Papers

Achieving and quantifying ultrastrong magnon-magnon coupling (USC) remains a key challenge for quantum magnonics. Here, we demonstrate widely tunable USC between chiral (right- and left-handed) and acoustic or optical magnon modes in the van der Waals antiferromagnet $CrPS_4$. Using a full quantum model, we decompose the interaction into three microscopic interaction channels: the co-rotating term $g_1$ (mode hybridization), the counter-rotating term $g_2$ (two-mode squeezing), and, uniquely in the chiral regime, the self-squared term $g_3$ that mediates single-mode squeezing. The normalized coupling ratio reaches $g/f_g$ $\sim$ 0.41, entering the USC regime. Most significantly, we establish a complete protocol linking these USC parameters to a measurable quantum phenomenon: a squeezed magnon vacuum state. Our simulations not only visualize the chirality and polarization evolution of the hybrid modes but also demonstrate how to directly extract quadrature fluctuations and a substantial squeezing factor (up to $\sim$ 9.7 dB) from thermal noise-driven magnetization dynamics. This work provides a material-specific quantum framework for USC and a practical pathway to detect and exploit non-classical magnon states in low-damping two-dimensional magnets, opening a route toward quantum-enhanced spintronics and hybrid quantum information platforms.

Near-term quantum approaches to combinatorial optimization are limited by qubit counts, circuit fidelity, sampling cost, and the difficulty of encoding constraints, while machine learning is increasingly used to configure and control quantum optimization workflows. We call such workflows adaptive: decisions conventionally fixed in advance, from formulation and penalties to shot budgets, backends, and whether to invoke a quantum processor at all, are made by learned policies that respond to the instance, the progress of the solve, or the hardware. This review examines three paradigms, AI for quantum optimization, quantum for AI-driven optimization, and AI-quantum co-optimization, and organizes the literature by the decision being learned rather than by application. A structured search identified a 119-paper corpus, of which 67 papers form an evidence core coded in detail. The evidence is considerably stronger for AI-assisted quantum optimization than for the reverse direction: learning already reduces quantum evaluations, improves initialization, supports decomposition and penalty control, and mitigates noise, whereas evidence that quantum computation improves learned optimizers remains largely confined to small-scale simulation. Experimental controls are thin: of 52 studies in the three paradigms, 22 include no classical baseline, the quantum contribution is fully isolated in 10 of 24 where an ablation applies, and the median largest experiment uses 16 qubits. We introduce an M0-M5 evidence hierarchy, from simulation to practical quantum advantage, and find no broadly convincing result at the highest level. We argue that scaling is increasingly a systems problem: the question is not only whether a problem fits on a quantum processor, but how classical and quantum resources should be allocated across the optimization process.

The Quantum Approximate Optimization Algorithm (QAOA) is a variational quantum algorithm used for solving combinatorial optimization problems, which is thought to be a promising application of near-term quantum hardware. However, high rates of noise in these devices can obscure meaningful results. Therefore, it is crucial to understand and suppress the effects of noise on the algorithm's output. Here, we find that the stability of the algorithm in the presence of noise is dependent on its variational parameters. Using a Pauli noise model, we derive an upper bound on the total variation distance between the noisy and noiseless circuit output as a function of these parameters. Results from noisy simulations support this bound and give insight into the best methods to use for parameter generation in the presence of noise. We also introduce new methods of optimization using error penalties and truncated search based on this bound to manufacture error resilience. We extend this analysis to the quantum adiabatic algorithm (QAA) by taking the continuous limit of the QAOA.

We present a non-perturbative framework for the quantum treatment of vibrational excitation in molecular systems driven by electric fields with arbitrary time dependence. For harmonic potentials with linear dipole coupling, the field-induced dynamics is exactly described by a displaced coherent state, whose evolution is completely determined by a complex phase-space coordinate. Closed-form expressions for this coordinate reveal a clear distinction between resonant and non-resonant regimes. The resulting vibrational populations follow a Poisson distribution determined by a dimensionless time-dependent phase-space displacement, for both resonant and non-resonant driving. Resonant driving results in an enhanced phase-space displacement, whereas finite detuning between the driving and vibrational frequencies leads to an exponential suppression of the phase-space displacement and vibrational excitation. While the approach reduces to the standard time-dependent perturbation theory in the weak-field limit, it remains valid in the strong-field regime, where perturbative treatments fail. Our results provide a transparent phase-space picture of vibrational control and enable non-perturbative state preparation in ultrafast spectroscopy.

Large quantum computations require high-fidelity error-corrected memory and fault-tolerant logical operations. To achieve these with superconducting circuits, quantum processors will need many components operating with low error rates. In practice, fabrication of monolithic superconducting devices produces unavoidable heterogeneity in component performance, which the quantum computer must accommodate. We implement strategies to operate a large dynamic compass code on an array of 156 superconducting qubits arranged on a heavy-hexagonal lattice, making use of the entire monolithic quantum processor and redesigning our measurement schedule to exclude underperforming components. We demonstrate improvements of up to $35\%$ in logical error probabilities for a memory experiment by using a noise-informed decoder combined with strategies to exclude the worst-performing qubits and couplers, along with post-selecting on shots with a low probability of leakage errors. In addition to these memory results, we also observe performance gains of up to $56\%$ when these strategies are applied to measurement-based logic, demonstrated by stability experiments. We furthermore demonstrate high-fidelity fault-tolerant logic through lattice surgery. Through pre-selection filtering techniques, we can obtain Bell fidelities above $77\%$, and further logical gap post-selection using exclusive decoding increases these fidelities to above $97\%$. Our experiments demonstrate that high performance can be maintained in key elements of fault-tolerant quantum memory and logic when working on monolithic superconducting quantum processors with underperforming components, by using a suite of noise-informed quantum error correction strategies.

Quantum optical sensing has evolved from isolated solid state spin defect platforms to increasingly bio-integrated systems designed for biomedical applications. This review presents a perspective on this transition, spanning nitrogen vacancy centers in diamond to emerging fluorescent protein based spin qubits. Advances in diamond fabrication have enabled photonic cavities, nanomechanical resonators, and microstructured devices that enhance spin photon interactions and room temperature sensitivity. Exploration of spin defects in alternative materials further expands the sensing landscape. Parallel progress toward biological compatibility includes chip based architectures for in vitro and in vivo studies, microfluidic integration, and minimally invasive nanodiamond probes capable of intracellular nanothermometry and nanorheometry. Improvements in surface functionalization have enhanced coherence and sensing reliability in complex environments. Collectively, these advances highlight the progress and remaining challenges toward application oriented quantum sensing for the life sciences.

We study dielectric properties of holographic insulators from the quantum geometry of the ground state. We realize the insulating state by the pseudoscalar interaction of holographic fermions and calculate the fermionic Green function to extract the effective hamiltonian. We then derive the quantum metric and Berry curvature to compute the transports and finally get the dielectric constant from the imaginary part of conductivity.

We investigate spin-outcome correlations and memory-assisted entropic uncertainty in tree-level Bhabha scattering, where an incident electron $A$ scatters with a positron $B$ initially entangled with a spectator electron $C$. For the fixed-angle post-selected final state, we compare the total memory-assisted uncertainty $U_A$ for three alternative Pauli measurements on $A$ with the entanglement entropy $S(\rho_A)$ across the $A|BC$ partition. We resolve $U_A$ into the separate uncertainties $U_B$ and $U_C$ and evaluate the corresponding outcome-memory mutual-information sums $G_B$ and $G_C$. This separates changes in the randomness of the outcomes on $A$ from changes in their correlations with each memory. In the parameter regions studied, enhanced $A|BC$ entanglement is accompanied by lower $U_A$, most prominently near high-energy backscattering. An analytic treatment of this limit shows that $B$ factorizes from $AC$: $G_B$ vanishes, whereas $G_C$ increases with the initial $B$-$C$ entanglement. An entropic complete complementarity analysis characterizes the accompanying loss of local helicity predictability in $\rho_A$ and changes in the coherence, predictability, and mixedness of the interacting pair $\rho_{AB}$. These results show that initial $B$-$C$ entanglement can lower the total memory-assisted uncertainty in high-energy backscattering by strengthening spin-outcome correlations with the spectator $C$, thereby identifying the distinct roles of the interacting particle and the spectator as quantum memories.

We propose a scheme for generating and controlling remote nonreciprocal magnon–magnon entanglement in a cavity magnonic system with coherent feedback.The two microwave cavities are driven by independent single-mode squeezed vacuum fields, with a rotating YIG sphere in the left cavity and a stationary one in the right cavity. For a fixed rotation direction, reversing the bias magnetic field applied to the rotating sphere changes the sign of the Barnett shift, leading to nonreciprocal magnon–magnon entanglement. By tuning the cavity detuning and feedback phase, entanglement can be generated for one direction of the bias magnetic field while it vanishes for the opposite direction, yielding complete nonreciprocity. Coherent feedback enhances the entanglement at an appropriate reflectivity, whereas stronger feedback can reduce it. The relative squeezing phase provides additional control, and an appropriate choice of unequal squeezing factors improves the entanglement at fixed total input photon occupation. With the squeezed inputs kept fixed, moderate feedback also increases the critical temperature for magnon entanglement.Our results provide a controllable approach to preparing remote nonreciprocal quantum correlations in cavity magnonic systems.

Randomized benchmarking (RB) with structured circuits is experimentally scalable, but gives biased short-depth fidelity estimates because incomplete ensemble mixing introduces transient modes. Waiting for these transients to decay in deeper circuits can push the signal below the noise floor. This is a well-established obstacle, e.g. in linear cross-entropy benchmarking (LinXEB). Here we overcome this obstacle solely through classical post-processing. We introduce a one-parameter family of estimators that interpolate between the standard LinXEB-type post-processing and a new post-processing technique we call the trace filter function. Under practical assumptions, the trace filter function provably suppresses transient modes, exposing an interpretable fidelity decay at short depth, with theoretical guarantees comparable to standard RB, at the cost of an increased variance. We bound the variance, analyze the evaluation complexity of the new estimators, and develop practical post-processing algorithms. Experiments on a Rigetti superconducting processor validate the method for one-dimensional circuits of up to 12 qubits: where the standard estimator requires depth beyond a 40-layer experimental window, the trace filter function yields consistent estimates below 10 layers. Trace-filtered randomized benchmarking therefore extends reliable fidelity characterization to relevant structured circuit ensembles and short-depth regimes that are inaccessible to conventional estimators.

Flow models generate trajectories from an initial distribution to a target distribution by solving an ordinary differential equation defined by a velocity field. Flow matching learns this velocity field by modeling the transport dynamics between the two distributions. Wavefunction flow establishes a formal connection between flow models and quantum dynamics by introducing a continuity Hamiltonian, which drives the Schrödinger evolution of quantum states. In this paper, we investigate accurate and efficient quantum simulation of the wavefunction flow, thereby realizing the efficient implementation of flow models on quantum computers. We first leverage a quantum read-only memory (QROM)-based phase kickback framework for the wavefunction flow simulation, generating probability densities that closely match those produced by the corresponding conventional flow model. To address the high circuit-resource cost, we further incorporate a trained quantum neural network (QNN) into the phase kickback framework, replacing QROM for data encoding. Numerical experiments demonstrate that our proposed method implements flow models on quantum computers more efficiently, since it maintains the accuracy of wavefunction flow simulation compared with the QROM-based framework, and significantly reduces the circuit resources.

A singular sextic oscillator in the finite-Hermite biconfluent-Heun hierarchy generates an exact four-member power-Liouville Hermite orbit. Power coordinate transformations with the Liouville amplitude map the hierarchy member $N=4$ to four half-line Schrödinger spectral charts while preserving the physical regular-recessive Wronskian zero set under energy-coupling reparametrization. Two charts are the previously studied $x^{2/3}$ and inverse-square-root conditionally integrable potentials; the orbit embeds this known power-dual pair together with the singular sextic and linear-plus-quadratic charts. On the selected physical slice, the degree-five accessory compatibility obstruction vanishes identically, while the transformed Frobenius index reproduces both published fractional-power centrifugal coefficients. The common endpoint condition yields an exact discrete sequence of quartic Sturmian eigencouplings for the sextic oscillator. Independent two-sided shooting confirms representative eigencouplings and node counts. A matched large-action analysis further derives the first matched-endpoint correction within the leading Langer action and improves the Maslov-shifted effective-level approximation. The construction thus connects exact Hermite solvability, energy quantization, coupling quantization, and power duality within a single spectral orbit.

Large-scale Quantum Key Distribution (QKD) networks rely on trusted repeaters, making the security properties of the selected communication path an essential part of end-to-end assurance. At the same time, network operators may be unwilling to disclose their internal topology. We present a topology-certification mechanism that lets a provider prove in zero knowledge that policy-compliant routes between two endpoints exist, without disclosing the routes in an individual presentation. Our main idea is to certify nodes and edges independently using multi-message signatures, rather than signing the complete graph as one object. For a route chosen in advance, proof size and cryptographic proving and verification work depend on its positions and attributes, independently of the overall network size, whereas route discovery and certification have separate graph-dependent costs. The construction hides the actual route length up to a public bound and sketches extensions to node-disjoint routes and monotonic additions within a graph epoch. We give a formal security model and conditional proofs of unforgeability and graph hiding for a generic construction. For a BBS-based construction, presentation-size estimates remain below $300$\,KiB at $\ell=m=n=50$, and measured generation and verification times remain below $400$\,ms at $\ell=64$ and $m=n=8$.

Superradiant phase transitions are fundamental phenomena in light-matter coupled systems. Here, we uncover a novel class of superradiant criticality that is topologically distinct from previously known superradiant transitions. Using cavity-mediated cluster-Ising chains as an illustrative example, we numerically demonstrate that the critical line separating the superradiant phase from the cavity topological phase hosts robust symmetry-protected edge degeneracies, a feature absent in conventional superradiant transitions. Remarkably, although its local bulk critical properties are indistinguishable from those of the previously identified topologically trivial superradiant transition, the two criticalities cannot be smoothly connected without breaking the protecting symmetries or passing through a multicritical point. We further show that such topological superradiant criticality is generic, also occurring in cavity-mediated $\mathbb{Z}_{n}^{}$ cluster-qudit chains, as supported by complementary lattice simulations.

As superconducting quantum processors scale toward hundreds of qubits, manual calibration becomes increasingly costly and difficult to sustain. Here we address two system-level factors governing automated calibration, namely, crosstalk induced by parallel operations and temporal drift of control parameters. On a 66-qubit superconducting processor, cross-entropy benchmarking shows that single-qubit calibration tolerates full-chip concurrency with minimal fidelity loss, whereas CZ calibration requires a minimum coupler-graph distance of four to avoid elevated control errors. Continuous monitoring of representative qubit and coupler parameters further yields quantitative refresh rules that assign refresh priority by error-budget consumption. These results turn two conventionally heuristic choices, the concurrency density of calibration tasks and the refresh priority of each control parameter, into measurable operating rules. Implemented within an automated calibration framework, the rules support a six-qubit Greenberger-Horne-Zeilinger state with a zero-noise-extrapolated fidelity of 89.64%, distance-dependent logical-error suppression in a single-cycle repetition-code benchmark, and a reduction of the mean single-qubit error from 0.023 to 0.011 on a 337-qubit processor, providing an experimentally grounded reference for the automated calibration and maintenance of current and future large-scale superconducting quantum systems.

We develop an iterative Bayesian variational quantum eigensolver in which the unknown ground state, parametrised as a real unit vector, is inferred through a von Mises–Fisher distribution sequentially updated from Hadamard-test measurements on a single ancilla qubit. Building on a companion paper that treated a single success outcome via exact moment matching, we generalise the scheme to condition on $m$ success outcomes for the likelihood function per iteration. Since exact moment matching becomes impractical for $m>1$, we exploit the large-concentration regime, in which a first-order expansion of the log-likelihood yields a closed-form von Mises–Fisher posterior with $m$ entering only through a multiplicative weight. We prove that the two convergence properties of the single-outcome scheme—non-decreasing overlap and non-decreasing concentration—are preserved provided $m$ lies within an explicitly characterised range. Based on the theory, we propose a measurement-based algorithm and illustrate the convergence on randomly generated three- and four-qubit Hamiltonian matrices, on $\mathrm{HeH}^+$, and on $\mathrm{H}_2$.

Quantum technologies witness rapid contemporary developments transitioning from abstract scientific ideas and fundamental demonstrations, into systems of sufficient quality and scale, enabling real applications. Photonic quantum technologies are playing a pivotal role in these developments, since photons are robust, easily controlled, detect and measured, thus qualify as flying carriers of quantum information and entanglement distributers. The efforts to develop photonic quantum technologies benefit from the maturity of the classical optical technologies. It was shown that even a source of heralded three entangled photons is sufficient for building large scale quantum computers using otherwise classical optical elements. Here, we demonstrate a novel semiconductor quantum dot based device, which deterministically generate at GHz rates, indistinguishable single photons in a robust Greenberger-Horne-Zeilinger (GHZ) state of more than a dozen photons. The device utilizes novel natural spin echo concept, provided by the opposite precession directions of the negative and positive carriers' spins in the excited and ground levels of the periodically excited dot, respectively. The excitation rate is finely tuned to nullify the phase acquired by both spins' precession. Our record long GHZ state producing device can yet be feasibly improved to provide higher-rate, brighter and more robust deterministic GHZ source, significantly reducing the overhead requirements for photonic quantum technologies.

Quantum key distribution (QKD) offers an approach for secure communication over quantum channels, based on the principles of quantum mechanics. However, the inevitable imperfections in QKD systems can introduce critical vulnerabilities, posing significant challenges to the deployment of QKD in terms of both practical security and performance. In this work, we present a comprehensive security analysis of QKD in the practical scenarios involving imperfections in modulation spaces. Specifically, our analysis focuses on the imperfections related to encoding, intensity modulation, and their characterization. We provide a unified framework based on the operator dominance method to overcome these issues and achieve a tight estimation of the secret key rate (SKR). The simulation results show that the SKR in practical scenarios, with parameters characterized from commercial QKD systems, closely matches the SKR under ideal conditions. In the finite case, the maximum transmission distance can reach up to 250 km with total pulse number $N=10^{12}$ and the SKR closely approaches the asymptotic limit up to 250 km with $N=10^{14}$. This validates the robustness of our method against imperfections in state preparation and characterization. Furthermore, the feasibility and robustness of method in measurement-device-independent (MDI) QKD have also been demonstrated. Our analysis not only promotes advancements in enhancing practical security and performance but also highlights the feasibility of deploying QKD for actual applications.

Quantum key distribution (QKD) promises theoretically secure communication. However, it encounters challenges in implementation security and performance due to inevitable device imperfections. Since the proposal of measurement-device-independent (MDI) QKD, the critical step toward practical security is to secure QKD with imperfect sources. The source imperfections manifest as state-preparation uncertainty (SPU) in various aspects, e.g., encoding uncertainty, intensity fluctuation, and imperfect vacuum states. Here, we perform an MDI-QKD experiment and achieve both high practical security and superior performance. We address the general form of SPU and guarantee a tight estimation of the secret key rate based on the operator dominance method. We achieve secure key distribution over 303.37 km, which not only represents the farthest distance in experiments involving SPU but also considers the most SPU scenarios. Our experimental results represent a significant step toward promoting practical and secure quantum communication.

Quantum annealing must be sufficiently slow to prevent defect formation. We study this problem in the random transverse-field Ising model via the adiabatic theorem to obtain the limiting rate at which defect formation can be avoided. Our approach based on the strong-disorder renormalization group (SDRG) technique views the annealing process as a gradual aggregation of strongly coupled clusters, giving access to the elementary events of error formation. We present a scaling theory of the statistics of these events in general dimensions and confront it to an extensive numerical analysis carried out in one, two, and three dimensions by an efficient implementation of the SDRG method. This approach is also validated by exact diagonalization in one dimension by means of the free-fermion technique. Our results consistently show a logarithmically slow decrease of the error density with the annealing time, characterized by the dimension-dependent critical exponents of the corresponding infinite-disorder fixed point of the model. Furthermore, we provide a map of individual events of potential defect formation in the excitation energy - control parameter plane, which may help in the design of optimal annealing paths.

We study, within a toy model, how a thermal bath of cosmological perturbations can decohere the minisuperspace degrees of freedom of the universe, treating the perturbations as an environment in the framework of open quantum systems. Instead of tracing out the perturbations from a semiclassical ansatz for the total wave function, as in earlier approaches, we incorporate their backreaction on the background through an effective second-order coupling and derive a master equation. The model describes a spatially flat semiclassical universe during slow-roll inflation with a dust clock field, while scalar cosmological perturbations in a phenomenologically assumed thermal state constitute the environment. The master equation is non-Markovian, since the bath correlation functions do not decay in time. Within this framework, we find that, for a representative set of parameter estimates, the characteristic decoherence timescale corresponding to the thermal contribution can be shorter than the Hubble timescale. In addition, we address the question of whether the pointer-state structure induced by the decoherence in such a framework could provide a criterion for the choice of semiclassical states in quantum cosmology.

We study a strong form of genuine multipartite nonlocality (GMNL), where an $n$-partite scenario admits a quantum strategy generating outcomes belonging to a restricted set with certainty, whereas every strategy built from nonclassical resources shared among at most $k<n$ parties fails this criterion with positive probability. This generalizes what is referred to as strong contextuality/nonlocality, or pseudotelepathy, beyond ruling out local models. For the simplest five-party Bell scenario of two binary-outcome measurement settings per party, we use the inflation technique to demonstrate that a game with a perfect quantum strategy witnesses a robust separation from models built from bipartite resources under local operations and shared randomness (LOSR), establishing the behavior is LOSR-GMNL. We provide broader context for this result by investigating its simulability with resources shared among three or four parties under different resource models and alternative definitions of GMNL. A central open question is whether $n$-party quantum resources can achieve such a separation from models built from $(n-1)$-party resources, for $n\ge 3$. We make progress here by constructing a family of robustly LOSR-GMNL games with $\epsilon$-optimal quantum strategies experimentally indistinguishable in the limit from true probability-one-winning strategies for any desired level of precision.

Gate insertion (GI) quantum error mitigation replaces involutory gates such as CZ and CX with 2j+1 repetitions of the same gates to nominally amplify noise by the same factor. Analytical and experimental results show that this amplification scaling fails for non-commuting gate noise, as typically encountered in realistic devices. Here we introduce Heisenberg-echo symmetrization (HES), which combines standard GI with an echo inspired by the Heisenberg representation to cancel the leading GI error. In our simulations, HES reduces the absolute fidelity error by one to two orders of magnitude compared with GI. Unlike the more accurate Layered-KIK method, HES is compatible with any hardware and requires only circuit-level access. It enables virtual noise scaling across platforms, potentially reducing sampling overhead substantially. Its agnostic noise amplification also provides full resilience to temporal noise drift. For pure initial states, however, high-rank observables can substantially increase the echo variance relative to non-echoed circuits, whereas rank-one observables incur no additional sampling overhead compared with GI or Layered-KIK. HES is therefore particularly suited to rank-one or nearly rank-one observables.

Multi-photon interference is the resource most native to photonic quantum machine learning, yet experiments on photonic reservoirs have reported advantages, null results, and train-only effects. These outcomes cannot be compared: each measures task-dependent accuracy on different tasks and platforms. Here we resolve the question task-independently through the kernel geometry of boson-sampling feature maps. Interference redistributes feature variance across roughly twice as many effective dimensions as distinguishable-particle statistics, generating a large geometric separation between the corresponding kernels. The separation grows superlinearly with indistinguishability, is linear in Hong–Ou–Mandel visibility at small visibility for two to four photons, and retains approximately 80% of its magnitude at the source quality of current quantum processors. Under experimental sampling budgets the separation is learnable on adversarially constructed tasks (accuracy advantage +0.22 plus or minus 0.05) and an order of magnitude smaller on natural tasks, gated by kernel–task alignment. The results reconcile the existing experimental record and supply a pre-experimental protocol: kernel geometry establishes that an interference-specific learning resource exists, and task alignment determines whether a given task can access it; both are computable before committing significant hardware resources.

Nitrogen-vacancy (NV) centre ensembles are leading room-temperature magnetometers, but their sensitivity is usually extracted from a single resonance and relies on external microwave and bias-field hardware. This work proposes a chip-scale NV magnetometer built around a one-dimensional YIG/CoFeB magnonic crystal, in which a single structural defect forms a passive magnonic cavity and integrated permanent magnets supply the bias field. Micromagnetic simulations show a defect-localised spin-wave mode at 2.910 GHz inside the 2.5-3.0 GHz magnonic band gap, 40 MHz from the NV zero-field splitting, with a band structure that matches an independent plane-wave calculation. A Tavis-Cummings/Lindblad model in which the microwave reaches the NV ensemble through this mode predicts a hyperfine-resolved optically detected magnetic resonance spectrum that is strong only within the mode linewidth, and a dispersive homodyne response with one steep edge per $^{14}$N hyperfine line. The master-equation solutions agree with the closed-form homodyne steady state ($R^2 > 0.9999$) and with an approximate analytic ODMR theory (peak positions within 0.012 MHz). For a critically coupled readout with room-temperature electronics, combining the three edges gives a projected sensitivity of 93 pT/$\sqrt{\rm Hz}$, a $\sqrt{3}$-fold gain over the best single edge. Mapping the sensitivity against the NV-magnon coupling reveals an optimum near $g_{\rm ens}/2\pi \approx 0.2$-$0.4$ MHz, where it reaches 72 pT/$\sqrt{\rm Hz}$ for a 0.64 MHz spin linewidth and 19 pT/$\sqrt{\rm Hz}$ for 0.17 MHz, with thermal limits of 6.6 and 1.7 pT/$\sqrt{\rm Hz}$. The antenna-mode coupling, the NV-magnon coupling and the spin linewidth are therefore the main design levers.

Integrated photonic quantum chips have emerged as a promising platform for realizing fault-tolerant photonic quantum computers. Compared with bulk-optics systems, integrated photonics offer compact device footprints, enhanced programmability, and exceptional stability, attributes that are essential for executing large-scale and computationally demanding quantum tasks. In this review, we provide a comprehensive overview of recent advances in both discrete-variable and continuous-variable universal photonic quantum computation. We survey progress in fault-tolerant architectures and state-of-the-art integrated platforms and highlight the key challenges that must be addressed to scale photonic systems toward full fault tolerance. Finally, we outline future opportunities and research directions aimed at bridging the gap between current proof-of-principle demonstrations and fully scalable quantum microprocessors.

Constraint-preserving exchange drivers allow many coupling graphs that preserve the same feasible sector, but exhibit different minimum gaps along an annealing path. We derive an exchange-resolved sensitivity of the normalised minimum gap for fixed-cardinality Laplacian drivers sharing a Dicke ground state, and apply it to identify locally favourable modifications of the driver. Numerical experiments indicate this sensitivity reliably predicts beneficial infinitesimal changes, but its reliability decreases when the same direction is extended to a finite edge replacement. The gap landscape tracking reveals one mechanism of this loss of reliability. Improving the active bottleneck can expose a competing minimum, with a more extensive reorganisation of the low-energy subspace. We call this the "repair-and-expose" mechanism and observe it in both dense quadratic and sparse frustrated objective families. This motivates relinearizing the response when competing minima become co-active. In the tested oracle setting, a tied-minimum max-min update is substantially more reliable than continuing the original direction or optimizing only the incoming minimum. Supporting finite-size search and selector tests show that this local information can remain useful beyond the infinitesimal limit, while its practical extraction depends on the driver geometry and identification of the relevant low-energy competitors. These results connect local exchange-resolved gap sensitivity to bottleneck migration and conditional driver redirection.

Variational quantum algorithms are often limited by barren plateaus: gradients vanish as circuit size and depth increase, making quantum neural networks difficult to train. We propose Q-Capsule, a localized capsule-based quantum neural architecture that mitigates this problem through register partitioning, local readout, sparse inter-capsule coupling, trainable data re-uploading, and Quantum Fisher Information Matrix (QFIM)-guided adaptive depth growth. By restricting the dominant support of each observable to a small capsule and controlling inter-capsule entanglement, Q-Capsule preserves useful gradient signals while retaining communication between local quantum representations. As the register width increases, Q-Capsule consistently maintains stable gradient variance, whereas globally entangling baselines exhibit exponential suppression with a log-gradient-variance slope near -ln 2 per qubit. Q-Capsule also produces more structured optimization landscapes, higher parameter efficiency, improved robustness to depolarizing noise, and lower measurement requirements. Its adaptive policy achieves 98.1% accuracy on binary classification and 97.7% on four-class classification, while using approximately 73% fewer two-qubit gates than the fixed-deep model on the multiclass task.

Conditional mutual information (CMI) probes spatial non-Markovianity and plays a central role in a recently developed framework for defining mixed-state phases based on local reversibility. This framework sharply distinguishes exponentially decaying from algebraically decaying CMI, since the latter obstructs equivalence to a state with finite Markov length. Here we show that states that flow to the same renormalization-group (RG) fixed point can nevertheless exhibit qualitatively different CMI. Starting from a critical Gibbs state of a finite-range local classical Hamiltonian, whose CMI vanishes beyond the interaction range, we show that an RG-irrelevant perturbation that breaks detailed balance generically generates algebraically decaying CMI. Crucially, these power-law tails are cutoff-suppressed: although they lead to an infinite Markov length at every fixed lattice cutoff, they vanish as a positive power of the cutoff in the continuum limit. We construct solvable models that exhibit this phenomenon and predict that the Ising-symmetric critical point of Toom's cellular automata generically exhibits such behavior. We also find analogous cutoff-suppressed CMI in the high-temperature paramagnetic phase of the long-range Ising paramagnet, in contrast with the genuine power-law CMI at the finite-temperature critical point in this same model that survives the continuum limit. We also derive a general result that in one spatial dimension, CMI decays faster than the inverse square of the buffer length if and only if the long-distance physics is Markovian.

We study a hybrid system of coupled cavities, with or without two-level atoms doped inside. By employing a building-block construction facilitated by nonlinear Stark coupling, we identify a manifold of exact many-body eigenstates that remain analytically tractable across arbitrary lattice geometries and atom distributions. We demonstrate that these exact states exhibit a dual physical nature depending on their spectral positioning: when embedded within the chaotic many-body spectrum, they manifest as quantum scars that violate the eigenstate thermalization hypothesis and undergo weak ergodicity breaking; conversely, as ground states within fixed-total-excitation sectors, they exhibit off-diagonal long-range order and form polariton condensates. Furthermore, numerical calculations of local excitation-number fluctuations suggest that negative Stark coupling shifts the Mott-insulator to superfluid transition toward weaker inter-cavity hopping. Our findings provide a versatile framework for engineering both coherent quantum phases and non-thermalizing states in diverse light-matter architectures.