efficient circuit construction using shift operators. We analyze $p$th-order Trotter-Suzuki formulas and derive splitting-error and CNOT-gate estimates, under the assumptions of smooth auxiliary initialization and solution-state recovery. Comparison with classical partitioned splitting methods identifies a polynomial improvement in spatial-resolution dependence for the quantum state-evolution subroutine. Noiseless circuit simulations of a forced periodic problem and an impedance problem illustrate the constructions and quantify their errors against exact solutions and classical reference computations.

Space-based quantum information networks require simulation tools that capture orbital dynamics, probabilistic quantum operations, and classical coordination. We introduce QNETSIM, a modular discrete-event simulator for the design and performance evaluation of satellite and hybrid space-ground quantum networks. The framework integrates orbital geometry, free-space optical and fiber channels, quantum memories, entanglement generation, and Bell-state measurements within a common event-driven architecture. Physical models account for optical loss, atmospheric turbulence, detector imperfections, finite memory capacity, and storage-induced decoherence. Space-time routing and segmented nesting support entanglement distribution across changing topologies, while a software-defined control plane coordinates generation, storage, and swapping. Configurable scenarios encompass onboard repeaters, satellite constellations, ground-based repeaters, and direct satellite distribution. Through explicit interfaces between physical models, network protocols, and orchestration, QNETSIM links component characteristics and operational policies to entanglement fidelity, throughput, latency, availability, and memory utilization, enabling systematic exploration of architectural and resource-management trade-offs in future space-based quantum information networks.

We compare two three-particle lattice models on the square lattice at total quasimomentum zero: three identical bosons with attractive contact interactions, and a two-fermion plus one distinguishable particle system with attractive interspecies contact. Using the Birman--Schwinger principle combined with symmetry reduction and strong-coupling asymptotics, we distinguish shared methodology from model-dependent spectral conclusions. For bosons, the ground-state energy behaves as minus three times the coupling plus six minus three over twice the coupling plus higher-order corrections, and exactly two bound states exist below the threshold for large coupling; the second lies at a finite distance 0.03542 below the threshold, a genuine eigenvalue rather than a threshold resonance. For fermions, the critical mass ratio is pi divided by pi minus two, approximately 2.75194; above it, a doubly degenerate level appears at strong coupling. Near onset, the binding energy follows a linear-over-logarithmic law. The results are compared with numerical finite-grid Faddeev computations and with recent three-dimensional classifications of threshold states.

We establish an equivalence between matrix samplers and quantum-proof randomness extractors. The classical sampler--extractor equivalence is established by a seminal work of Zuckerman (Random Structures & Algorithms, 1997). Using this equivalence, we construct explicit strong matrix samplers with optimal randomness overhead and near-optimal sample complexity via constructing quantum-proof extractors. Specifically for matrix dimension $D$, accuracy $\varepsilon$ and failure probability $δ\leq\varepsilon$, our matrix sampler uses $m+O_α(\log(D/δ))$ random bits and $O_α(\varepsilon^{-2-α}\log^{1+α}(D/δ))$ samples, for any constant $α>0$. Compared with the matrix sampler of Xun and Zuckerman (CCC 2025), our construction has improvements in two aspects. Under the same optimal random seed length, we can replace the $\operatorname{poly} D$ dependence in the number of samples by $O(\log^{1-γ} D)$. Under the same scale of sample size, we can remove their $\log\log D$ factor in the length of the random seed. Our underlying strong quantum-proof extractor has output length $n-O_α(a+\log(1/η))$ and seed length at most $(1+α)\log a+(2+α)\log(1/η)+O_α(1)$ for $n$-bit sources with conditional min-entropy $n-a$ and error $η$. We also obtain strong quantum-proof extractors for every constant entropy rate, for any error as small as $2^{-Ω(n)}$, having optimal seed length $O(\log(n/η))$ and output length $Ω(n)$, improving previous constructions.

Training the circuit of a quantum generative model is hampered by barren plateaus, where gradients vanish exponentially with the number of qubits. In the present work we propose a generative protocol based on the paradigm of quantum extreme learning machines, in which the circuit is never trained. A random latent vector is encoded into a quantum state, evolved with a fixed unitary and measured, and only a linear output layer is trained. The encoding of the latent variable determines the functions available to the model, while the unitary decides which combinations of them are seen by the trained layer. With the help of Pauli propagation we show that for a Clifford unitary each feature is a single product of sines and cosines of the encoded angles, so that a Clifford circuit, even a strongly entangling one, does not create new functions. Doping the circuit with $T$ gates mixes these products and changes the nonstabilizerness of the state, but the space of functions remains the one fixed by the encoding. For brickworks of Haar-random two-qubit gates the features are no longer single products, and their variation with the latent variable decreases with the depth of the circuit. For the proposed encoding and for one- and two-dimensional distributions, generated both from expectation values and from single measurements, neither the entanglement produced by a Clifford reservoir nor the additional nonstabilizerness of Haar-random brickworks systematically improves the generator, and a reservoir with no gates at all is competitive with entangling circuits.

Certifying motional entanglement generated by weak forces between levitated nanoparticles requires distinguishing entangled from separable states using finite, noisy measurement records. We show that the number of measurements required to certify Gaussian entanglement can vary among equally entangled states, and quantify this variation. We derive an attainable lower bound showing that, near the separability threshold, the required number of measurements diverges inversely with the square of the distance from this threshold. We translate the required number of measurements into an experimental certification time, comparing two protocols under comparable experimental conditions: release--recapture, in which particles evolve freely before measurement, and continuous monitoring, in which the steady state is measured continuously. We find that release--recapture enables entanglement certification at interaction strengths several orders of magnitude weaker. Moreover, minimizing certification time can favor states with less entanglement, revealing a trade-off between entanglement generation and its certification. These results highlight the role of certification in the design and optimization of ongoing efforts to probe weak-force-mediated entanglement between levitated nanoparticles.

Recently, strong-to-weak spontaneous symmetry breaking (SW-SSB) has been established as a framework for describing quantum phases in open systems. However SW-SSB cannot be characterized by conventional charged two-point correlators. In this work, we show that, for strongly $\mathbb{Z}_2$-symmetric states with local charged involutions, SW-SSB manifests as a persistent deficit from the maximal quantum Fisher information (QFI) under symmetry-neutral pair rotations. A model-independent inequality hierarchy establishes the equivalence of this deficit with fidelity and Rényi-1 correlators as asymptotic long-range-order diagnostics. It thereby connects finite-angle state overlaps to a constraint on the infinitesimal Bures geometry along the same pair-generated orbit. For symmetry-projected Gibbs states, we further derive a lower bound on the deficit governed by the mean energy injected by the pair operation. Crucially, locality keeps this energy cost uniformly bounded in system size and endpoint separation, maintaining a finite gap below the maximal QFI at any fixed finite temperature. When ordinary charged long range order is absent, this persistent geometric constraint provides a quantitative information-geometric characterization of thermal SW-SSB.

The properties of quantum vacuum are highly sensitive to the underlying spacetime geometry and boundary conditions. We investigate in this paper the decoherence dynamics of a two-level system (detector) coupled to a vacuum scalar field through the $\hatσ_z$-coupling scheme under various boundary environments. By rigorously evaluating the reduced density matrix of the detector, we derive an exact general expression for the detector's decoherence function, $γ(Δt)$, and use it to characterize the dynamical decoherence of a detector in three scenarios: free space, a perfectly reflecting boundary, and a cavity formed by two parallel reflecting boundaries. We find that in free space the detector's coherence decays monotonically with time, indicating that vacuum fluctuations alone inevitably lead to a complete loss of coherence. In the single-boundary case, by contrast, the detector's coherence displays non-monotonic time evolution: $γ(Δt)$ increases with time up to a maximum and then settles to a steady value, indicating that the initial coherence can be partially preserved due to the presence of the boundary. When the detector is placed inside a cavity, its coherence evolution exhibits oscillatory behavior, and a significant fraction of the initial coherence survives. Moreover, for the same detector-boundary distance, more coherence is preserved in the cavity case than in the single-boundary case. These results provide a viable route for engineering quantum coherence via boundary conditions.

The detection and localization of gamma-ray sources via maximum-likelihood analysis is a complex parameter optimization problem. We address this challenge using quantum annealing, a computational approach that solves optimization tasks by encoding them into the ground state of an Ising Hamiltonian. Specifically, we apply this method to observations from AGILE's Gamma-Ray Imaging Detector (GRID) in the 30 MeV-50 GeV band. We reformulated the standard analysis as a Quadratic Unconstrained Binary Optimization (QUBO) problem. We tested this method on a set of AGILE observations generated with AGILEpy, solving the QUBO with simulated quantum annealing. The method reproduces the classical flux and position estimates within their statistical uncertainty and identifies the correct grid node among the candidate positions in 97% of the maps. These promising results demonstrate that quantum annealing could be used in this optimization problem, laying the ground for its deployment on actual quantum annealers.

The time-evolving matrix product operator (TEMPO) method efficiently simulates non-Markovian open quantum system dynamics by contracting a two-dimensional tensor network representing the time-discretized Feynman-Vernon influence functional. The standard form of this network has an unfavorable scaling with the size of the system. We show that, within the usual second-order time-step error, the dimensions of all internal network bonds can be reduced to $(2m+1)(m+1)$, where $m$ is the number of independent coupling channels. This dimension does not depend on the number of distinct eigenvalues of the coupling operators. The system size only enters in the final boundary layer of the network, making large system sizes accessible to TEMPO methods. This structure was discovered by Claude Opus 5.5 during guided algorithm development.

In theories with compact extra dimensions, the four-dimensional effective description is obtained by Kaluza-Klein reduction. The state available to a four-dimensional observer is the reduced density matrix obtained by tracing the higher-dimensional vacuum over the tower of massive modes, and it need not be pure. In this paper we study the momentum-space entanglement of this state for a five-dimensional scalar on $M_4\times S^1$ with a cubic or quartic self-interaction. We compute, at leading order in the coupling, the mutual information $I_n$ between the zero modes below a resolution scale $μ$ and a single Kaluza-Klein level $n$. When the zero modes couple linearly and without derivatives to pairs of tower modes, $I_n$ falls as $1/m_n$, where $m_n$ is the mass of level $n$. In the cubic theory, this tail is independent of the ultraviolet cutoff, with coefficient $(μR)^2/1024π^3$ for compactification radius $R$, and the mutual information with the whole tower grows logarithmically with the number of levels. In the quartic theory, the tail is masked by states containing additional hard quanta, which make $I_n$ depend on the cutoff. Compared with the corrections the tower makes to low-energy amplitudes, which are dominated by the lightest levels and captured by local operators, the mutual information with the tower is not dominated by any finite set of levels and arises from the time-nonlocal part of the effective action. The local four-dimensional effective theory therefore describes the low-energy observables of the reduced system but not its state. Unbroken supersymmetry cancels the vacuum energy of the compactification but not the mutual information, which at leading order is a sum of squared amplitudes.

We present a novel approach to embed node-attributed graphs onto neutral-atom quantum computers, and propose an application to digit recognition. Our approach extends PASQAL's quantum evolution kernel (QEK) by introducing a node-level feature encoding based on three-level quantum states. To this purpose, we present a prototype showing how the resulting embedding can be leveraged to extract correlation-based information for classification tasks. The entire quantum process is simulated using Pasqal's Pulser library, which inevitably imposes constraints on the size of the experimental datasets. We compare our method with classical baselines to evaluate its potential. We show that, for the digit recognition task, our method achieves a higher mean accuracy than the more commonly used Jensen-Shannon distance-based methods by utilizing the Wasserstein distance.

Mutation testing assesses test suites by introducing program changes and checking whether tests detect them. In quantum programs, a surviving mutant may leave program behavior unchanged, produce a change hidden by the chosen input or measurement, or remain undetected because statistical evidence is insufficient. We develop a circuit-aware framework to distinguish these causes and guide execution planning and test changes. The framework covers ideal, noiseless programs and mutations that replace one gate or subcircuit. The method traces how a mutation can affect measured outputs and combines established mathematical checks with statistical estimates. For supported cases, we establish conditions under which a test cannot reveal a mutation and exact formulas for its effect when the required state information is available. Under stated assumptions, we bound the mutation score while retaining surviving and unresolved mutants, and identify a restricted circuit family whose mutation effects admit efficient classical classification. The deliverables include a decision procedure, mathematical guarantees, worked examples of test changes and their implementation requirements, and a small-circuit reference implementation for differential expectation tests. These results help testers decide what to execute, what to change, and what remains unknown. The evidence is limited to proofs and executable examples under the ideal model.

We study the persistent quantum and classical memory required for exact heralded storage and retrieval of quantum measurements. Given only black-box access to the measurement channel, we construct an exact compression of the port-based program into an outcome-type record and a quantum register, with total dimension polynomial in the query count. For every universal retrieval processor we prove the bounds $Q+C\ge\log_2 n$ and $2Q+C\ge\log_2\bigl((n-1)d^2+1\bigr)$ on the numbers $Q$ of qubits and $C$ of bits of the program, for $n$-outcome POVMs on $\mathbb{C}^d$ with $d\ge2$. For $n\ge2$, no finite classical memory removes the need for quantum memory: any such processor requires a quantum program of dimension at least $d$, at that dimension its classical alphabet must have at least $n$ symbols, and both minima are attained by a single-query protocol with success $1/d^2$. Combining direct-program compression with a converse from approximate measurement programming gives logarithmic total-memory scaling in $1/(1-p)$ as the uniform success probability $p$ approaches one, at fixed $d,n\ge2$. At fixed input dimension and target success below one, the optimal total-memory scaling is logarithmic in $n$. We also construct self-contained programs under branch-decomposition access and compare the quantum and classical costs of all constructions, including where the outcome-type record is kept: for POVMs with $n$ nonzero rank-one effects the direct program admits a purely quantum allocation whose register is never larger than that of the minimal-Naimark unitary program and which succeeds more often whenever $n>d$.

Shuttling-based trapped-ion quantum computers (QCCD) rank among the most mature hardware platforms. Existing and envisaged devices exhibit architectural differences in terms of register layout and connectivity. Platform-specific compilers are required to translate quantum circuits into resource-optimized hardware-level command chains. Hardware platforms and compiler software stacks are mostly developed independently of one another by different research communities. This work aims to bridge these communities by abstracting QCCD architectures and native operations, enabling computer scientists to address compilation problems using generic methods without requiring a deep background in the physical operating principles of the platform. The resulting design space is organized into a small set of architectural archetypes, each posing its own compilation problem. We then select and apply compilation methods to one- and two-dimensional QCCD architectures, finding that the routing overhead scales approximately cubically with the number of qubits for the one-dimensional architecture and approximately quadratically for the two-dimensional one. Extending this to compilation with a quantum error-correction layer reveals additional differences and similarities between the physical and logical levels. We conclude that co-design is a requirement rather than an option, and this work provides the vocabulary, archetypes, and compilation abstraction it needs.

We show that interblock correlations can reverse magic-state distillation even when every input exceeds the threshold for independent states. For the five-to-one Bravyi-Kitaev protocol with independent local Clifford twirls, we express the output in terms of measurable target-axis moments. Fourth-order correlations determine acceptance, while third- and fifth-order correlations determine the output polarization. This relation yields a direct sign test for distillation gain and opposite gains for inputs with identical single-qubit and two-qubit reduced states. We connect this mechanism to neutral-atom resource preparation through finite-range Ising dynamics. Block separation suppresses detrimental interblock coupling, and locally addressed Clifford phases release interaction-generated magic from a spin-squeezed precursor by changing the symmetry selected by code projection. A protocol that retains accepted source outputs achieves positive gain above a source-contrast threshold set by circuit errors and storage dephasing. The same moments specify a finite-sample experimental diagnostic. These results connect the correlation structure of a resource state to its preparation, acceptance, and distillation gain.

Decoherence of qubits is one main limitation in quantum information processing, where the qubits themselves can be mixed because of decoherence and additional decoherence may generated through interactions with a bath. Here, we present a complete study of qubit-environment entanglement in the case of interactions that lead to pure dephasing of the qubit by allowing the initial state of the qubit to be mixed, exceeding previous restrictions. We find that the criteria for separability that hold for pure initial states of the qubit are reduced to witness status. Yet, the evolution of the witnesses reflects the array of features that entanglement can exhibit in the mixed case but are forbidden in the pure-qubit case. Most notably, this includes sudden birth of entanglement as the initial phase of the evolution is typically separable. Moreover, there is a stark numerical advantage to the study of entanglement for large environments when using the witness rather than the traditional measures available. We include the study of entanglement generated between a spin qubit and a sparse spin environment to illustrate the peculiarities of the evolution of entanglement in this case, as well as to emphasize the level of reliability of the entanglement witness.

Effective field theories (EFTs) offer a powerful method to unify diverse models under a small set of control parameters, allowing systematic expansions around well-established theories. While these techniques were traditionally developed for particle physics experiments with clean, isolated initial states, realistic macroscopic environments are often noisy and dissipative. Recognising the limitations of traditional EFTs has recently sparked intense progress at the interface of high-energy physics and condensed matter. These developments motivate a new approach to gravitation and cosmology, one that models the gravitational sector as evolving in the presence of an unobservable medium. Open Effective Field Theories provide a systematic, controllable framework for this endeavour. This chapter presents this versatile framework and illustrates how the Schwinger-Keldysh formalism captures the influence of unknown environments, manifesting as dissipation and noise, on observational probes. These notes are based on a series of lectures held during the La Ricotta Summer School "The Disordered Universe 2025" from 21 July to 1 August 2025.

Bosonic-qubit encodings provide diverse approaches to storing and processing quantum information, with logical operations often implemented through encoding-specific physical strategies. Here, we identify a class of bosonic Fock-based qubits in circuit QED for which distinct implementations of arbitrary Z rotations share a common structure. We formulate this structure as a six-step protocol that provides a unified procedure for implementing arbitrary Z rotations across this class of bosonic cQED qubits. The applicability of the protocol is determined by a specific condition on the encoding, providing a criterion for identifying bosonic Fock-based cQED qubits that admit the common implementation.

The performance of a quantum battery depends not only on its ability to retain stored energy against unwanted discharge but also on the amount of useful work that can be extracted from it. Here, we investigate these complementary aspects in an ensemble of V-type qutrits coupled to a lossy cavity. By applying a finite splitting pulse to the two excited states of each qutrit, cavity-bright excitations are converted into atomic dark states, whose populations remain protected upon restoring degeneracy, even while the light-matter coupling remains active. Simulations with finite-duration pulses reveal a capture window governed by the competition among energy transfer, bright-to-dark conversion, and photon leakage. We further show that if the energy is stored in the fully symmetric atomic subspace, the passive energy is bounded by twice the transition energy for number of atoms $N\geq2$. Consequently, if the stored energy scales extensively with $N$, the ratio of extractable work to stored energy approaches unity in the thermodynamic limit. Comparing different initial preparations at equal mean input energy, we find that coherent-state can yield greater finite-time ergotropy despite capturing less energy, whereas Fock-state favors greater extractable work in the stationary component. Our results demonstrate how controlled dark-state population trapping in an atom-cavity coupled system can protect stored energy while providing a conditional route toward high extractable work.

Additive codes over $\Ffour$ that are self-orthogonal under the trace inner product correspond to binary quantum stabilizer codes. We study 1-generator $(1,2)$-quasi-cyclic (QC) additive codes and their exact quantum distances. For composite lengths $n=\ell m$, an ancestor-lifting theorem transports dual words of the folded ancestor to the length-$n$ code. A two-layer decomposition for $\ell=2$ and a CRT splitting for odd $\ell$ yield dimension laws and explain equality, escape, and mixed-branch behavior in the certified examples. A palindromic criterion ensures symplectic self-orthogonality, while reversal pairing and a symplectic Gram rank formula describe broader construction families. Exact distances are established by information-set decoding screening, Brouwer--Zimmermann computation on the additive dual, and independent witness verification. We certify twenty-one record-breaking binary quantum codes across twenty entries of Grassl's code table, with twenty-eight certified members in total. Propagation improves thirty-four further entries, and explicit constructions are supplied for three table-tying GV entries marked Code Missing Construction. Six additional candidates are reported only with rigorous upper bounds and heuristic screening evidence. The results connect divisor-lattice structure in additive quasi-cyclic codes with reproducible certification of exact quantum distances.

We present a state preparation procedure that takes binary registers containing the real and imaginary parts of a complex number $z=x+iy$ and prepares an amplitude approximating $z/α$, where $α$ is a normalization constant. The magnitude and argument are computed using the Coordinate Rotation Digital Computer (CORDIC) algorithm. We then encode the magnitude into an amplitude, and apply phase gates to introduce the argument. A reversible in-place multiplier allows the coordinate updates to use fixed precision while clearing their temporary workspace. The procedure uses $O(n^2)$ $T$ gates and $O(n)$ additional qubits. Compared with separately encoding the real and imaginary parts and combining them through LCU, the construction can allow a smaller normalization and reduce amplitude-amplification costs. The computed polar representation also remains available for further arithmetic before amplitude-encoding.

For two Gaussian preparations of a detuned degenerate parametric amplifier below threshold, the trace distance shows a lasting Mpemba reversal, whereas the relative entropy eventually restores the initial order and the Hilbert--Schmidt distance alternates indefinitely. All three diagnostics agree on the initial order, and these orders persist on open sets of preparations and quadratic generators. The disagreement is possible because a real relaxation mode and a complex-conjugate pair share the leading decay rate, a coincidence that holds for any single-mode quadratic oscillator with linear damping in the elliptic regime. Number symmetry hides their competition in the undriven trace-distance tail, and parametric driving exposes it. Near a pure stationary state, the relative entropy strongly weights changes of the symplectic eigenvalue, which approximately follow the nonoscillating energy deviation; thermal occupation weakens this preference. A first-order splitting rule shows that weak number dephasing and two-photon loss favor the real branch, whereas a Kerr interaction with the same sign as the detuning favors the pair. We quantify the thermal-occupation and dephasing tolerances and estimate the measurement precision needed to observe the disagreement. Whether a Mpemba reversal is lasting therefore depends on the diagnostic and on the observation window.

We investigate the nonequilibrium dynamics of a kinetic slush state realized via facilitated excitations in a two-dimensional dissipative Rydberg atom array. Utilizing kinetic Monte Carlo simulations in the strong dephasing regime, we show that tuning the laser detuning to compensate for nearest-neighbor interactions enables facilitated dynamics, while residual next-nearest-neighbor interactions induce kinetic frustration. This competition gives rise to an emergent slush phase characterized by pronounced dynamical heterogeneity and the coexistence of liquid- and solid-like configurations. By probing its nonequilibrium real-time evolution, we uncover a dynamical crossover from isotropic spreading to one-dimensional constrained growth, which can be continuously tuned by the frustration strength. Within this crossover regime, the slush dynamics generate fractal cluster geometries and generalized Ornstein-Zernike spatial correlations. Finite-size scaling analysis supports the system's proximity to criticality. Our findings establish driven-dissipative Rydberg systems as a highly controllable platform for engineering complex nonequilibrium soft-matter phenomena.

Variational quantum algorithms are leading candidates for practical utilisation on noisy intermediate-scale quantum (NISQ) processors, but accumulating noise bounds the usefulness of circuit depths. For the quantum approximate optimisation algorithm (QAOA), this trade-off has mostly been addressed by searching for the best depth for a given device. In this work, we consider the inverse question: how much noise each depth can tolerate. Using GPU-accelerated noisy QAOA simulations for MaxCut on three graph families with 6 to 18 vertices, depths up to 10 and three noise channels, we fit the approximation ratios with a generalised logistic surface. We propose the effective noise threshold as the inflection boundary of the logistic surfaces, a noise boundary separating reliable and unreliable QAOA approximation regimes. In general, the threshold decreases as depth rises, indicating that deeper circuits demand for stricter noise requirement for reliable approximation. Its best and worst values over depth divide the noise axis into three regions: every depth remains effective, depth must be chosen with care, or no depth induces effective optimisation. Assessing on the ibm_marrakesh processor, although modelled gate errors understate factual noise, the threshold modeling remains beneficial in informing qualitative depth-dependence structure and identifying dominating noise channel in noisy QAOA.

Gauge-Higgs theory in flat spacetime provides a prime theoretical model of multiple phases of matter with distinct entanglement structures. More recently, there has been interest in hyperbolic space and the influence its extensive boundaries have on these structures. Entanglement transitions between non-equilibrium phases, such as topological phases, can be realized by the competition of non-commutating measurements. Here we study the entanglement phases of gauge-Higgs models on hyperbolic lattices described by measurement-only dynamics. We chart 2D phase diagrams by employing topological entanglement entropy and introducing a generalized measurement-induced entanglement tailored for hyperbolic Higgs phases. Utilizing duality, we find a phase absent in Euclidean space, wherein the bulk lattice hosts separated clusters of symmetry-protected topological order. Transitions between this "archipelago" phase and neighboring topological and trivial phases feature a critical exponent $δ$ belonging to a mean-field universality class. Our essential tool is a 3D resource state inspired by measurement-based quantum computation that simulates the spacetime evolution of the 2D quantum state with a third direction of entanglement. This allows us to analyze spacetime "sponges" of entanglement, which map to classical percolation theory and allow us to infer values of critical points on our phase diagrams' boundaries.

We study the minimum number of orthogonal projective measurement settings needed to estimate multiple observables without bias for arbitrary input states. We derive structural bounds that go beyond dimension counting and combine them with explicit constructions to certify minimum setting counts for selected target spaces. A classical variational algorithm searches for shared measurement bases and optimizes their readout coefficients and sample allocation. For the collective first and second moments of two qubits, we certify that four projective settings are necessary and sufficient. For this task, a numerically optimized four-setting design achieves a Haar-averaged variance within approximately $0.0341\%$ of a lower bound valid for any number of projective settings in our fixed-allocation, unbiased linear estimation model. Numerical examples show that shared measurements can improve precision relative to the comparison protocols. For finite-depth circuits, we account for reconstruction bias and identify finite-sample regimes in which this advantage persists.

Fisher zero lines of the Loschmidt amplitude in non-Hermitian quenches can exhibit anomalous structures in the complex time plane, such as divergence, separation, and the restriction of all branches or a specific branch to the real or imaginary axis. Here, we use the biorthogonal framework to reveal the origin of these structures and determine the corresponding critical momentum conditions by analyzing the values of $m_k=\hat{\mathbf{h}}_0\cdot\hat{\mathbf{h}}_1$, the dot product between the normalized prequench and postquench complex Bloch vectors. When Fisher zeros continuously cover the real-time axis, the density of Fisher zeros is further introduced to identify the critical times within these critical regions, at which the rate function becomes nonanalytic. We verify our results in a generalized non-Hermitian SSH model by quenching the Peierls phase and the non-Hermitian gain-loss strength, and also use the Jordan form to analyze the dynamics at postquench exceptional points, where the conventional Fisher zero formula is not applicable.

We study with the semiclassical model the dynamics of a particle moving in a orthorrombic lattice by the hopping mechanism in the presence of a static Coulomb field and a rapidly oscillating homogeneous field. Based on results for the anisotropic Kepler problem, where a chaotic trajectory arises due to different masses of the particle in the X and Y directions, and since this result is also obtained in the rectangular lattice at the continuum limit, the application of the oscillating field allows reparameterizing the effective masses so that they become equal in both directions. Thus, the result is an elliptic trajectory in the continuum limit of the lattice. This chaos-order transition is confirmed by the calculation of Lyapunov exponents for the different trajectories. It is also found that the application of an external magnetic field in the Z direction of the lattice yields chaos control which can be generalized beyond the simple case of the circular trajectory shown in this work. The previous scheme of chaos control was extended for trajectories in 3D in the continuum limit of the orthorrombic lattice which is also equivalent to the far region approximation where the particle moves with respect to the Coulomb field origin. In this case it found that the chaos control technique permits to observe two different dynamical regimes which, although consistent with Bohr-van Leeuwen theorem, suggests that an observable way to distinguish one from the other is to be sought.

Coherent spin-photon interfaces are essential for scalable quantum networks, but their realization requires optically bright transitions, long-lived spin coherence, and complete coherent control. Donor-bound electron spins in II-VI semiconductors offer an attractive platform for optically active spin qubits because they combine strong donor-bound exciton transitions in a direct-bandgap material with a potentially nuclear-spin-free environment. However, coherent control of an individual optically active donor spin has remained elusive. Here we demonstrate optical initialization, coherent control, and readout of a single donor-bound electron spin in ZnSe. Using spin-selective donor-bound exciton optical transitions, we initialize the electron spin and directly resolve its spin-relaxation dynamics. We achieve coherent spin control with off-resonant picosecond optical pulses, as demonstrated by spin Rabi oscillations and Ramsey interference. We further coherently drive two spin-selective optical transitions and observe high-contrast coherent population trapping, demonstrating the formation of an optically controlled dark state. At higher driving strengths, multiple dark resonances reveal the hyperfine interaction between the electron and the I = 3/2 Cl nucleus. These results establish the first coherent optical control of a single donor electron spin in a II-VI semiconductor and identify isolated optical donors as a promising platform for solid-state optically active qubits.

Two new Bohr-Sommerfeld (B-S) type quantization conditions for $d$-dimensional radial potentials are proposed for non-singular and singular potentials, respectively. The power-like potentials \hbox{$V=\operatorname{sign}(m)\,r^m$} for $m=-3/2,-1,-1/2, 1,3,4,6$ and $V=\log r$ (that corresponds to $m=0$) are studied in detail for radial quantum numbers $n_r \in [0,100]$ and for angular momenta $\ell=1,2,3,4,5$ in dimensions $d=2,3$. It is shown that for large $n_r$ the B-S energies $E_{BS}$ always tend to the exact ones. For $m=2$ (the radial harmonic oscillator) and $m=-1$ (the $d$-dimensional analogue of the $3D$ Coulomb potential) the B-S spectrum coincides with the exact one for the first and second quantization conditions, respectively. In general, up to a small parametric shift of the radial quantum number, the analytic formulas for the energy spectrum can be written for arbitrary power-like potential. A comparison of $E_{BS}$ with the energies $E^{(L)}_{BS}$, obtained for the radial potentials modified by the Langer correction for $d=3$, are in good agreement in general: in detail, it was checked for the quartic oscillator $V=r^4$. It is demonstrated that introducing a dimensionless {\it WKB correction} $γ$ into the r.h.s. of the proposed B-S type quantization condition allows us to reproduce the exact energies with $γ$ being very small for positive degrees $m \geq 0$ and sufficiently small for non-positive ones $m < 0$ for all $n_r, \ell$ studied.

Spin-orbit coupling makes the mean position of a spinning particle transform anomalously under a Lorentz boost, with an additional shift known as a side jump. In this work, we develop a trace method to derive an exact but compact transformation kernel for the probability center of a general three-dimensional Dirac wave packet under an arbitrary finite Lorentz boost. The expression includes the physics of finite momentum width, spin-momentum correlations, and coherent phase structure without a semi-classical expansion. We identify texture-dependent side jumps even at fixed initial mean momentum, spin, and orbital angular momentum, as well as a non-monotonic mass dependence for Gaussian packets at fixed momentum width. The explicit kernels further resolve the spin and orbital angular-momentum contributions for massive and massless fermions, providing a kinematic basis for covariant particle-based spin transport that retains wave-packet information.

Consensus algorithms are mechanisms driving nodes of a network to agreement. In quantum networks they also redistribute information encoded in the global quantum state, allowing global properties to be inferred from local measurements without reconstructing the global state. Motivated by this, we investigate decentralized quantum consensus in qudit networks governed by discrete random unitary dynamics. We characterize the analytic asymptotic dynamics, identify global information preserved by the evolution, and derive conditions for which different notions of quantum consensus emerge. A general theorem is derived that establishes a unified framework for extracting globally encoded information from local measurements beyond consensus states. First, we analyze CNOT networks and determine which global information can be recovered by individual nodes and which requires joint measurements on cooperating nodes. The CNOT model is well understood and presents a case with entanglement creation - a characteristic quantum feature of networks worth analyzing in detail. Second, we identify the complete class of two-qubit interactions that asymptotically achieve consensus on the average number of excitations, thereby establishing a quantum analogue of classical average consensus. We further show that joint measurements on k cooperating nodes recover exactly the first k moments of the excitation-number distribution.

Cavity quantum magnonics has ushered in an unprecedented era of hybrid light-matter interfaces in which microwave photons, collective spin excitations, and superconducting or spin qubits can be coupled within a single device architecture, facilitating a versatile platform for quantum information processing. Realizing their full potential, however, requires a theory that can treat non-reciprocal magnetic media, material dissipation and open-cavity radiation losses, as well as finite-temperature fluctuations rigorously and without significant approximation. The dissipative magnonic resonances of such systems are described as quasinormal modes (QNMs), yet a consistent quantization procedure for lossy gyrotropic resonators has remained elusive. In this work, we present a finite-temperature quantum QNM theory, based on macroscopic quantum electrodynamics for non-reciprocal media and complex coordinate transformations, that achieves QNM quantization for a wide class of spatially inhomogeneous, dissipative and dispersive, cavity magnonic systems. We demonstrate the predictive capabilities of our theory via applications to hybrid dielectric-magnonic resonators interacting with both spin and superconducting qubits, evidencing modal interference effects, a continuous transition from coherent to dissipative coupling, spatiotemporal quantum field dynamics, and magnon-mediated qubit synchronization, at both zero and finite temperatures. By addressing the intricacies of modal loss and non-reciprocity in a fully quantum theory of cavity magnonics, our approach enables the quantitative design of hybrid quantum devices that operate under realistic open-system and thermal conditions, without recourse to ad hoc quantization schemes.

As superconducting quantum processors scale to large qubit counts, unwanted microwave drive crosstalk becomes an important source of coherent errors. Here, we investigate the role of parasitic coupling paths in the suppression of drive crosstalk in a processor with two fixed-frequency transmon qubits and a tunable coupler. To account for the many different coupling paths, we develop a detailed circuit model to capture the dependence of crosstalk on the coupler frequency. We experimentally demonstrate suppression of crosstalk, finding that the suppression does not originate solely from cancellation of the effective qubit-qubit coupling, but also is a result of interference between other coupling paths. Building on these insights, we show that drive crosstalk can be suppressed with the right choice of parasitic capacitances, which otherwise often are treated as unwanted design imperfections. Our results provide practical guidance for low-crosstalk device design of superconducting quantum processors and point toward a broader strategy in which parasitic coupling paths are engineered rather than simply minimized.

For finite-dimensional quantum channels compatible with a faithful conditional expectation, we show that conditional hyperboundedness and strict GNS contraction together yield a relative entropy contraction. For KMS-symmetric quantum Markov semigroups, a conditional $2\to q$ hyperboundedness at time $t_0>0$ combined with a GNS gap $λ>0$ implies a modified logarithmic Sobolev constant \[ α=\frac{λ(1-2/q)} {12(λt_0+\log M+1-2/q)},\] where $M$ is the hyperboundedness constant. As a consequence, completely bounded hyperboundedness over auxiliary systems gives complete versions of entropy contraction with the same rates.

Quantum networks are built from independent sources, and their nonlocality has mostly been studied with sources that emit bipartite entangled states. A source of three entangled qubits is richer, since its nonlocality can be tested by the Mermin or the more demanding Svetlichny inequality. We ask how network nonlocality relates to these two single-source notions and find that the answer depends on the wiring. When two central nodes without inputs share every source, Bell-state measurements turn every Svetlichny violation into a network violation, and even all entangled generalised Greenberger-Horne-Zeilinger states violate the network inequality. When a single central node is shared, the relation reverses, and a network violation requires a Mermin violation of the source. With more sources, the maximal violation depends on whether their number is even or odd, and we give tight bounds for both cases. These results show that the way multipartite sources are wired decides which kind of nonlocality a network inherits.

We study discrete-time quantum walks with Fourier, Grover, and Hadamard coin operators on disordered square lattices, alongside classical random walks. Edges in the lattice are absent with a probability, $p$. In this case, both classical and quantum walks exhibit an essentially identical degradation of transport. We then study a general version of this model, in which the existing edges are retained. However, the absent edges are no longer absent, but now become partially transmitting, with a transmission coefficient $f$. We find that the response is now quite sensitive to the walk protocol and coin symmetry. The classical walk exhibits asymptotic stability of the anomalous diffusion exponent, $β(t)$. In comparison, quantum walks exhibit a monotonically decaying $β(t)$ beyond the initial transient regime, leading to the absence of quantum diffusion in two dimensions. We map the transport regimes in the $(f,p)$ plane and identify the contour for $β=1$, which separates the subdiffusive and superdiffusive regimes. We also examine the effective diffusion coefficient, the inverse participation ratio, and the first two moments of edge transmission. We restrict ourselves to analyzing bulk propagation prior to finite-size boundary reflections. The results indicate that quantum transport depends significantly on coin-specific interference and cannot be fully described by transmission statistics alone.

Discrete nonlinear dynamical systems arise in population models, iterative optimization, and numerical simulations, where computing many iterations can be costly in high dimensions. We study Carleman embedding for forced quadratic discrete systems and its application to quantum state preparation. Under explicit stability and initial-state assumptions, we prove that the truncation error decreases geometrically with the embedding degree, uniformly over all iterations. A central obstacle in discrete time is that the lifted update can become dense even when the original coefficient maps are sparse. We overcome this obstacle by constructing an exact auxiliary linear-system representation that applies the coefficient maps one tensor factor at a time, with row and column sparsities bounded independently of the truncation degree. After rescaling, the associated history system has a condition number that grows linearly with the iteration count, uniformly in the truncation degree. These results yield a quantum algorithm for preparing an approximation to the normalized $n$th iterate with constant success probability. Under coherent input-access assumptions, and for fixed sparsity, stability parameters, and a known positive lower bound on the final-state norm, the oracle query complexity is linear in $n$ and polylogarithmic in the inverse accuracy. Numerical experiments in one and three dimensions illustrate the convergence of the truncated embedding.

We describe a family of convex continuous functions $E_{F,\varepsilon}$, $\varepsilon\in(0,1]$, on the set of states of a bipartite quantum system (consisting of finite-dimensional or infinite-dimensional subsystems) obtained by applying the Mora-Piani-Briegel construction of $\varepsilon$-measure (proposed in [Phys. Rev. A 109, 052413]) to the Entanglement of Formation (EoF) with the use of the trace norm distance in the role of basic metric. These functions are non-increasing in $\varepsilon$ and converge pointwise to the EoF as $\varepsilon\to0^+$. We conducted a detailed analysis of properties of the functions $E_{F,\varepsilon}$, using (among others) the relationship between the family $\{E_{F,\varepsilon}\}_{\varepsilon\in[0,1]}$ and the family $\{E^λ_F(ρ)\}_{λ>0}$ of Moreau-Yosida approximations of the EoF explored in [arXiv:2609.30246]. We obtain a variational expression for the functions $E_{F,\varepsilon}$ (which for $\varepsilon=0$ turns into the standard variational expression for the EoF). We also describe the weak subadditivity property of the functions $E_{F,\varepsilon}$ and analyse their continuity properties. The semicontinuity bounds for the EoF (presented in [Lob.J.Math., 46, 2632-2658],[arXiv:2404.07978]) allow us to obtain easily computable upper bounds on the rate of uniform convergence of the function $E_{F,\varepsilon}$ to the EoF as $\varepsilon\to0^+$ on the sets of states with bounded rank/energy of one of the marginal states. Applicability of the obtained results to other entanglement measures, in particular, to the relative entropy of entanglement, is discussed. As an auxiliary result, it is shown that for any state of an infinite-dimensional bipartite quantum system, there exists a nearest separable state w.r.t. the trace norm distance. The non-uniqueness of such a state is also shown.

We construct a controllable imaginary-time Mpemba effect in quantum spin systems using spatially modulated local rotations without changing initial bipartite entanglement spectra and correlation magnitudes. This feature unambiguously isolates the redistribution of spectral weights as the sole driver of the anomalous relaxation. Using the compact-boson description, we reveal that these twists act as precise mode selectors: higher-harmonic twists exclusively populate high-energy standing waves, structurally bypassing slow-decaying infrared modes to accelerate convergence. We derive exact analytical crossing times for these reversals and demonstrate that intentionally reintroducing the slow-mode population systematically delays the ITME. This exact mechanism is validated beyond the fixed-point theory via calculations on interacting XXZ chains and ladders. Furthermore, a twelve-qubit simulation of variational quantum imaginary-time evolution reproduces the reversals and their controlled delay, providing a concrete route to realize this protocol in realistic quantum circuits. Ultimately, these results provide a strictly controllable and exact starting point for realizing and investigating the imaginary-time Mpemba effect, establishing a foundational paradigm to harness anomalous non-equilibrium relaxation in quantum ground-state preparations.

Tantalum thin films are used in low-loss superconducting quantum circuits, yet the growth conditions governing selection of $α$-Ta(110), $α$-Ta(111), and metastable $β$-Ta on c-plane sapphire remain uncertain. We deposited 100 nm Ta films by dc magnetron sputtering on Al$_2$O$_3$(0001) at 300-900 $^\circ$C while varying the O$_2$ partial pressure from a $5.5\times10^{-11}$ Torr ultrahigh-vacuum baseline to $2.23\times10^{-4}$ Torr. Absorption-corrected X-ray diffraction texture coefficients were used to construct a ternary phase-orientation growth map in terms of temperature and the oxygen-to-Ta impingement flux ratio ($2Φ_{O_2}/Φ_{Ta}\leq4.8\times10^{-6}$ to 19). Without added oxygen, $α$-Ta(110) dominated at every temperature. At an O$_2$ pressure of only $2.5\times10^{-9}$ Torr ($2Φ_{O_2}/Φ_{Ta}=2.2\times10^{-4}$), $α$-Ta(111) accounted for 98-99% of the normalized texture weight from 300 to 700 $^\circ$C, decreasing to 65% at 900 $^\circ$C. Substantial $β$-Ta formed only at the highest oxygen dose, dominating at 300 $^\circ$C and disappearing at 900 $^\circ$C. The apparent $β$(001)/$α$(110) selection energy of $1.07\pm0.16$ eV is comparable to the activation energy for oxygen diffusion in Ta, consistent with oxygen transport influencing phase selection. Oxygen also produced orientation-dependent changes in crystallite size and microstrain. These findings establish oxygen-controlled processing windows for phase- and orientation-selective growth of Ta films for superconducting devices.

Higher-dimensional theories distinguish the dimensionality of a microscopic description from the number of directions accessible to a physical observer. Relating these notions requires not only dimensional reduction, but also a consistent preservation of operational independence across different levels of description. We establish sufficient conditions under which a compositional operational rank is preserved first as the dimension of a smooth integral leaf and then as an observable Fisher-information rank. The key requirement is closure-faithfulness: the smooth realization must preserve the dependency relations of the operational closure, rather than merely its total rank. Together with real representability, constant rank, involutivity, and observer/scale compatibility, this yields a local integral leaf whose dimension equals the operational rank. A further primary-identification condition is required at the measurement level. If an independently specified observer image coincides locally with the primary integral distribution and the admissible protocols provide local resolution, finite labeled-mixture closure, and locally constant outcome support, then the same rank can be realized by a finite composite Fisher-information protocol. The construction holds for arbitrary finite rank. At r = 4 it provides a conditional operational criterion for dimensional reduction in higher-dimensional theories: a viable reduction must preserve the relevant operational dependency structure, not merely produce four effective coordinates. Quantum-hardware negative controls further show that the same restricted Fisher rank can conceal different larger ranks under a broader pre-specified measurement protocol. The framework therefore constrains the operational outcome of dimensional reduction without imposing a universal four-dimensional bound on microscopic state spaces.

We introduce a family of positive maps on qudits whose Choi operators combine two competing coherence patterns: independent exchange couplings and a collective set of diagonal couplings. For every mixed member of the family, we derive exact conditions for positivity, complete positivity, and all intermediate levels of k-positivity, and we determine the complete phase structure of decomposability and atomicity. The higher-positivity thresholds depend on the channel multiplicities, whereas the exact decomposability boundary is universal in scale-free coordinates. Its proof combines an explicit positive-plus-copositive decomposition with a matching family of positive-partial-transpose (PPT) states. The latter form PPT edge states whose detection region is an ellipse, or a disk after collective rescaling. An embedded-qutrit certificate shows that indecomposability and atomicity coincide throughout the mixed family. In contrast, the purely collective endpoint is decomposable over its entire positive interval. Finally, at maximal coherence, an explicit positive subtraction produces an atomic optimal entanglement witness with the spanning property and a strictly larger PPT- detection set. The study thus provides an exactly solvable setting in which k-positivity, decomposability, atomicity, PPT-edge-state geometry, and witness optimality can be compared in arbitrary local dimension.

Real-time decoding is a fundamental necessity for building fault-tolerant quantum computers. In this work, we introduce decoding with alternating weighted graph sparsification (DAWG), an ensemble based approach that combines Tanner graph sparsification with ensembling belief-propagation (BP) decoders. The DAWG decoder runs BP decoders over the full detector error model Tanner graph for certain iterations to then transfer the posteriors to a sparsified graph in which additional rounds of BP are run. Each of the decoders in the ensemble uses a different transfer matrix to map the posterior information to the sparsified graph. We use the serial schedule for the minimum-sum BP decoders and, thus, employ Vibe decoding ideas by randomizing the schedules of each of them. The performance of the DAWG decoder is then numerically studied for bivariate bicycle codes and superdense color code circuits to be compared with other state-of-the-art decoding approaches. Importantly, the DAWG decoder shows a similar performance to Relay belief-propagation and Vibe decoding when combined with an order-$0$ Localized Statistics Decoding (LSD-$0$) post-processor. Crucially, the post-processor is called an order of magnitude less times than for Vibe with the same ensemble size, indicating that the introduced latency tail will be minimal. Furthermore, LSD-$0$ operates on a sparsified decoding graph of a fraction of the size of the full detector error model, which simplifies the resources required by specialized hardware to support it. Overall, the DAWG+LSD-$0$ decoder represents a viable low-cost BP-based decoding algorithm for quantum error correction codes.

Quantum batteries are quantum systems that potentially serve as fuel for other quantum devices by receiving and supplying energy. In this work, we propose a theoretical scheme to enhance ergotropy and charging power of quantum Battery in the system under consideration through squeezed light. Moreover, The system comprises a coherently driven charger cavity, a strongly dissipative auxiliary cavity acting as a mediator, and an energy--storage battery cavity. Quantum nonreciprocity and directional energy flow are established via destructive quantum interference between the direct coupling path and the loss--engineered indirect path. A degenerate optical parametric amplifier integrated into the charger cavity acts as an active, phase--sensitive energy source that injects two--photon quantum excitations and anomalous correlations. Using a strictly open--quantum--system framework derived directly from the Lindblad master equation, we obtain the full expectation--value dynamics and stationary states. We show that active parametric driving drastically increases the stored energy and peak charging power while maintaining nonreciprocal energy trapping in the battery. We achieve a multi-order-of-magnitude boost in the battery's stored energy, charging power, and ergotropy. We also analyze the effects of pure dephasing on the charging power, ergotropy, and extractable work quality.. Although two--photon pumping introduces photon--number fluctuations that slightly lower the fractional ergotropy ratio ${\cal W}_{\rm B}/{\cal E}_{\rm B}$, the absolute extractable work remains substantially elevated compared to unassisted configurations.

We prove continuity of distillable entanglement, the optimal asymptotic rate at which copies of a bipartite state can be converted into maximally entangled pairs by local operations and classical communication (LOCC) with vanishing error. We establish an explicit asymptotic continuity bound that holds for arbitrary bipartite states and depends logarithmically on the system dimension. This bound has the same structure as known continuity bounds for conditional entropy, entanglement cost, and relative entropy of entanglement. Our proof constructs an explicit LOCC protocol that converts either of two arbitrary bipartite states into the other at an ebit cost that vanishes as their trace distance tends to zero.

We recently proposed an entanglement distillation protocol based on local operations and classical communication that probabilistically and universally distills a maximally entangled Bell pair from multiple copies of an unknown two-qubit state [Phys. Rev. Lett. 135, 260202 (2025)]. Here, we investigate the robustness of this protocol against imperfections in its implementation. We consider several incoherent and coherent gate-error models, as well as measurement readout errors, and determine the regimes in which distillation enhances the fidelity with the target Bell state. We find that the protocol remains effective over substantial error ranges, although its robustness depends strongly on the type of error. We further analyze asymmetric errors between the two parties and identify conditions under which complementary postselection outcomes yield identical distillation dynamics, allowing the success probability to be enhanced.

Generative models use training data to produce new samples that resemble the original, with applications in classification and recommendation systems. Restricted Boltzmann Machines (RBMs) are at the core of generative models but suffer from the computational intractability of training, which relies on sampling an unknown Boltzmann Distribution (BD). The Quantum Approximate Optimization Algorithm (QAOA) can assist RBM training, potentially providing benefits over strictly classical strategies. One particular problem is determining the quantum circuit depth for an arbitrary problem size that yields the expected sampling results. In this study, we evaluate QAOA-assisted sampling of BDs using Qiskit's Aer Simulator by analysing the inverse effective temperature of the distribution, $κ$, for tractable problem sizes. The results provide numerical evidence, based on Qiskit Aer simulations, that parameterized annealing-scheduled QAOA (PAQ-QAOA) can approximate RBM Boltzmann sampling for the tractable instances considered, while hardware performance and scaling remain open questions.

We propose a hybrid quantum-classical method for reconstructing energy-level degeneracies and thermodynamic properties of spin systems. A single ancilla qubit is used to measure the partition function at imaginary inverse temperatures. For spectra lying on a known equally spaced energy grid, the inverse discrete Fourier transform allows exact reconstruction of degeneracies in the absence of noise, without spectral leakage. The quantum circuits are optimized using commuting interactions and Eulerian ordering. We demonstrate the method for frustrated Ising antiferromagnets on periodic Kagome graphs with up to 36 spins, using the ibm_kingston quantum processor. Despite substantial circuit depth and hardware noise, the reconstructed spectra retain their dominant features, and the calculated heat capacities reproduce the main temperature dependence of the exact results. Keywords: partition function, imaginary temperature, Ising model, heat capacity, ancilla qubit, quantum computing.

Quantum-optimization-based computed tomography (CT) reconstruction has demonstrated quantum supremacy in reconstruction accuracy over conventional classical methods under sparse-view and corrupted-sinogram conditions. However, scaling this approach remains challenging because larger images require increasingly many binary variables and interactions in the underlying quadratic unconstrained binary optimization (QUBO) model. Even with iterative region-of-interest (ROI) refinement, a 60 by 60 ROI with three X-ray mass attenuation coefficients requires 10,800 binary variables under our encoding. As an initial step toward larger quantum CT images, we investigate simulated annealing (SA) followed by spin-error mitigation for optimisation (SEMO), without altering the CT-QUBO objective. We evaluate three 54-view ROI reconstruction instances and nine-view reconstruction with detector-row corruption, comparing SA and SEMO with selected hybrid quantum-classical solver results. For the ROI cases, SEMO reduced the numbers of incorrectly reconstructed pixels in low-budget SA outputs from 13 to 1, 38 to 0, and 54 to 15. With 20 percent detector-row corruption, three of four selected SA and SEMO pairs achieved exact reconstruction. Applying SEMO to one hybrid-solver output reduced its ROI error from 78 to 1 pixel. Improvements were instance-dependent: in one corrupted-sinogram case, QUBO energy decreased while image-domain error increased slightly; in one ROI case, the refined image retained 15 incorrect pixels despite having lower QUBO energy than ground truth. At the evaluated problem sizes, SA and SEMO attained reconstruction accuracy comparable to or better than selected unmitigated hybrid-solver results, providing an initial solution-quality benchmark for future larger-scale, parallelized quantum CT image reconstruction.

Quantum metrology relies on observables that maximize information about the parameter of interest, but are often hard to access. We develop a protocol that combines Pauli moments estimated from a fixed ensemble of randomized local measurements into an optimized method-of-moments estimator. For local Pauli classical shadows, we derive the shadow information which determines estimator variance and sample-complexity guarantees. Identifying the separable-state sensitivity limit, we show that entanglement can lead to a constant-factor sensitivity enhancement, as illustrated with one-axis-twisted probes. This protocol allows for efficient circuit-based metrology without choosing an observable.

In 2021, a low-background experiment at the Gran Sasso National Laboratory searched for spontaneous radiation predicted by the standard Markovian Diósi-Penrose (DP) dynamics and obtained the new bound $R_0 > 5.4 \times 10^{-11}\,\mathrm{m}$ at $95\%$ probability for the short-length cutoff parameter. For germanium at the experimental temperature, the parameter-free prescription identifying $R_0$ with the spatial quantum spread of a nucleus gives $R_0 \simeq 5 \times 10^{-12}\,\mathrm{m}$. That particular combination, Diósi's stochastic dynamics and the Penrose-motivated mass-density resolution, was therefore excluded. Subsequent searches strengthened the cutoff bound. The Majorana Demonstrator improved it in 2022, and XENONnT has now obtained the world-leading limits $R_0 > 4.9 \times 10^{-10}\,\mathrm{m}$ at $90\%$ confidence level and $R_0 > 4.5 \times 10^{-10}\,\mathrm{m}$ at $95\%$ confidence level. These advances reinforce the 2021 exclusion but do not alter its logical scope: they \emph{parametrically constrain} the Markovian, effectively white-noise DP dynamics, not Penrose's (and Diósi's) lifetime criterion independently of a dynamics, and not all colored-noise, dissipative, or otherwise modified gravity-related spontaneous collapse theories. We reconstruct what Gran Sasso did and did not rule out and place that conclusion in the present experimental context.

Equilibrium propagation (EP) is a powerful training algorithm for self-learning physical systems that is widely used for a variety of machine learning inspired tasks. It relies on the existence of an energy function that depends on tunable training parameters, and can be extended to apply to many-body quantum systems in equilibrium. A key challenge however is the need to repeatedly relax to the system ground state after each parameter update. We show here a route for circumventing this problem by extending EP to many-body driven-dissipative quantum systems, where the dynamics naturally relaxes to a parameter-dependent non-equilibrium steady state. Despite the lack of a free energy, we find that for a class of open systems, a quantum detailed balance symmetry still allows for an efficient EP strategy. This relies crucially on a new class of non-equilibrium static susceptibility relations that we derive in detail. We analyze examples of our new non-equilibrium training paradigm for two experimentally-relevant models: a driven-dissipative transverse field Ising model, and a parametrically-driven bosonic lattice.

Motivated by the search for non-equilibrium phases of matter beyond the Floquet paradigm, we propose a route to realize perfect revivals and time quasicrystals (TQCs) in a Fibonacci-driven central-spin model with Ising interactions between the central and satellite spins in the absence of disorder. We analytically demonstrate that when the interaction strength, $λ$ is tuned to $2 m π$, no entanglement is generated between the central and satellite spins at stroboscopic times, independent of the strength of the transverse driving field and the drive sequence. This leads to indefinitely long-lived quasiperiodic oscillations in satellite spin magnetization. Furthermore, for initial states with a definite bath magnetization, no entanglement is generated when the transverse driving field, $θ$ is tuned to $π$ for any value of $ λ$, and the satellite spin magnetization oscillations exhibit period-3 revivals at Fibonacci times. Examining the robustness of these oscillations away from this fine-tuned limit, we identify a parameter regime where the quasiperiodic response does not decay over the timescales probed, giving rise to a long-lived $π$-pulse-proximate TQC regime. We further show that at special Clifford points, the system exhibits perfect quasiperiodic oscillations of the satellite spin magnetization, with a parity-dependent Fourier response. This response persists over the timescales probed, even away from the Clifford points for an even number of satellite spins, leading to the formation of a Clifford-proximate TQC. Finally, we demonstrate that at this Clifford points, the system is steered along an entangled trajectory, leading to the dynamical generation of Bell-cat and spin-cat states. These states exhibit magnetization of collective spin fluctuates quadratically with the number of satellite spins, thereby enabling Heisenberg-limited metrology.

We highlight three geometric aspects of fault tolerance. First, we construct an operator-algebraic formulation of the fiber bundle framework for fault tolerance, and show that a generalization of the Knill-Laflamme conditions implies a flat connection for this framework. Next, we develop this framework for Gottesman-Kitaev-Preskill (GKP) codes. We show that, for each polarization type, their moduli space embeds smoothly into a Grassmannian of finite-dimensional subspaces of a regularized distribution space. Finally, we explain how GKP codes associated with Jacobians give rise to magic states that can be obtained by code space projections of Gaussian states and identify a $\rm CCZ$-type magic state arising this way.

The splitting method estimates logical error rates of quantum error-correcting codes deep in the rare-event regime, where direct Monte Carlo sampling is prohibitively expensive. It relies on a Markov chain Monte Carlo (MCMC) sampler of faulty configurations, usually driven by one-bit-flip proposals. However, one-bit flips have been reported to be trapped on some codes, which biases the estimate. To address this issue, we propose a new kernel that combines locally balanced one-bit-flip proposals with a cluster-exchange move. We benchmark both kernels and direct Monte Carlo on twelve codes under code-capacity bit-flip noise in two ways, by comparing the mean fault weight with an MCMC-independent reference and by measuring the computation time to reach a fixed accuracy. In the first, our kernel agrees with the reference on every code, including those where one-bit flips are trapped. In the second, it is faster than one-bit flips wherever they are trapped, by orders of magnitude on some codes. Furthermore, at the lowest error rate, it is faster than direct Monte Carlo on every code, by more than four orders of magnitude on some.

The earlystage of factory layout planning has a direct effect on the operating costs, efficiency, and productivity of manufacturing systems. Conventional automated planning approaches often face a trade-off between solution quality and computational effort. Recent studies have investigated the potential of quantum annealing (QA) for solving factory layout planning problems. However, existing studies have mainly focused on individual QA-based formulations, whereas current hybrid QA solvers support multiple model types that combine QA and classical methods. To explore the potential of QA for factory layout planning, this paper benchmarks four QA based approaches implemented with the corresponding solvers, including an iterative binary quadratic model (IBQM), a hybrid discrete quadratic model (HDQM), a hybrid constrained quadratic model (HCQM), and a hybrid nonlinear model (HNLM). To improve scalability, an iterative decomposition strategy is developed for IBQM, while a candidate selection procedure is introduced for HDQM. The approaches are benchmarked against genetic algorithm, particle swarm optimization, and a hybrid tabu search and simulated annealing approach on 14 layout instances with different layout sizes, geometric complexity, spatial restrictions, and transport route configurations. The comparative analysis considers solution quality, computation time, and scalability. The results show that QA-based approaches achieve competitive solution quality and substantial computational advantages, reducing computation time by up to 94.51% relative to the classical reference methods. Among them, IBQM obtains the best solution quality in 78.6% of the instances, with a maximum improvement of 17.41% associated with an 81.34% reduction in computation time. These findings provide a basis for their further application in industrial layout planning.

We study the entanglement between an electron and the photon it scatters, resolved in real space and time. Starting from nonrelativistic QED in Fermi's oscillator representation, we write Fock's coupled equations for components with fixed photon number in the photon configuration space, in the length gauge, where the photon is created around the atom through a nonlocal kernel. Truncated at one photon, the equations are solved numerically without the rotating-wave approximation for a one-dimensional model atom in a waveguide with a single transverse mode and enhanced coupling. The atom is driven by a short, off-resonant laser pulse, with the electron and photon represented on real-space grids. The global electron-photon entanglement is largely transient. It peaks during the pulse and decreases as the polarized electron cloud returns to the core, leaving a state close to a product of the electron state and a superposition of the field vacuum with a single scattered photon. Local entanglement, obtained from walkers sampled across both photon-number components, exhibits opposite spatial patterns for the two particles. The electron entropy is smallest at the nucleus and maps the local strength of the dipole coupling, whereas the photon entropy is largest near the atom, where photons are created and absorbed, and smaller in the outgoing wave packets.

We study the nonequilibrium steady states of an open anisotropic quantum Rabi trimer. Combining semiclassical and quantum mechanical treatments, we map out the system's phase diagram and elucidate the critical phenomena induced by anisotropic light-matter coupling, cavity dissipation, and complex photon hopping, which give rise to abundant multistable phases. Counterintuitively, the frustrated superradiant phase (FSP) can be stabilized by both positive and negative photon hopping, a feature absent in closed Rabi and Dicke trimers. We further uncover two independent dissipation thresholds for the normal superradiant phase and the FSP. Unlike isotropic open quantum Rabi trimers, both phases are suppressed once the dissipation exceeds their respective critical values. The rotating and counter-rotating interaction terms exhibit mutually reciprocal effects on the quantum phase transitions. By analyzing universal scaling behaviors with quantum fluctuations incorporated, we reveal an unprecedented finite-fluctuation critical exponent for the FSP. Moreover, the critical exponents of individual phases are coupling-strength dependent. The multistability and FSP can be tuned by anisotropy and dissipation. Our results broaden the scope of nonequilibrium quantum phase physics in few-body systems and hold promising applications for quantum state engineering and cavity/circuit quantum electrodynamics.

We characterize quasiclassical state conversion under thermal operations through population capacities: the maximum population that thermal operations can concentrate on each set of energy levels. These capacities form a normalized, nondecreasing submodular rank function whose base polytope is exactly the thermally reachable population region. Their bounds therefore provide a complete system of accessibility constraints. Every nested chain of capacities can be simultaneously saturated by a reachable state, yielding the maximum expectation value of any prescribed observable, including the system Hamiltonian. For a prescribed target, its thermomajorization prefixes suffice to certify exact conversion through at most $n-1$ binary work-extraction probes. For approximate conversion, we construct a distinguished reachable state from active capacity constraints using a weighted principal sequence in $O(n^2 \log n)$ operations. At fixed comparison weights, this state minimizes every weighted convex separable residual cost and realizes a common first contact with the corresponding target-centered smoothing regions. Finally, the optimal trace-distance error equals the largest capacity advantage of the target over the initial state. This gap is attained at a target prefix and equals the largest positive optimized energy-storage deficit among the same binary probes, divided by their energy gap. Thus a common population capacity geometry determines accessibility, observable optimization, conversion certificates, and universal approximation.

Multiplexing and photonic-electronic integration offer a route to scalable and high-throughput quantum key distribution (QKD) networks through parallel transmission and compact hardware suited to volume manufacturing. Realizing this route requires multichannel transmitters and receivers, and a security analysis accounting for mode coupling. Here we present a CMOS-compatible photonic-electronic multimode continuous-variable QKD architecture, using polarization multiplexing as a two-mode example. Silicon-photonic transmitter and receiver chips prepare and detect two polarization modes in parallel. The receiver is co-integrated with a dual-channel 28-nm CMOS transimpedance amplifier, providing shot-noise clearances exceeding 20 dB in both channels. Pilot-assisted unitary digital recovery removes the need for active optical polarization control, while a multimode security analysis accounts for the mode crosstalk. At 2 percent residual crosstalk, the multimode analysis extends the simulated secure distance from 39 to 84 km, near the crosstalk-free limit of 89 km. Over 10 km of deployed fibre, the mean total finite-size secret-key rate estimate is 6.69 Mbit/s, 12 percent above the single-mode analysis from the same digitally recovered data. These results establish a route to scalable multimode quantum-secured networks built on technology suited to mass production.

Entanglement equilibration need not mark the end of quantum-information dynamics in quantum thermalization. We show that the complete Schmidt spectra of a fixed tripartition can become stationary while its multipartite correlation structure, distinguished by local-unitary invariants, continues to evolve. This separation occurs exactly within a finite window in self-dual kicked-Ising dynamics and asymptotically in Haar-random circuits. We further demonstrate an independently tunable timescale for multipartite dynamics using quantum-error-correcting codes. When coupled to a locally scrambling bath, ordinary entanglement approaches equilibrium through rapid local scrambling, while weak logical--bath coupling drives a slower reorganization of multipartite correlations. These results reveal a deeper distinction than the ordering of equilibration times: bipartite entanglement and multipartite correlation structure can probe distinct physical channels of quantum-information dynamics, rather than merely different stages of the same relaxation process.

Dissipative algorithms for preparing thermal and ground states typically require a total Hamiltonian simulation time that grows at least linearly with system size $N$, even when their mixing time grows only polylogarithmically. We achieve sublinear simulation time for free fermions by engineering local interactions with a bath whose size grows in proportion to the system size. Starting from arbitrary initial states, our thermal state preparation algorithm achieves trace-norm error $ε$ in total simulation time $\widetilde{O}(\sqrt{N}/ε)$ at fixed inverse temperature and bounded single-particle bandwidth, while ground state preparation of gapped systems requires only $\mathrm{polylog}(N/ε)$ time. We further establish lower bounds for thermal state preparation within the bath protocols considered, identifying two obstacles to faster preparation, namely fourth-order deviations from the target thermal state and fluctuations induced by a random frequency shared by all bath qubits. Our results demonstrate that the linear simulation time barrier in dissipative state preparation can be overcome and clarify the bath and filter-design constraints that govern further complexity improvements.

For the quantum phase estimation (QPE) algorithm we study the minimal space of observables that is sufficient to predict the entire output distribution under open dynamics of the counting register. Building on the general Krylov theory of reduction, we compute the structure of this space explicitly for the full Fourier measurement. The outcome probabilities are determined by cyclic sums of the state matrix. If the adjoint generator is diagonal on the matrix units, the spectral classes inside the residue classes of the index difference modulo the register dimension $M$ give a constructive basis, an exact dimension formula, and attainable bounds: the dimension of the visible space lies between $M$ and $M^2-M+1$. The class includes independent qubit dephasing, and an analytically solvable reference model of Gorini--Kossakowski--Lindblad--Sudarshan (GKLS) type yields a damped Fejér kernel; two random-unitary channels with the same Ramsey contrast show that higher harmonics are distinguishable in the QPE distribution. For approximate reduction we use a finite-time Gramian and an a posteriori residual estimate, with a quadratic error order for a reducing unperturbed subspace and a compatible initial state. Numerical calculations check the consistency of the representations and the behaviour of the error under non-Toeplitz perturbations.

Rydberg-atom sensors have emerged as a promising quantum technology for broadband radio-frequency detection owing to their intrinsic calibration, wide frequency coverage, and high sensitivity. However, their potential for intelligent identification of real-world wireless signals remains largely unexplored. Here, we demonstrate a quantum-enabled framework for mobile signal classification based on Rydberg electromagnetically induced transparency spectroscopy and deep learning. Three types of wireless emissions, including cellular voice call, Wi-Fi, and 5G signals from three commercial smartphone brands, are measured to construct a spectral-fingerprint dataset. A convolutional neural network trained on this dataset achieves an initial baseline classification accuracy of 93.44\%. To compensate for spectral drifts induced by temporal and environmental variations, a progressive fine-tuning strategy is employed to continuously adapt the pretrained model, enabling robust classification across diverse deployment scenarios. Furthermore, continuous real-time monitoring is demonstrated under dynamically varying wireless conditions, including cellular voice call, Wi-Fi, and their coexistence. The proposed system achieves an overall frame-level recognition accuracy of 87.67\% over a 60-s measurement. These results establish a pathway toward intelligent quantum radio-frequency sensing and highlight the potential of Rydberg-atom platforms for real-time wireless signal awareness and spectrum monitoring.

The integration of bidirectional (V2G) charging allows electric vehicle (EV) fleets to operate as distributed energy assets. However, the joint optimization of charging schedules and trip assignments is NP-hard. Moreover, bidirectional power flows create non-monotonic state-of-charge (SoC) dynamics that weaken standard dual-based Benders cuts. We propose a hybrid quantum-classical Benders decomposition framework. To overcome the qubit overhead associated with encoding feasibility cuts, we introduce logic-based conflict cuts, which require near-zero auxiliary qubits. Furthermore, we develop a sparse recursive SoC formulation that reduces the constraint-matrix density by a factor of T/3 in the horizon length T. We demonstrate that our framework recovers MILP-optimal solutions on benchmark instances with a low auxiliary-qubit budget, and, as a minimal proof of concept, we execute a small instance end-to-end on IBM quantum hardware.

We identify the phase of a Bargmann invariant of two matter-wave interferometers as a quantum gravity signature that cannot be reproduced by any branchwise-definite classical gravitational field. For matter coupled linearly to linearized gravity, the interferometric coherence factorizes exactly into a conservative Newtonian phase, the characteristic functional of the graviton state, and a commutator phase. For Wigner-positive graviton states, the first two are classically reproducible; therefore, decoherence alone cannot certify that gravity is quantized. The Bargmann phase isolates the commutator, which is independent of the graviton state and of all Newtonian interactions and is bounded by which-path decoherence. For gravity, this radiation-reaction effect is sixty orders of magnitude below experimental reach, but trapped-ion analogs can test it at order unity.

Universal fault-tolerant superconducting quantum computers are expected to require millions of physical qubits; yet extending the prevailing dedicated-control-line paradigm to this scale would exceed the wiring density and cooling-power budget of dilution refrigerators. Microwave frequency-division multiplexing (FDM) revolutionized classical communications by enabling many independent channels to share common transmission infrastructure. Translating this principle to superconducting quantum control, however, requires an all-microwave architecture and experimental validation of frequency-multiplexed gate control. Recent work in quantum error correction has demonstrated microwave-based readout, single-qubit gates and leakage suppression, whereas two-qubit gates remain predominantly driven by unipolar pulses and thus constitute the missing element of an all-microwave architecture. Here, we propose a periodically extensible hybrid multiplexing framework in which all gate operations are frequency-division multiplexed using polychromatic microwave pulses and band-pass filters, thereby reducing the required control-line count by one to two orders of magnitude. In a 1:4 demonstration, we achieve average errors of $(6.4\pm0.2)\times10^{-3}$ for parallel FDM CZ gates and $(10.6\pm0.2)\times10^{-4}$ for parallel FDM $XY(π/2)$ gates, without statistically significant multiplexing-induced degradation. Together with on-chip DC sources, this FDM-based gate-control scheme completes the last missing module in a scalable multiplexed-control architecture toward universal fault-tolerant quantum computing.

In quantum simulation of electronic structure it is often expected that the estimate of the ground energy converges to the continuum basis limit at a rate of $\mathcal O(N^{-1})$ for a basis of size $N$. This has been found in analytical and numerical studies, but without a rigorous treatment of the error in the quantities considered in quantum algorithms. Here we show the $\mathcal O(N^{-1})$ scaling of the error for a wide range of cases needed for quantum simulation of chemistry. We show the error in the ground energy scales as $\mathcal O(N^{-1})$ for plane-wave as well as spatial grid bases. For the spatial grid we consider both a periodic system and a non-periodic system with open boundaries. For time evolution, our bound on the error in the state itself is weaker than $\mathcal O(N^{-1})$, but we show that the error in observables scales as $\widetilde{\mathcal O}(N^{-1})$ in important cases. In particular, we may consider a smoothed observable that describes the position of particles. We show that this error scales as $\mathcal O(N^{-5/3}+tN^{-1})$ for time $t$, again both for plane-wave and spatial grid bases. For the non-periodic grid case we use a condition that the true evolution would not result in significant leakage past the boundaries, which introduces basis error unrelated to the resolution of the discretisation. We also show the error in the kinetic energy of a particle scales as $\mathcal O((t+\log N)/N)$ for the plane-wave and grid bases. Together, these results show that $\mathcal O(N^{-1})$ scaling of the error holds for many of the relevant cases for quantum algorithms (with a trivial log factor for kinetic energy).

A Hybrid Quantum Neural Network (HQNN) is applied to recover the photometric redshift of a galaxy dataset built using data from two astronomical surveys, the Kilo-Degree Survey (KIDS) and the VISTA Kilo-Degree Infrared Galaxy (VIKING), which provide data with coverage from the optical to the near-infrared electromagnetic spectrum. The results are then compared with those obtained by a classical neural network. We see that HQNN consistently recovers the reference photometric redshift with a high statistical fidelity. Furthermore, both the $R^2$ and the MSE found by the HQNN are consistently better than those found by the classical counterpart (albeit consistent in the error range), proving the worth of further investigating these novel technologies for this particular astrophysical application.

In the multimode regime of cavity quantum electrodynamics (cQED), light-matter coupling can be strong enough such as to allows a quantum emitter to couple with multiple resonant field modes. This regime leaves distinctive signatures in the behavior of both the field and the emitter, which are already accessible by modern experimental techniques. To model such effects in lossy cavities, effective discrete-mode approaches have been widely employed, despite their accuracy beyond two modes remaining rarely benchmarked. In this work, we demonstrate the necessity of employing multiple modes to describe the multimode signatures by analyzing the dynamics of an atom in a one-dimensional lossy resonator. The atom's dynamics is simulated using the formalism developed in Weitzel et al. (2026) (arXiv:2512.18478), where a resonance quantization prescription is provided. We investigate its dependency with respect to two different parameters: the light-matter coupling strength and the atom's position. In the former case, we find that the minimal number of modes necessary to capture the essential features of the atom's dynamics increases with the coupling strength. In the latter, we further observe that the multimode regime leads to a strong position-dependency of the atom's dynamics. In all cases, we discuss the physical interpretation of our results and further discuss about how the employed formalism can be used to recover physically relevant quantities.

We characterize the exact trade-off between internal and external entanglement in asymmetric two-mode Gaussian states at fixed local symplectic eigenvalues. Internal entanglement is quantified by the negativity $\mathcal{N}_{A:B}$ between the two modes, while external entanglement is quantified by the negativity $\mathcal{N}_{AB:CD}$ across a Gaussian purification. Numerical sampling suggests the boundary structure of the attainable region in the $(\mathcal{N}_{AB:CD},\mathcal{N}_{A:B})$ plane, which we then determine analytically. Parametrizing the global symplectic spectrum yields a closed admissible interval for the remaining spectral parameter at fixed $\mathcal{N}_{AB:CD}$. We prove constructively that every point in this interval corresponds to a physical covariance matrix, implying that all intermediate values of $\mathcal{N}_{A:B}$ between the resulting sharp bounds are achievable. The upper bound is attained for opposite-sign correlations of equal magnitude, while the positive branch of the lower bound occurs when one global symplectic eigenvalue equals unity. We also identify two external-entanglement thresholds, derive a saturated monogamy-type inequality, and recover the symmetric-state limit.

We review how external electric fields reshape the information content of spatially confined atoms, and we contrast the response to a uniform static field with that to a monochromatic, time-dependent laser field. The central quantities are the Shannon entropies in position and momentum space, Sr and Sp, and their sum ST = Sr +Sp, which obeys the BBM bound. Using the confined hydrogen atom (CHA) and the particle in a spherical box (PISB), its tight confinement limit, as reference systems, we first show that the field-free total entropy of the CHA depends non-monotonically on the confining radius whereas that of the PISB is strictly scale invariant. We then present Stark maps of the entropies for the ten lowest m = 0 levels at the confining radius of 6 a.u. The ground-state polarizability is reduced from the free-atom value 4.5 a.u. to 4.06 a.u. in the CHA but is 46.8 a.u. in the PISB, and the entropic response of the two systems differs correspondingly.

Comparing solvers for quadratic unconstrained binary optimization (QUBO) requires distinguishing solution quality from optimality certification. We compare classical, tensor-network, and fixed-schedule quantum approaches on 180 benchmark instances from ten families with 14-48 variables, supplemented by harder synthetic instances with known optimal solutions, extending to 128 variables. On the main benchmark, a general-purpose branch-and-cut solver matches all reference energies and certifies 176 instances within a 600,s cap. When the known optima are moved to randomly chosen bitstrings, the search comparison changes: at n = 48 the branch-and-cut solver finds only four of ten optima and certifies none, whereas parallel tempering reaches every optimum in every tested run at a 60,s budget. Structural and trajectory diagnostics explain aspects of tensor-network performance. A treewidth bound ranks trajectory bond-dimension demand at Spearman $ρ= 0.78$ in sample and $0.73$ out of sample, but provides only a coarse runtime estimate. Controlled experiments identify excited-state trapping during warm-started density-matrix renormalization group (DMRG) sweeps and demonstrate mitigation by restarting the variational search. These diagnostics do not yield a validated solver-selection rule. The tested linear-ramp quantum approximate optimization algorithm (LR-QAOA) runs offer no solution-quality improvement over the classical comparators. In the separate Wishart scaling study, on the harder setting, none of the classical methods tested reaches the optimum at the sampled sizes from n = 72 onward within the tested budgets. While this does not provide evidence for quantum advantage, it identifies a domain for further investigation.

In classical simulations of quantum circuits, sampling shots (measurement outcomes) from the final state is a routine but costly step. In widely used software, including Qiskit and PennyLane, its cost grows linearly with the number of shots $S$, even when the simulation has already produced the full state vector, because every shot is generated and processed individually. If only the measurement counts are needed, this is unnecessary. The counts can be drawn directly from a multinomial distribution, decomposed into a sequence of conditional binomial draws, each performed in expected constant time by the BTPE algorithm. The sampling cost is then independent of $S$. We describe an implementation of this approach, which also shortens the computation for states whose probability is concentrated on a few outcomes, and compare it with Qiskit's sampling primitives for up to 20 qubits and $10^6$ shots. Our implementation is faster in every configuration tested, by a factor that grows with the number of shots and exceeds $10^3$ in most configurations at $S = 10^6$, and its samples are statistically indistinguishable from those of the reference implementations.

We construct self-correcting 3D surface codes over $\mathbb Z_q$ with local dimension $q$ growing with system size. The model preserves the local geometry and stabilizer support of the ordinary 3D surface code and remains translation invariant in the bulk, while modifying only the stabilizer Pauli powers. We use the Lee metric to characterize error weight and consider local Metropolis dynamics with single-qudit $X^{\pm1}$ and $Z^{\pm1}$ updates, each changing the energy by at most a constant independent of $q$ and system size $N$. We prove that, below the critical temperature, when the local dimension scales as $q=Θ(N)$, the memory times in both error sectors grow at least as $\exp\left[Ω(N^{1/3})\right]$. Our numerical results further support these analytical results. Together, these results establish growing local Hilbert-space dimension as a new resource for designing self-correcting quantum memories while retaining simple local geometry and local thermal dynamics.

Characterizing nitrogen-vacancy (NV) ensembles requires connecting their collective spectra to individual centers that experience different local environments. We develop a symbolic-regression pipeline that carries single-center spin structure into a calibrated ensemble model by generating individual spectral responses and combining them with explicit weights. A constrained search selects Hermitian operator terms from single-center optically detected magnetic resonance spectra, fits their coefficients, and retains the selected expressions as source models for the ensemble. Ensemble calibration then accounts for resonance shifts, local disorder, orientation, and optical response while keeping the individual spectral contributions accessible. On public single-center and ensemble data, the zero-field ensemble held-frequency root-mean-square error decreases from 0.008835 to 0.003872 in normalized photoluminescence, a 56.2% improvement over matched uncorrected composition. In controlled QuTiP ensembles of 128 sites spanning four NV orientations, models calibrated at 0 and 3 mT predict an independently held-out 5.17 mT spectrum with errors of 0.000207-0.000228 across three random seeds, comparable to the 0.000200 noise standard deviation. Resolving the simulated response into its individual-center contributions shows how local spectral diversity combines into the ensemble line shape. By retaining the source Hamiltonians while calibrating sample-dependent spectral differences, the pipeline connects local spin physics to collective optical readout and makes the contributions to an ensemble line shape available for physical interpretation.

We propose an arbitrary waveform generation architecture based on charge-coupled devices (CCDs) for qubit control. Waveform samples are stored as charge packets in CCD channels and sequentially clocked out as voltage samples. Multiple channels are operated in parallel and time-interleaved to achieve high effective sampling rates. The generated baseband waveforms are then upconverted to microwave frequencies to drive qubit operations. By representing waveform information as stored charge rather than as continuously generated or transmitted microwave signals, the proposed architecture provides a path to reducing cryogenic interconnect density and lowering heat load in scalable quantum control systems.

A state over time (stote) pairs a state $ρ$ with a channel $\mathcal{E}$ as the Hermitian, generally non-positive operator $(ρ\otimes\mathbf{1})\star J_\mathcal{E}$. Characterizing the convex cone $\widehat{\mathcal{Q}}$ these operators generate was posed as an open problem in~\cite{HoogstederCalsamigliaWinter2025}. We exhibit a linear copy of the bipartite separable cone as an exposed face of $\widehat{\mathcal{Q}}$: for output systems of the form $B = A'R$ with $A'$ a copy of the input, there is an explicit witness $W_0\in\widehat{\mathcal{Q}}^*$ and an explicit injective linear map $L$ with $σ\in \mathrm{SEP}_{+}(A{:}R)\iff L(σ)\in\widehat{\mathcal{Q}}(A{:}A'R)$. Composing with the NP-hardness of separability shows that exact membership, weak membership, and weak optimization are NP-hard for $\widehat{\mathcal{Q}}$ and its dual. A quantitative stability bound makes the weak-membership reduction valid at inverse-polynomial accuracy. Thus polynomial-time membership tests do not exist unless $\mathrm{P}=\mathrm{NP}$. Independently of this complexity assumption, Fawzi's theorem implies that $\widehat{\mathcal{Q}}(A{:}A'R)$ admits no finite semidefinite representation when $d=\dim A\ge2$, $r=\dim R\ge2$, and $d+r>5$.

Free-electron quantum optics has recently emerged as a promising platform for coherent electron-light interactions, yet its potential for quantum-enhanced metrology remains largely unexplored. Here, we investigate the fundamental precision limit of coupling-strength estimation in multi-electron photon-induced near-field electron microscopy (PINEM), demonstrating that the quantum Fisher information scales quadratically with electron number. We then propose an experimentally accessible scheme combining squeezed-light probing and optical homodyne detection that attains Heisenberg scaling with respect to electron number, provided the electrons exhibit nonzero inter-electron coherence, while surpassing conventional PINEM sensing in photon-number enhancement as well. We further analyze the effect of imperfect electron preparation, showing that electron phase noise is converted into a fluctuating optical displacement and eventually limits the precision. To overcome this limitation, an auxiliary optical mode coupled to the same electron ensemble measures the displacement noise in the signal mode, allowing its conditional suppression and recovery of the Heisenberg scaling. Our work establishes multi-electron coherence as a resource for free-electron quantum metrology and opens the route to precision measurements of nanoscale electron-light interactions.

We investigate the control and protection of two-qubit entanglement through engineered interactions between two auxiliary harmonic oscillators. Each qubit is coupled to a local oscillator via a dephasing interaction, while the oscillators interact through independently tunable position-position and momentum-momentum couplings. Employing the characteristic-function representation, we obtain analytical solutions for the composite-system dynamics and examine how the stability properties of the coupled oscillators determine the evolution of two-qubit concurrence. Our analysis reveals distinct dynamical regimes exhibiting entanglement revivals, suppression, or decay, and identifies configurations in which oscillator interactions effectively reduce entanglement degradation. We further investigate the influence of thermal dissipation using local and global master-equation descriptions, demonstrating that suitable oscillator couplings can preserve substantial two-qubit entanglement under the dissipative conditions considered. These results establish a connection between the dynamical stability of auxiliary bosonic modes and the controllability of entanglement in discrete-variable quantum systems, providing a potential strategy for entanglement protection through engineered oscillator interactions.

Quantum software development is challenged by quantum-mechanical semantics and fragmented software development kits (SDKs), which complicate cross-SDK code translation and execution. In this paper, we propose an LLM-based approach for translating executable programs between high-level quantum SDKs. We develop a quantum-aware translation workflow whose prompt design and validation reflect quantum semantics and accommodate the version evolution of quantum ecosystems. We conduct a preliminary evaluation of 4 LLM configurations on 43 tasks, translating Qiskit programs to PennyLane and Q#. LLMs achieve a zero-shot Pass@1 of up to 72.33%, while one-shot prompting further improves the translation effectiveness. These results suggest potential for quantum code translation by LLMs.

The Leggett--Garg inequality (LGI) constrains temporal correlations under the assumptions of macrorealism and noninvasive measurability. We study the four-time quantity \(K_4\) for two-flavor neutrino oscillations using a pseudo-density matrix (PDM) under static conditions, instead of non-invasive measurement. With this approach, it becomes possible to examine a Horodecki-type criterion for the temporal Pauli-correlation tensor. The Horodecki criterion had been proven for CHSH inequality (R. Horodecki et al. Phys. Lett. \textbf{A200}, 340), For any unitary qubit evolution, the corresponding scalar is \(M_R=2\). Although, this result characterizes the correlation tensor and the optimized temporal construction, it does not imply that a fixed flavor observable violates the LGI at every neutrino energy or baseline. We therefore evaluate \(K_4\) explicitly for flavor measurements in matter of constant density. The numerical examples illustrate how matter effects modify the temporal correlations, with a pronounced matter--vacuum separation near the MSW resonance for the chosen parameters and generally smaller differences in the selected off-resonance cases. This finding motivates further investigation of matter-induced temporal correlations in atmospheric neutrinos and their potential relevance to future studies with long-baseline and atmospheric-neutrino experiments, including DUNE and Hyper-Kamiokande.

Rotational symmetry ($C_n$) constrains chiral phonons, but how other symmetries affect their interactions remains largely unexplored. We perform a theoretical and computational study of chiral phonon coupling to parity-time ($PT$)-degenerate electron doublets in $2H$-bilayer MoS$_2$. Although $PT$ suppresses phonon singlet chirality, chiral phonon doublets can helically interact with $PT$-partner electronic states via a mechanism similar to pseudospin. Selection rules are then analyzed with the interplay of $PT$ and $C_3$. Our computational results of $2H$-bilayer MoS$_2$ suggest chiral phonons may be used to resolve intravalley electronic states in $PT$ systems.