Papers

Open photonic systems provide a versatile platform for non-Hermitian physics, enabling control over complex spectra, transport, and light-matter interactions. Exceptional points (EPs), at which eigenvalues and eigenvectors coalesce and the governing operator becomes defective, play a central role because they combine branch-point spectral topology, nonanalytic perturbative response, and controllable eigenstate conversion. This Review provides a unified framework for EP photonics by systematically distinguishing exceptional degeneracies according to the underlying operator, spectral variable, boundary conditions, and experimentally accessible observables. We discuss Hamiltonian EPs, absorbing EPs associated with scattering zeros, real-frequency scattering-matrix and Jones-matrix EPs, Bloch and Floquet EPs, and Liouvillian EPs in open quantum systems. We review their spectral topology, static and dynamical encircling, higher-order exceptional structures, and coexistence with bound states in the continuum, together with applications in sensing, lasing, coherent absorption, directional scattering, polarization and wavefront control, nonlinear optics, optical storage, nonreciprocal photonics, and quantum photonics. We also critically assess the current limitations, practical challenges, and future perspectives of EP-based photonic technologies, with particular attention to robustness, noise, scalability, and experimentally measurable performance.

Sampling from the Boltzmann distribution is central to computational physics, yet hard when the energy is known only through a stochastic estimate, such as with machine-learned molecular potentials, in variational Monte Carlo, or on quantum computers, because a noisy energy biases the sampled distribution. The penalty method of Ceperley and Dewing corrects this but requires the noise variance and becomes intractable when it is large. We introduce the Poisson product estimator, an unbiased, non-negative estimator of the Boltzmann weight that only needs an upper bound on the energy estimator and remains efficient at high noise. Using it to optimize a variational quantum circuit gradient-free, we recover the $H_3^+$ ground-state energy in a minimal basis and, by sampling rather than following a single trajectory, also map the variational energy landscape.

We present a unifying description of dynamical phase transitions in the unitary evolution of an isolated quantum particle and the dissipative relaxation of a classical Brownian particle, based on a dynamical generat- ing function. In the semiclassical and weak-noise limits, Fisher zeros of this function condense in the complex- time plane and reach the corresponding physical axes, producing dynamical phase transitions through a competition between return trajectories. This establishes a direct connection between quantum and classical (finite-time) dynamical phase transitions, where the semiclassical limit plays the role of the thermodynamic limit. In particular, the established link naturally provides a classical version of the Loschmidt amplitude and shows how dynamical quantum phase transitions, typically associated with isolated many-body systems, can arise in a single-particle quantum system. The dynamical phases are distinguished by a unifying, trajectory- based order parameter, realized as a classical correlation function and a sequential quantum weak value.

In quantum metrology, adaptive and causal-superposition strategies are proven to be beneficial over parallel schemes for a finite number of channel uses, but their advantages disappear in the asymptotic limit. We show that quantum operations with indefinite time direction, specifically, time-flip (TF)-assisted strategies, referred to as indefinite time-directed metrology (ITDM), can overcome this asymptotic equivalence. Using semidefinite programming, we rigorously demonstrate that TF-assisted protocols can achieve quantum Fisher information (QFI) strictly exceeding the maximum value attainable by parallel, adaptive, and causal-superposition strategies, both for finite and asymptotically many channel uses. Moreover, we identify a class of Pauli noise channels for which ITDM achieves Heisenberg scaling, while all parallel, adaptive, and causal-superposition strategies remain restricted to standard scaling. We call this phenomenon as metrological activation. Interestingly, this activation can be used to exhibit that the quantum time-flip and transposition supermaps cannot be simulated by conventional quantum circuits or causal-superposition strategies using any finite number of channel queries, thereby establishing indefinite time direction as a genuine resource for quantum metrology.

We formulate an energy-consistent quantum-optical representation of finite paraxial laser pulses in free space. The formulation is based on a continuous-mode description and provides a step toward a unified treatment of coherent and nonclassical strong-field drivers. Starting from plane-wave quantization, we construct a transverse vector-mode reduction in which the selected mode can reproduce an arbitrary normalized spatial–polarization profile. For a coherent pulse, the measured pulse energy and full laboratory analytic signal determine the frequency-dependent coherent-state displacement $(\alpha(\omega))$, without introducing a physical quantization volume. For nonclassical pulses, the same first-order field data and total energy do not uniquely specify the quantum state. Additional correlation information or model assumptions are required. We incorporate this information through normal and anomalous covariance kernels and discuss $g^{(2)}$-based diagnostics of squeezed pulses. We also derive a phase-sensitive convergence criterion for numerical frequency-bin discretizations. An exactly solvable continuum-mode free-electron application shows that the coherent displacement reproduces the semiclassical mean trajectory, whereas the field covariances determine the electron wave packet width. The framework offers a convenient, energy-consistent interface between measured free-space pulses and quantum-optical calculations.

Optomechanical membrane-in-the-middle systems that comprise several coupled compliant membranes offer enhanced optomechanical coupling and collective dynamics. Recent realizations were fundamentally restricted to two membranes and to limited structural optimization of the involved membranes due to their intricate fabrication and experimental integration. Here, we present a fiber-based Fabry-Perot microcavity incorporating monolithically integrated double-membrane resonators fabricated by 3D direct laser writing. We realize controllable mechanical mode hybridization of membranes with coupling rates of up to $J_{\mathrm{mech}}/2\pi = 0.16$ MHz, exceeding the mechanical linewidths. We demonstrate enhanced collective optomechanical coupling of the membrane stack's breathing mode, reaching collective coupling strengths of up to $g_{\mathrm{col}}^{(-)}/2\pi \approx 0.1$ MHz. Our transfer-matrix calculations predict further substantial enhancements with realistic reductions of membrane thickness and spacing, and a larger number of membranes. Our results establish direct laser-written membrane arrays as a scalable platform for multimode cavity optomechanics, combining tunable mechanical interactions, enhanced collective optomechanical coupling, and scalability towards larger mechanically coupled resonator systems.

We establish the general form of the evolution equation and study scattering and tunneling in real quantum mechanics. We prove an analogue of Stone's theorem for a real Kahler space and derive the corresponding general evolution equation, whose evolution operator is both orthogonal and symplectic. We formulate scattering theory in terms of real wave operators and the associated S-matrix. For the class of potentials considered, we show that the differential scattering cross section is equivalent to that obtained in standard complex quantum mechanics. We also show that the tunneling probability in real quantum mechanics is identical to that in complex quantum mechanics.

Stress-tensor fluctuations carry information that is absent from the mean semiclassical Einstein equation, but their observable effect depends as much on the response of the geometry as on the noise itself. We formulate an effective, quasistationary spherical model organized by the response–noise structure of a quantum Langevin equation. A prescribed mean dressing and a horizon-localized colored source are varied independently. For every source realization we reconstruct the lapse, locate its outer trapping horizon, and evaluate the adiabatic Hayward–Kodama temperature from the slope at that same root. As the mean lapse approaches an inner–outer root merger, its inverse slope acts as a geometric susceptibility: a fixed source covariance produces enhanced horizon fluctuations, horizon–temperature covariance, and a positively skewed, greybody-filtered luminosity. The specific advance is a single-realization map from colored metric noise to correlated geometric, thermal, and radiative statistics, together with an explicit separation of reservoir strength from near-critical amplification. The model is a stochastic-semiclassical testbed, not a microscopic evaluation of Unruh-state response and noise kernels.

This paper introduces QXymb, a general framework for constructing observational declarative twins of quantum circuits, and develops QILP-0, its first complete order-0 specialization. QILP-0 constructs a finite multi-valued propositional logic program from observed circuit behaviour within a declared observational scope. The pipeline traverses a declared family of quantum observables incrementally according to a reproducible structural grading and a declared observational reference horizon. Progress is quantified through reference-relative coverage against a fixed target-independent reference. Observable responses are organized through target-independent geometry, while retained latent structure is mapped deterministically back to original observable columns before symbolic processing, preserving observational semantics and provenance. Selected observable profiles are converted into a finite relation through admissible target-independent discretization. The target is used only afterwards to audit twin-admissibility and induce the declarative theory. A theory is certified as an exact observational declarative twin when it completely and correctly reconstructs the resulting finite task-conditioned discrete relation. Logical exactness is therefore separated from numerical, backend, provider, and discretization uncertainty, which is retained as audit metadata. Validation uses two complementary QML settings. Exhaustive Bars & Stripes experiments compare product and grid-CZ embeddings from 16 to 100 qubits and exercise the native-discrete branch. Low-Depth MNIST analyses all 14,708 digit-0/1 instances before and after a trained variational quantum transformation and exercises continuous discretization. In every reported relation, the induced QILP-0 theory achieves complete, conflict-free reconstruction with strict accuracy equal to one.

Quantum compilers typically follow the circuit model, representing programs as fixed sequences of gates. This static view breaks down in hybrid quantum-classical applications, where gate choices depend on runtime data or measurement results. We introduce a new Intermediate Representation (IR) that elevates gates to first-class values, enabling their dynamic creation, composition, and control. This unified representation allows classical computation to steer quantum behaviour, capturing phenomena including stochastic gate selection, adaptive error correction, and measurement-driven computation within a single framework. Case studies in noise modelling, randomised compilation, error correction, and measurement-based quantum computing show that our IR expresses these programs compactly and supports optimisations that were not possible in the circuit model. Evaluation on a benchmark suite of hybrid quantum-classical programs indicates that our IR represents programs compactly and facilitates compiler analysis and transformation.

The Dirac quantum walk (a 1+1 dimensional space-time discretization of the Dirac equation) has a $2\mu$ mass gap both at the center and at the corner of the quasi-energy-momentum Brillouin zone. Gupta and Short recently noted [Quantum 9, 1845 (2025)] that the Dirac vacuum can create a particle-hole pair at the zone corner with the release of an energy $2\mu$ to the environment. They removed this vacuum instability at the expense of fermion doubling, the appearance of a second low-energy Dirac cone. Here we show that an alternative discretization scheme, with a tangent rather than a sine dispersion relation, offers stability while retaining a single Dirac cone. The key step is the Cayley transformation from the unit circle of Floquet eigenvalues $e^{-i\varepsilon}$ to the real line of unbounded energies $E=2\tan(\varepsilon/2)$. We compute the Schwinger effect (particle-hole pair creation in a uniform electric field) for tangent fermions and show that the pair-production rate agrees with the continuum result for a single Dirac cone. The zone corner is exactly decoupled if the scalar potential is coupled through the Hermitian generator of the quantum map. If it is coupled as a split operator, in order to preserve exact gauge invariance on the lattice, the corner does contribute - with a weight that vanishes quadratically with the lattice constants, in contrast to the Dirac quantum walk where the zone-corner instability survives the continuum limit.

Photonic fusion operations are a central primitive in photonic quantum information processing and are commonly characterized by their success probability and resource cost. Here, we identify an additional way in which different implementations of fusion operations differ, namely in how they transform partial distinguishability. We consider distinguishability originating both from imperfect entangled resource states and from imperfect single photons. We find that different successful fusion events can induce markedly different distinguishability transformations depending on the fusion protocol, heralding outcome, and error model. Under a collective resource-state error model, we identify a modification to an existing fusion protocol that improves the fidelity of the remaining state on average. Generally, however, these transformations adversely affect distinguishability, and many successful fusion outcomes are accompanied by distinguishability degradation. Our results show that partial distinguishability is dynamically shaped by interference and measurements and should be considered alongside overall fusion success probability when evaluating photonic fusion protocols.

Wavefront shaping is a key technique for mitigating scattering in complex media, enabling advanced imaging and optical communication. Yet existing approaches are inherently local, requiring active correction elements - such as spatial light modulators or deformable mirrors - to lie directly in the optical path of the scattered light, which limits their integration into compact imaging systems. Here, we experimentally demonstrate nonlocal wavefront shaping using spatially entangled photon pairs. By applying a phase correction to a photon that never interacts with the scattering medium, we compensate for the distortions experienced by its entangled partner and restore their initial spatial correlations. Our approach physically decouples the wavefront correction from the scattering medium, paving the way for imaging through complex media in compact and otherwise inaccessible systems.

Gaussian boson sampling requires control of how closely finite optical matrices follow Gaussian reference laws. We prove an explicit total variation bound of order $N^2/M$ between a rescaled Haar transpose Gram block and its Gaussian transpose Gram counterpart, where $N$ is the detected photon count and $M$ is the number of optical modes. The bound establishes quantitative product hiding uniformly over every number of squeezed inputs. The proof combines Stiefel recursion, centered circular orthogonal ensemble scores, and a rectangular entropy estimate. Applications combine hiding with local hafnian bounds to obtain relative probability guarantees and connect them to sampler error through exact photon-sector normalization.

We discuss an information-geometric framework for characterizing quantum states in non-equilibrium dynamics. Using the transverse-field Ising chain model as a laboratory, we investigate the quantum Fisher information metric with particular emphasis on the mixed metric component $g_{ht}$ and related geometric observables, where $h$ is a controllable post-quench Hamiltonian parameter and $t$ is real time. The framework treats $h$ and $t$ as coordinates of an extended information manifold $(h,t)$. The geometric observables characterize the speed of evolution on the manifold and the alignment between the temporal and parameter-deformation directions. Correlations between these geometric quantities and two widely used measures of non-equilibrium dynamics, the entanglement entropy and the Loschmidt echo, are analyzed.

The quasienergy spectrum of a strongly driven two-level system as a function of the driving parameters exhibits conical intersections, which are enabled by hidden time-nonlocal symmetries. We show that each such crossing carries a quantized topological charge: the Floquet–Berry phase acquired along an adiabatic loop around a cone is equal to a $\mathbb{Z}_2$-valued charge. We further identify a second family of degeneracies that occurs at vanishing driving amplitude, when the level splitting matches $m$ energy quanta of the field. Along the Stark-shifted resonance line, the minimum quasienergy gap opens as $|A|^m$, and the charge is nontrivial only for odd $m$. We analytically derive both results from a perturbative reduction to a spin-$1/2$ in an effective two-dimensional magnetic field and confirm them numerically through the Bargmann invariant. Moreover, we propose a chirality-based protocol that cancels the dynamical phase to isolate the geometric one, and an ancilla-based Ramsey readout that renders the topological charge directly observable.

We investigate driven dynamics across critical and exceptional points in the one- and two-dimensional imbalanced-pairing Kitaev models using both the wave-function normalization approach and the biorthogonal framework. For a positive pairing imbalance parameter, the quasiparticle spectrum remains real, and a pairing imbalance neither shifts the equilibrium phase boundaries nor generates imaginary eigenenergies. In this regime, the defect density follows the conventional Kibble–Zurek scaling in one dimension and the extended Kibble–Zurek scaling, arising from a gapless manifold, in two dimensions within both frameworks. The corresponding scaling exponents are therefore governed by those of the Hermitian transition. For a negative pairing imbalance parameter, time-reversal symmetry is broken, the quasiparticle spectrum develops complex eigenvalues, and the gap closes at exceptional points. For ramps ending at an exceptional point, the defect density follows the modified Kibble–Zurek scaling in the wave-function normalization approach, whereas it obeys the conventional Kibble–Zurek scaling in the biorthogonal framework. When the ramp traverses the time-reversal-symmetry-broken region, a finite density of defects remains even in the adiabatic limit, leading to defect freezing in both frameworks. Although this frozen background indicates a breakdown of adiabaticity, the excess defects generated on top of this background continue to obey the conventional Kibble–Zurek scaling in one dimension and the extended Kibble–Zurek scaling in two dimensions.

High-fidelity CZ gates are central to superconducting quantum processors, but implementations based on flux tuning are still sensitive to pulse distortion. Conventional predistortion, typically used for an isolated gate, can recover the desired flux at the chip but it fails if the flux line memory exists, causing the fidelity of repeated CZ gates to drop rapidly. To address this issue, we model the flux line distortion as the dynamics of a stateful classical actuator coupled to a quantum system. Using a first-order Dyson expansion, we derive the error generators induced by variations in the initial flux-line state. We then design a robust CZ gate by optimizing the flux pulse to suppress these generators and minimize the residual flux line state at the gate exit. A one-pole flux line model shows the expected first-order robustness plateau. For a more practical three-pole model, the optimized CZ pulse achieves $F_{\mathrm{avg}}=99.998\%$, suppresses all first-order error generators, and brings the residual flux line state close to zero. With no additional waiting time between gates, our robust pulse achieves $F_{\mathrm{avg}}=99.97\%$ for the complete ten-gate sequence and reduces the sequence infidelity by a factor of about $2.3\times10^{3}$ relative to the baseline under the same predistortion protocol. These results show that explicitly accounting for flux line memory maintains high-fidelity CZ operation across repeated gate sequences and addresses a key limitation of conventional predistortion.

We develop a finite-temperature Gaussian-state formulation of quantum energy teleportation in the one-dimensional harmonic chain. For Gibbs states, the optimized measurement-feedback protocol reduces to thermal two-point functions. In the single-site protocol, the extracted energy is governed by a single correlator, which makes the thermodynamic and near-critical limits analytically tractable. At fixed finite temperature, the extracted energy is exponentially screened with distance and is controlled by a thermal correlation length for both critical and non-critical $\alpha$. In the zero-temperature critical limit taken after the thermodynamic limit, we derive the exact asymptotic law $E_{\mathrm{ext}}\sim d^{-4}$. Numerical results confirm both regimes and resolve the crossover responsible for the apparent drift of the effective decay exponent at intermediate distances. We also analyze squeezed Gaussian measurements and show that they modify the extraction prefactor: $p-$squeezing enhances the extracted energy, whereas $q-$squeezing suppresses it, without changing the large-distance scaling.

Selecting mutually compatible natural gas transportation contracts is a practically important optimization task in which operators must choose from many candidate agreements subject to temporal, infrastructural, and flow-related constraints. As the number of candidates grows, the resulting search space becomes difficult to explore exhaustively. We study a pairwise abstraction of this task, formulated as a Maximum Clique problem on a contract-compatibility graph, or equivalently as a Maximum Independent Set (MIS) problem on the complement graph. Building on recent work, this paper studies a quantum-classical framework for solving large-scale MIS instances within the limitations of noisy quantum hardware. The approach combines iterative classical graph reduction with quantum-guided optimization to progressively simplify the search space while maintaining high solution quality. This enables large candidate spaces to be reduced to smaller subproblems that are more suitable for execution on current quantum computers. We evaluate the approach on fifteen benchmark instances from the Quantum Optimization Benchmarking Library (QOBLIB), obtaining an average approximation ratio of 0.996 and recovering optimal solutions for fourteen instances, including graphs with up to 186 vertices. We further evaluate the algorithm on six synthetic pairwise contract-compatibility graphs containing up to 900 contracts, where the proposed method achieves an average approximation ratio of 0.989 and obtains optimal solutions in four cases. These experiments demonstrate the ability of the hybrid MIS solver to reduce industrially motivated graphs. The pairwise abstraction serves as the first step of a two-stage screening procedure that narrows the candidate contracts to a smaller set of mutually compatible ones, which can then be verified against pipeline-capacity constraints.

One of the main advantages of the Loop-Tree Duality representation of scattering amplitudes is that it makes the origin of infrared and threshold singularities particularly transparent. This talk reviews recent progress in describing how singularities emerge and cancel at the level of scattering and vacuum amplitudes, discusses a novel strategy to efficiently construct finite integrals, and presents a complementary perspective based on encoding the underlying causal and singular structure in terms of qubits and quantum circuits.

The multi-controlled Toffoli (MCT) gate is a fundamental primitive in quantum circuit design, with applications in quantum arithmetic, cryptanalysis, and algorithmic implementations. Being a high-level logical operation, the efficient decomposition of MCT gates into lower-level netlists has remained a major optimization challenge for decades. While emerging quantum error-correcting codes such as bivariate bicycle (BB) codes drastically reduce fault-tolerance overhead, realizing non-Clifford circuits on modular BB-code architectures introduces complex compilation bottlenecks governed by inter-module routing, factory density, and layout. Consequently, the mapping of MCT gates onto BB-code architectures remains relatively unexplored. In this paper, we overcome these challenges by mapping optimal-Toffoli-depth MCT decompositions (Dutta et al., PRA, 2025) onto BB-code-based fault-tolerant architectures via direct $\lvert \mathrm{CCZ} \rangle$ state injection from an external magic state factory. We introduce a targeted placement strategy that exploits the binary-tree structure of MCT decompositions to co-locate interacting subtrees. This approach reduces inter-module instruction counts by up to $\mathbf{16.02}\%$ compared to a naive sequential first-fit placement. We also evaluate the impact of factory placement across different topologies, demonstrating that grid-based layouts yield up to a $\mathbf{23.7}\%$ reduction in inter-module instructions relative to linear architectures (Yoder et al., arXiv, 2025). Finally, we validate the practical viability of our compiled circuits by analyzing aggregate execution errors and logical failure probabilities using the bicycle-ISA error estimator bicycle_numerics provided by the Qiskit community, https://github.com/qiskit-community/bicycle-architecture-compiler.

Bell's theorem rules out developing a locally causal theory to describe quantum phenomena. Many take this to imply that any model of quantum entanglement must employ variables (called beables by Bell) which follow nonlocal rules, even though signaling is local. The alternative is to adopt an all-at-once (block universe) approach, with beables which may depend on both past and future inputs, even though signaling is causal. Within this lenient-causality approach (a.k.a. retrocausal), simple cases of entanglement have been successfully described by locally mediated stochastic toy models, i.e.,~toy models which are local in a sense which generalizes Bell's local causality. Developing a widely applicable reformulation of quantum mechanics along these lines is a grand challenge. This work presents a general framework for such models and theories, and identifies the corresponding ontic and epistemic states. The epistemic state is closely analogous to the quantum state, yielding an explanation for the collapse of the wavefunction. In the case of the models of the framework, it is clear what the information is about. The expression for the empirically verifiable predictions of the models in terms of the ontic and epistemic states displays remarkable parallels to the Born rule. A toy-model example is discussed.

Maximizing gas throughput in transmission networks under hydraulic and operational constraints is a combinatorial problem whose complexity grows exponentially with network size, making it computationally intensive to solve exactly. This paper addresses the graph-based optimization problem by optimizing nodal-pressure assignments under the Panhandle-B hydraulic equation. By framing the problem as a search over discretized nodal-pressure assignments coupled with a cost Hamiltonian that encodes both the delivery objective and physical-constraint penalties, we establish a unified formulation suitable for the Quantum Approximate Optimization Algorithm (QAOA). The mathematical model is adapted to a Quadratic Unconstrained Binary Optimization (QUBO) formulation and implemented using the Classiq quantum software platform. In simulator-based experiments, QAOA recovered the maximum-throughput valid operating point, consistent with classical exhaustive evaluation and classical hydraulic simulation reference solutions. A distinctive contribution of this work is the end-to-end execution of a reduced problem instance on the IonQ Forte-1 trapped-ion quantum processor. Remarkably, the hardware implementation used only $p=2$ QAOA layers, substantially fewer than the $p=30$ layers used in the simulator-based study. Despite this significant reduction in circuit depth, the QPU produced physically valid and interpretable candidate solutions that bracketed the continuous classical optimum, with each located within one pressure-discretization step of it. These results demonstrate that meaningful gas-network optimization behavior can be obtained using considerably shallower QAOA circuits than initially expected and provide an end-to-end proof of concept for near-term quantum-assisted gas-network optimization.

Conventional quantum-code constructions encode pure logical states as pure code states, but this restriction can sacrifice performance. We show that intrinsic encoding randomness can improve optimal entanglement fidelity. We bound the loss from imposing a rank-one encoder and prove it is at most quadratic near perfect recovery after joint optimization. The optimized advantage survives small noise perturbations. An explicit noise family requires higher-rank encoders arbitrarily close to perfect recovery, with every optimal encoder mapping pure inputs to mixed code states.

We report the development of flux memory for use with superconducting circuits. This technology stores persistent currents in superconducting loops on-chip to be used to provide flux biasing for superconducting circuits, like qubits. We developed three types of flux memory and draw comparisons among them for circuit design. We demonstrate the utility of flux memory by using an in-situ flux detector and characterize each approach and further demonstrate that once flux is set in a memory cell, benchtop DC control sources can be powered off, leaving the on-chip flux bias in place. We propose that flux memory can be arranged in a two-dimensional configuration to multiplex control signals and reduce how line counts scale (N^2 devices -> 2N control lines), and our experimental results pave the path to the proposed scalability. We demonstrate the use of flux memory to flux bias a transmon qubit and show the tunability of the qubit state to a target frequency which remained stable on-chip for 20 hours.

Fermionic cohomology detects zero-energy states of supersymmetric Hamiltonians. Previous work showed that deciding nonzero cohomology in an input-specified particle-number sector is $\mathrm{QMA}_1$-hard and belongs to $\mathrm{QMA}$. We study total cohomology on the unrestricted full Fock space, where a NO instance must exclude zero-energy states in every sector and in their superpositions. We prove that this global problem is $\mathrm{QMA}_1$-complete. The input differential is an operator that raises fermion number by one and squares to zero on the full Fock space. It is given as an exact list of local fermionic monomials, each involving at most $41$ modes. The reduction encodes each data site by one fermion in a block of modes. Every sector violating this occupation rule has energy at least one. An exact quantum verifier accepts a suitable witness with certainty on every YES instance, establishing containment with perfect completeness. We also prove $\mathrm{QMA}_1$-completeness for the problem in an input-specified particle-number sector. Its hard instances use $30$-mode terms and admit a one-dimensional block-chain realization.

Quantum metrology exploits quantum states to achieve an estimation sensitivity beyond classical limits. In the continuous-variable (CV) regime, the squeezed state has been used to implement deterministic quantum sensing, but the quantum metrology sensitivity of this state is significantly affected by losses or detection inefficiencies, which restrict its applications. In this work, quantum distributed sensing is proposed using optical parametric amplified multimode entanglement generated from squeezed states. It is found that the sensitivity is robust to loss or detection inefficiency when large-gain optical parametric amplification (OPA) is introduced, where a two-mode Einstein–Podolsky–Rosen-entangled state and a four-mode cluster state are exploited for analysis. The quantum sensitivity is greatly improved compared to that without OPA in almost all loss scenarios. The quantum Fisher matrix is calculated for both states to obtain the optimal bound in comparison with our scheme, and it is found that even with a small or moderate OPA gain, quantum sensing can be improved compared with the traditional scheme. The states are also compared with corresponding single-mode squeezed states, finding the parameter ranges where entangled states perform better. This study provides a method for realizing large-scale quantum metrology in real-world applications despite losses or detection inefficiencies.

Multimodal evaluations cannot say whether a vision-language model misread an image or misreasoned about it, because every existing method for separating the two places a second model in the loop. We introduce the render ceiling, a model-free reference for benchmarks built by rendering known objects: inverting the frozen cameras and re-solving cross-view correspondence recovers exactly the answer the images support. We prove the ceiling fails only through an enumerable set of projection coincidences and certify that set empty on 2,160 rendered crystal structures, so every point of a model's deficit belongs to the model. Across fourteen vision-language models, supplying exact geometry as text lifts every model yet closes under half the gap for thirteen, while a supervised vision model with no language component reads the same images at 0.8952, above every vision-language model. The instrument exposes extraction-stage fabrication that downstream accuracy would misattribute to reasoning, yields camera-placement rules for benchmark builders, and transfers to any benchmark with an invertible forward rendering.

Feedback can convert continuously monitored quantum jumps into a thermodynamic resource. We formulate full counting statistics for open quantum systems under unital jump feedback by incorporating the feedback maps into the tilted generator. The resulting trajectory ensemble determines both current fluctuations and the Fisher information of the measurement record. We show that feedback can enhance reservoir-parameter estimation and clock precision without necessarily changing average thermodynamic currents. This enhanced precision is not bounded by reservoir entropy production alone. By embedding the reduced dynamics in an enlarged measurement-feedback process, we derive a feedback-modified thermodynamic uncertainty relation in which the information entropy production of the feedback apparatus supplies the missing cost. A charge-monitored double quantum dot illustrates the framework: jump-conditioned feedback improves thermometry and chemical-potential sensing, and stabilizes a quantum clock defined by output-current ticks.