Papers

Finding efficient schemes for non-Clifford logic or magic state preparation is one of the central challenges on the way to fault-tolerant quantum computation. Many of the proposed schemes rely on diagonal non-Clifford logical gates acting on CSS codes in space or decorating CSS-type syndrome-extraction circuits in spacetime. Here we propose and implement efficient algorithms to find all (spacetime) logical gates of a given CSS code (circuit) composed from a prescribed set of ansatz gates. Depending on the choice of ansatz gates, this means finding transversal gates, more general locality-preserving logical circuits, folding gates, or similar. While we focus on qubit diagonal gates in the Clifford hierarchy, we also discuss the generalization to arbitrary diagonal non-hierarchy gates, certain non-diagonal gates, as well as prime and composite-dimensional qudits. Our method works by rephrasing code-space preserving gates as the kernel of the “pullback” of the $X$ check matrix onto phase functions, which maps between finite abelian 2-groups. We implement a fast “filtration” method to find this kernel. The runtime for finding fault-tolerant logical gates in a qLDPC code with $O(n)$ qubits or a circuit with $O(n)$ gates in a naive dense implementation is $O(n^3)$, with potential for improvement making use of sparsity.

We continue the study of Phase Retrieval in the Quantum Information setting in the style of \cite{liu2023phase}, in a manner which is more general in two primary ways: (a) Instead of only pure states we consider also states (and positive semidefinite operators) of bounded rank, as is done in Quantum Tomography; (b) We consider general super operators instead of only quantum channels. We show that in order to have phase retrieval with respect to positive semidefinite operators of bounded rank, it suffices to discriminate between perfectly distinguishable pairs (i.e. those with orthogonal supports). From this we prove that phase retrievability is always Lipschitz stable with respect to the trace norm, and then we use the Fuchs-van de Graaf inequalities to deduce stability with respect to the Bures–Wasserstein distance (thus generalizing the known stability results for phase retrieval in Frame Theory). For Hermitian-preserving super operators taking values in block-diagonal matrices, we characterize phase retrievability in terms of conditions inspired by the classical complement property from Frame Theory.

We develop a framework for quantum simulations of lattice SU($N_c$) gauge theory with quarks. Staggered and Wilson lattice fermions are considered in two and three spatial dimensions and a theta angle is included in three dimensions. The physical, gauge-invariant Hilbert space is formulated in a representation basis, where gauge and fermionic degrees of freedom are encoded by irreducible representations of SU($N_c$) that tensor at each lattice site to contain a singlet. We discuss algorithms for simulating time evolution on quantum computers and carry out noiseless simulations of lattice quantum chromodynamics ($N_c=3$) on small lattices with up to 32 qubits, showcasing theta angle effects, hadronic states, string dynamics, and a baryon chemical potential for the first time in three spatial dimensions.

Hong-Ou-Mandel (HOM) interference-based optical neural networks can offer complexity advantages on benchmark learning tasks, but conventional readout compresses the coincidence spectrum into a single scalar, limiting its use in complex settings such as continuous-action reinforcement learning. Here we introduce a spectrum-resolved HOM (SR-HOM) architecture that promotes the photons' spectral degrees of freedom to a trainable computational resource and use it to construct a compact optical actor-critic agent. Diagonal spectral responses generate continuous actions, while higher-order spectral correlations provide nonlinear state-action features for value estimation. Across five continuous-control benchmarks, SR-HOM outperforms parameter-matched multilayer-perceptron baselines, including a \(4.4\times\) improvement in sample efficiency and a \(74.0\%\) increase in best 100-episode moving-average return for LunarLanderContinuous-v3. Applied to online calibration of drifted tunable-coupler CZ and iSWAP gates for transmon qubits, simulations show it restores fidelities to \(0.9917\) and \(0.9952\) respectively, exceeding \(99.8\%\) of their drift-free calibrated values.

Excitonic quantum batteries, based on organic fluorescent molecules embedded in optical microcavities, offer a room-temperature platform for studying collective effects in energy storage and developing applications. Recent experiments have offered evidence of superabsorption, a collective enhancement to the light absorption rate of organic molecules which leads to a scalable power density. However, they have also highlighted the challenge posed by rapid radiative decay of fluorescent molecules, which limits the energy storage lifetime. Current strategies to overcome this trade-off focus on controlling the coupling between the absorbing manifold and that used for energy storage. In this chapter, we review three implementations of this design principle: transferring energy from optically excited states to long-lived dark triplet states, generating triplet pairs and higher-spin states through singlet exciton fission, and forming charge-separated states. We discuss each mechanism from both theoretical and experimental perspectives, with particular emphasis on recent device implementations that have extended storage times by several orders of magnitude. We conclude with a cross-platform outlook on the role of metastable states across coherent and room-temperature implementations, from neutral atom arrays to masers and colour centres.

The Klein-Gordon-Fock (KGF) theory is presented as a single-particle relativistic quantum theory. A Schrodinger-type equation for a single-component wave function is derived. In addition to the KGF Hamiltonian, operators for momentum and orbital angular momentum for a scalar boson are identified, which act within the space of single-component wave functions. This theory is applicable to both massive and massless scalar bosons.

The best known lower bound for the minimum Kochen-Specker vector system in $\mathbb{R}^3$ – 24 vectors – rests on a computational proof whose combinatorial half emits DRAT proofs but whose geometric half does not: the non-embeddability of thousands of candidate graphs is established by Z3's nonlinear real arithmetic, which produces no checkable proof objects. We close this gap for the proof's blocking database. We introduce exact rational case-tree certificates of real non-embeddability, whose splits are polynomial factorizations and rational sum-of-squares decompositions and whose leaves are discharged by injectivity, ideal-membership, or Positivstellensatz-shaped positivity arguments, and we certify all 291 source lines (180 distinct graphs) of the published pipeline's order-10 to order-13 blocking lists. Certificates are replayed by two independent checkers that share no code with the generator: a pure-Python replay over exact fractions, and a total checker implemented and proved sound in Lean 4. The soundness theorem – acceptance implies that no injective-on-rays, orthogonality-respecting assignment of nonzero real vectors realizes the graph – is kernel-checked with axiom closure {propext, Classical.choice, Quot.sound}, and a gcd-free rational arithmetic layer makes the entire verdict computation kernel-reducible, so each per-graph non-embeddability result is a closed kernel theorem proved by decide. The formalization surfaced findings about the published pipeline, including a load-bearing injectivity side condition in its embeddability notion, hidden WLOG case obligations invisible to Z3-based workflows, and an unreproducible candidate count that we resolve against the published artifacts. All certificates, checkers, and proofs are available and replayable from a single build.

This study evaluates a protocol-guided large language model (LLM) agent workflow for quantum program synthesis and execution. A versioned YAML protocol specifies interface and quantum-semantic requirements while leaving circuit design to the model. The workflow combines Qiskit circuit generation, evaluator-guided repair, and quantum processing unit (QPU) deployment. A matched ablation evaluates four LLM endpoints using the variational quantum eigensolver (VQE) for H$_2$, the quantum approximate optimization algorithm (QAOA) for MaxCut, and Fashion-MNIST quantum-kernel classification. Across 240 trials, protocol guidance increased evaluator completion from 80.0% to 99.2%, reduced mean repairs from 2.56 to 0.75, and reduced mean agent time from 55.70 to 30.58~s. Provider-reported token use decreased for three of four endpoints. Completed VQE trials meeting chemical accuracy increased from 16/40 to 29/40, while valid QAOA approximation ratios remained comparable. Semantic review identified rank-one fidelity kernels, reinforcing the distinction between evaluator completion and semantic validity. A 210-run IBM QPU study evaluated the combined generation-and-selection pipelines and confirmed deployment feasibility. The results support protocol guidance as a software-reliability layer that must be complemented by quantum-semantic validation.

We propose a quantum sensor network for direct detection of quantum chromodynamics (QCD) axion dark matter using entangled superconducting qubits. In the presence of a static magnetic field, the oscillating axion field induces a coherent qubit rotation described by an encoding angle proportional to the axion-photon coupling and an unknown dark-matter phase. Treating the phase as an additional unknown parameter turns axion detection into a two-parameter quantum estimation problem. We formulate these signals in Cartesian coordinates, thereby avoiding the singularity that arises in the weak-signal regime and establishing a regular framework for multiparameter quantum estimation. Using this framework, we optimize the quantum sensor network and combine it with Bayesian inference to reconstruct the axion-photon coupling. The optimized protocol accurately recovers the KSVZ and DFSZ benchmark couplings over the mass range $m_a\in[0.1,10]~\mu{\rm eV}$, generalizes to previously unseen masses, and remains robust against realistic superconducting-qubit decoherence and gate errors.

Early transformer fault diagnosis is challenged by nonlinear dissolved-gas interactions, overlapping fault signatures, and limited labeled data, while practical deployment further requires reliable performance under realistic computational constraints. This paper presents a simulation-driven modeling framework for dissolved gas analysis-based transformer fault diagnosis, in which a carefully engineered variational quantum classifier (VQC) is employed as the computational core and systematically analyzed through simulation. The framework integrates domain-aware feature modeling derived from Duval geometry with a lightweight two-qubit quantum representation, enabling nonlinear gas-interaction effects to be captured within a shallow parameterized circuit. A hybrid ZX-YY quantum feature map is designed to model non-commuting feature interactions, while a full-entanglement EfficientSU2 ansatz provides adequate expressive capacity under strict resource limits. Model behavior is evaluated using a comprehensive simulation pipeline including noise-aware circuit emulation, cross-dataset validation, and limited hardware-in-the-loop execution, allowing key effects of circuit depth, noise, and optimization strategy to be examined. Simulation results on benchmark dissolved-gas-analysis datasets demonstrate high diagnostic accuracy, strong generalization capability, and robustness to realistic noise levels with minimal quantum resources. The results highlight the effectiveness of simulation-informed modeling for practical transformer diagnostic applications, offering a reproducible and resource-efficient pathway for evaluating quantum-enhanced fault diagnosis methods.

\abstract{The Lamb shift, one of the most fundamental interactions in atomic physics, arises from the interaction of H atoms with the electromagnetic fluctuations of the quantum vacuum. The energy shift has been computed in a variety of ways. The energy shift, as Feynman and Power demonstrated, equals the change in the vacuum energy in the volume containing the H atoms due to the change in the index of refraction arising from the presence of the H atoms. By using this result and a group theoretical calculation of the contribution to the Lamb shift from each frequency of the vacuum fluctuations, we can obtain an expression for the size of the region of vacuum energy for each frequency \texorpdfstring{$\omega$}{{\omega}} around the H atom due to the Lamb shift. The ground state atom is surrounded by a region of positive vacuum energy that extends well beyond the atom for low frequencies. This region can be described as a steady state cloud of virtual quanta. For energies \texorpdfstring{$E=\hbar\omega$}{E=hbar omega} eV less than 1 eV, the radius of the positive energy region is approximately 14. 4/E Angstroms. For a vacuum fluctuation of wavelength \texorpdfstring{$\lambda$}{lambda} the radius is \texorpdfstring{$(\alpha/2\pi)\lambda$}{(alpha/2pi) lambda}. Thus, for long wavelengths, the region has macroscopic dimensions. The energy-time Uncertainty Relation predicts a maximum possible radius that is larger than this by a factor of \texorpdfstring{$1/ 4\alpha$}{1/(4 alpha)}.} \keyword{Bethe; radiative shift; shift spectral density; spectral volume; vacuum fluctuations; vacuum field; Lamb shift; QED; energy field, renormalization, zero point fluctuations; hydrogen atom}.

The aim of this thesis is to explore the implementation of a special kind of quantum measurements, so called harmonic tight frames. To achieve this goal, representation theory is addressed, emphasizing its construction from irreducible representations and the relations they satisfy. These tools simplify the study due to the existence of symmetries, leading to the concept of group frames, defined as orbits under the unitary action of a group and characterized by their symmetry groups. Among the various groups, the simplest are the abelian ones, giving rise to harmonic frames, which are analyzed through the classification theorem of abelian groups and the characters of their irreducible representations. In the quantum mechanics context, the frame elements can be interpreted as pure states of a system. Therefore, the necessary and sufficient conditions for separability are explored, as separable states are easier to implement due to their local nature. Alternatively, when viewing frames as measurements, the concept of POVMs and Naimark's theorem are studied as key tools for designing measurements in quantum computers. Using this knowledge, a characterization of the harmonic frames is given from the abelian group structure theorem, which allows obtaining a necessary and sufficient condition for their separability. The conditions of maximum entanglement of these states for bipartite systems are also studied, obtaining a necessary condition on the dimensions of the subsystems. Finally, a quantum circuit is obtained that allows implementing the harmonic frames associated to cyclic groups as POVMs using a Fourier matrix and a permutation matrix. We conclude by giving simple examples where the results are applied to quantum computers and proposing future avenues of research that could serve to improve the circuit design and extend it to the case of all harmonic frames.

Parastatistics is an exotic type of exchange statistics beyond fermions and bosons. Paraparticles transform in higher dimensional representations of the exchange symmetry group, analogous to non-Abelian anyons, yet consistently defined in any dimension. Although paraparticles have long been proposed, they were widely believed to be physically equivalent to fermions or bosons. Nevertheless, a recent paper proposed a different theory, called $R$-parastatistics, and demonstrated that nontrivial $R$-paraparticles can emerge as quasiparticles in condensed matter systems, and are observably distinct from both fermions and bosons. This paper develops the theoretical foundation and several extensions of $R$-parastatistics, with particular emphasis on its observable consequences. Central to this paper is a general theory of local observables extending the basic family introduced before. First, we define local observables that distinguish particle types. Second, we formulate local observables at special point defects that probe the internal indices of $R$-paraparticles, crucial for observing $R$-parastatistics and for the proposed applications in quantum information. Third, we introduce local observables that create or annihilate particle-antiparticle pairs, important for building a relativistic quantum field theory for $R$-paraparticles. We further introduce generalized hidden symmetries that act on internal indices of $R$-paraparticles while preserving the local observable algebra, providing a basis for proving local indistinguishability and for connecting to a categorical description of $R$-paraparticles. This work sets a solid theoretical foundation for understanding the fundamental physical properties of $R$-paraparticles and pave the way for finding them in nature.

We present a novel slack-free, penalty-based framework for reformulating constrained binary optimization as Quadratic Unconstrained Binary Optimization (QUBO) on near-term quantum annealing hardware. Given a user-chosen penalty function that most naturally captures a constraint—typically non-quadratic, such as a Heaviside-function surrogate—and a target probability measure over the Boolean hypercube, our method returns the weighted least-squares projection of the chosen penalty function onto the subspace spanned by linear and quadratic Walsh–Fourier characters that correspond to physically realizable couplings on the target hardware graph. Within this restricted family, the resulting quadratic surrogate is uniquely and optimally determined by the normal equations: unlike state-of-the-art approaches, it introduces no per-constraint penalty coefficients to tune and avoids dense all-pairs couplings by construction. Two practical consequences follow. First, the projected penalty respects device connectivity, reducing chain lengths and physical-qubit overhead after minor embedding. Second, we show empirically that this hardware-native surrogate can outperform denser full-pairwise projections, despite being drawn from a strictly smaller approximation space. This advantage widens once the QUBO is embedded and sampled on quantum annealers, yielding samples with the lowest worst-case and mean objective gaps compared to unbalanced penalization and a hardware-blind projection onto all quadratic terms.

We construct quantum Turing patterns in Lindblad lattice dynamics and establish a rigorous theory of their nonlinear order and quantum fluctuations. For an explicit family of completely positive lattice generators with finite-range couplings, the first-moment equations undergo a supercritical instability at a nonzero wave number and admit analytic site- and bond-centered commensurate stripe branches. These branches are locally asymptotically stable in their reflection-fixed period-cell spaces, and projected coherent states exhibit extensive Bragg order on every bounded time interval in the semiclassical limit. We prove $O(N^{-1/2})$ convergence of microscopic covariances to a nonautonomous Gaussian Lyapunov flow, transferring strict partial-transpose uncertainty violations to sufficiently large $N$. In the homogeneous Gaussian sector, a single dimensionless ratio controls both the Turing stability determinant and the logarithmic negativity of opposite momenta, relating wavelength selection directly to quantum entanglement. Differential transport shifts the strongest opposite-momentum correlations from the infrared to the selected Turing scale. Numerical continuation and two-dimensional simulations display stripe, spot, and labyrinth morphologies whose Fourier modes and fluctuation spectra concentrate at the same selected wave numbers.

Interaction-free measurement (IFM) certifies the presence of an absorbing object without a photon ever being absorbed by it. When several candidate locations are available, existing protocols can also identify which one holds the absorber, but they do so by testing paths sequentially through two-path interferometers, resolving a binary presence question at each step. We propose a different approach: probing all candidate locations at once, with the photon prepared in a coherent superposition across every path before a single measurement resolves the outcome. We prove that a three-stage protocol built on a $d$-path interferometer attains the exact one-shot optimum for this task, and we extend it to $k$ absorbers among $d$ paths, where the no-absorption branch encodes the entire absorber subset coherently rather than revealing individual locations one by one. The dark port therefore ceases to be a mere witness of presence and becomes a location-resolving signal. We then move beyond single-pass strategies using the quantum-comb formalism, casting the problem as an exact optimization over all multi-pass strategies and showing that adaptive protocols surpass the one-shot ceiling. Enriching the interferometer geometry with one additional path guaranteed to be empty, we show that sequential scanning, bright-port recycling, and Zeno-type interrogation all become particular feasible strategies within this same optimization, rather than separate benchmarks to compare against. This unified formulation identifies the optimal interaction-free localization strategy for any given set of resources, opening a route toward loss-resilient quantum imaging protocols for the study of fragile, absorption-sensitive samples.

Dielectric loss due to two-level systems is a limiting factor for superconducting qubit relaxation times. These losses arise mostly from nanometer-scale interfacial defect regions in superconducting devices with planar dimensions of microns to millimeters, thus making it resource intensive to accurately simulate the electric field density in these regions with traditional electromagnetic solvers. In this work, we demonstrate a fast boundary integral equation solver that allows precise simulation of electric field density in these thin regions, showing a speedup of around two orders of magnitude over traditional solvers, with relative errors around $10^{-7}$ for a ten-minute solution runtime. By computing participation ratios through Green's first identity without squaring the electric field, our approach is less susceptible to the field singularities near conductor corners. We apply this solver to a basic untrenched coplanar waveguide cross-section, showing that the common assumption of participation ratio linearity with dielectric constant holds well for some interfaces and not others; in particular, while the metal-air (MA) top and corner follow this linear relationship strongly, the MA sidewall does not. We then compare isotropic and anisotropic etching, showing that the MA sidewall and the metal-air-substrate triple junction are the most strongly affected. We are currently leveraging this solver to explore geometries that will uniquely isolate the participation ratios of the different dielectrics. Finally, we are working to combine this solver framework with a full 3D microwave solver to accurately calculate participation ratios for the thin dielectrics that are known sources of loss in superconducting qubits.

We establish a connection between quantum resource theory and probability theory, under repeated application of free operations. We show that strong monotonicity of a resource measure implies that the resource is a supermartingale. We then use the optional stopping and martingale convergence theorems to derive bounds on the efficiency of post-selection, and other free adaptive strategies. We also describe the asymptotic dynamics of the conditional state, where resource fluctuations are necessarily absent, showing one of two distinct phenomena occurs: resource vanishing or resource freezing.

The MacWilliams extension theorem fails for module alphabets with non-cyclic socle, and the label alphabet of qudit stabilizer codes, $\F_{q^2}$ over $\F_q$, is such an alphabet. Quantum error correction, however, only ever sees self-orthogonal additive codes, and whether that rigidity rescues the theorem—equivalently, whether every weight-preserving isomorphism of stabilizer groups is implemented by local Cliffords and a qudit permutation—was asked by Gluesing-Luerssen and Pllaha and answered negatively by Pllaha for particular qubit codes. We develop the negative answer systematically and at the smallest possible scales. For every prime power $q$ we construct a pair of $[[q+1,q-1]]_q$ stabilizer codes and a weight-preserving isomorphism between them extending to no monomial transformation; the codespaces are inequivalent even under arbitrary local unitaries combined with permutations, though they share Shor–Laflamme enumerators. Self-orthogonality is automatic here, by two elementary lemmas which also show that Dyshko's threshold-length counterexamples were already self-orthogonal, unremarked. For qubits we prove by exhaustive search that length $3$ is minimal and the counterexample essentially unique. Dropping the “idle qudit” invariant that detects these, we find the minimal full-support lengths: $4$ for a non-extendable isometry, $5$ for a weight-isometric pair that is not monomially equivalent, realized by explicit $[[5,2]]$ codes; at length $6$ all nontrivial stabilizer elements can have weight $\ge 4$. Whether these codespaces are locally unitarily equivalent is posed as an open problem, connecting the extension problem to the LU–LC circle of questions.

Fault-tolerant topological quantum computing relies on identifying Majorana zero modes (MZMs), but reliable detection in realistic devices remains challenging. Conventional topological indicators are inherently biased in finite, disordered systems, blurring the distinction between true MZMs and trivial states. Furthermore, attempts to map these indicators to real observables via machine learning require dense, expensive conductance measurements, creating a severe scaling bottleneck. To simultaneously address topological bias and measurement limitations, we present MEDA: a Measurement-Efficient, Disorder-Aware framework for MZM detection in realistic devices. MEDA maps sparse, practically obtainable observables directly to the robust periodic disorder invariant (PDI). Using a novel sparse parameter regime, MEDA reduces measurement volume by 10x while maintaining predictive quality, even in moderate to strong disorder regimes that limit conventional methods. Furthermore, MEDA naturally prioritizes input features consistent with the topological gap protocol, demonstrating strong physical interpretability.

Optical quantum networks provide a natural route for connecting distant superconducting quantum processors, enabling distributed quantum computation, sensing, and communication. Piezo-optomechanical transducers are among the leading candidates for scalable microwave-to-optical quantum interfaces. However, prior one-dimensional piezo-optomechanical transducers remain limited by optical-absorption-induced heating and the resulting thermal noise. Two-dimensional optomechanical crystals offer substantially improved thermalization from better thermal anchoring, but their structural complexity has so far hindered the realization of a fully integrated two-dimensional transducer. Here, we overcome this challenge with a new design strategy based on band structure engineering. We fabricate the devices and experimentally characterize the response, measuring an electromechanical damping rate of 4.6 kHz at room temperature and electromechanical coupling rate of 0.17 MHz by wire-bonding to a multi-mode microwave resonator at 10 mK. Bidirectional transduction is performed with a calibrated internal efficiency of 0.85% in the continuous-wave operation, alongside pulsed photon-phonon pair generation near its quantum ground state. Our results represent a significant step toward high-efficiency and low-noise transducers for entangling remote superconducting qubits.

Measurement-based quantum computation (MBQC) is a universal model of quantum computation whose full power requires adaptivity. Contextuality is known to power quantum advantage in MBQC, yet it has resisted algebraic analysis in the adaptive setting. We show that if an adaptive $\mathbb{Z}_2$-linear measurement-based quantum computing protocol deterministically computes a non-affine Boolean function, then the underlying quantum resource satisfies an inconsistent set of linear equations. This witnesses an algebraic form of strong contextuality generalising Mermin's All-versus-Nothing arguments. Such algebraic contextuality can be detected cohomologically, resolving an open question posed by Raussendorf, who had established cohomological witnesses of contextuality for non-adaptive protocols, but left the adaptive case open. We prove this result constructively: we model adaptive measurement protocols as ordinary measurements on a larger scenario of tree-like measurements, and explicitly build the inconsistent equations inductively.

A recent Google Quantum AI experiment [\href{https://www.science.org/doi/10.1126/science.adr9680}{Gyawali et al., Science 393, 71 (2026)}] has exploited quantum parallelism to emulate disorder-averaged many-body dynamics, with conserved local degrees of freedom generating an effective disorder potential. We investigate how the local spectrum of these static variables controls localization in a flavor-extended ${\mathbb Z}_2$ lattice gauge theory, which maps onto a mixed-field Ising chain with $n$-level bond disorder. Combining finite-size spectral and entanglement diagnostics with infinite matrix-product state dynamics, we find a qualitative distinction between binary and multilevel disorder. For $n=2$, apparent localization ultimately gives way to thermalization; the long-lived transient arises from energy-scale separation, degenerate spectral towers, and approximate Hilbert-space fragmentation. By contrast, $n=4$ displays consistent localization signatures, including Poissonian level statistics, area-law eigenstate entanglement, nonthermal entanglement spectra, and persistent local memory over accessible times in the thermodynamic limit. Our results show that, despite its larger variance, binary disorder lacks the local amplitude diversity needed to suppress resonances. Thus, localization is governed not simply by disorder strength, but by the local disorder spectrum and the resulting resonant connectivity of the many-body Hilbert space.

Detecting nonstabilizerness requires full tomography and an optimization over exponentially many stabilizer states. A limited Pauli measurement set promises resource-efficient magic certification, yet the resulting reduced stabilizer polytope is generally difficult to characterize. We trace this difficulty into two coupled obstructions: the simultaneous measurability of measurements captured by their frustration graph structure, and the consistency of sign dependencies from stabilizer formalism. We show that the sign dependencies can be discarded exactly whenever active dependencies are absent, and that perfect frustration graphs then make this reduced polytope efficiently solvable. This solvable regime derives a closed form bounded by the clique number of the frustration graph, revealing a tradeoff between witness capacity and simultaneous measurability. Clifford covariance allows rotated measurement sets to enlarge the detectable state space without raising the capacity. Graph structure therefore emerges as both a certificate of tractability and a design principle for scalable magic resource detection.

Nonholonomic mechanics describes systems subject to non-integrable velocity constraints, such as rolling bodies and skating motion. These systems generally lack a canonical Hamiltonian formulation, obstructing standard quantization methods. Here we quantize nonholonomic systems as Markovian open quantum systems, with the nonholonomic constraint appearing in a large-dissipation limit. We find explicit Lindblad superoperators that reproduce the classical dynamics of the Chaplygin sleigh and the Suslov problem in the semiclassical limit. The master equation is numerically simulated, and the covariance is shown to satisfy a relation predicted by the theory of metastability in open quantum systems.

A central question in quantum information is whether a given set of states can provide an advantage in some information-processing task. We establish a universal connection between two such questions: how well a set of states can be discriminated, and whether it can power tasks whose advantage stems from generalized contextuality. Working in the framework of generalized probabilistic theories (GPTs), which includes quantum and classical systems as special cases, we show that any set of states able to provide a nonclassical advantage in a contextuality-powered task must obey nontrivial upper bounds on the success probability of every state discrimination task using the full set. Contextual advantage therefore implies limited distinguishability, exposing a trade-off between two basic operational resources. Importantly, this is more than a statement about the idealized limit: perfect distinguishability is not needed to preclude contextuality. Our thresholds lie strictly below unity, so any set whose discrimination performance exceeds them while still imperfectly distinguishable is already guaranteed to admit a noncontextual explanation. The bounds follow from a simple geometric property, linear dependence of the state set, take a closed analytical form, and depend only on the prior of the task and the convex geometry of the states. As an illustration, we apply them to generalized parity-oblivious multiplexing, where sufficiently high success in the task implies that at least one sub-ensemble of the codebook cannot power any contextual advantage.

Simulating the real-time dynamics of particle collisions is a promising application of quantum simulators, because classical methods such as tensor networks struggle to capture the highly entangled states generated in high-energy scattering. Realizing such simulations requires both the preparation of incoming wave packets and the detection of the outgoing scattering products. In this work, we propose protocols that address both challenges on programmable analog and digital quantum simulation platforms. Our state-preparation scheme uses a weakly coupled auxiliary qubit - or, more generally, a customized local quench - to inject a single quasiparticle with well-defined momentum. Because it relies only on conservation of energy, this scheme requires no fine-tuning or prior knowledge about particle eigenstates, making it robust against errors in calibration and implementation. The momenta of scattering products are then extracted, using only local measurements, from the interference pattern that arises when particles are reflected at the system's boundary. We validate our protocols through numerical simulations, first in a simple single-particle model and subsequently in two interacting many-body systems: a Rydberg atom chain and an Ising chain in a mixed field. We demonstrate how high-energy regimes, necessary to access inelastic scattering processes, can be reached through an adiabatic ramp, and how the wave packet shape can be optimized by spatially modulating the Hamiltonian. Finally, we show how the protocol can be generalized to systems with more than one spatial dimension. Our proposal provides a versatile approach to the quantum simulation of scattering phenomena, and is compatible with several quantum simulation platforms that are already experimentally available.

Generalized contextuality is a canonical distinguishing property of nonclassical generalized probabilistic theories, in particular quantum mechanics. Methods for certification and characterization of generalized contextuality of a given generalized probabilistic theory are well developed for prepare-measure and single-stage prepare-transform-measure scenarios. In a recent work [arXiv:2512.10000], a bottom-up, statistics-first linear-algebraic framework for contextuality in prepare-measure scenarios was introduced. We extend this approach to operational scenarios with sequential transformations with an arbitrary number of stages. We give a full decision procedure for contextuality of such scenarios within operational theories and analyze its computational complexity. In particular, our decision procedure has a complexity linearly exponential in the minimum generalized probabilistic theory (GPT) dimension, and polynomial in the number of procedures. We demonstrate our framework and approach through multiple examples, including Spekkens' toy theory and the 8-state single-qubit stabilizer theory. In particular, we construct an operational theory in which contextuality manifests itself only in the sequential structure of the transformations. Our findings thus shed new light on the significant role of compositional structures in the phenomenon of generalized contextuality.

Non-Abelian gauge theories with dynamical matter govern the strong interaction and a broad class of strongly correlated quantum systems, yet their ground-state properties remain difficult to obtain from first principles. Using a continuous-group variational Monte Carlo approach that retains the full SU$(2)$ gauge field without truncation, we determine the ground-state behavior of the SU$(2)$ lattice gauge theory with staggered fermions on an $L\times L$ square lattice. Treating the magnetic and electric couplings $\lambda$ and $g^2$ independently, we find a magnetic-flux transition at $\lambda^\ast=-0.040\pm 0.005$, with no resolvable drift of the transition point as the electric coupling is varied. Along the physical coupling line $\lambda=4/g^2$, for $L=4,6,8$, we uncover a gauge-matter delocalization crossover from a flux-disordered regime at strong electric coupling to an ordered unity-flux regime at weak coupling. The chiral condensate, a gauge-invariant Wilson-line meson correlator, and the local color density consistently reveal the emergence of coherent gauge-assisted matter dynamics. Together, these results provide a unified physical picture of how magnetic-flux ordering and fermionic coherence develop in an untruncated non-Abelian lattice gauge theory.

Determining the ground state of non-Abelian lattice gauge theories coupled to dynamical fermions is key to understanding confinement and the phase structure of gauge–matter systems. We present a variational Monte Carlo framework for the ground state of the untruncated fully-continuous SU$(2)$ lattice gauge theory coupled to dynamical staggered fermions on an $L\times L$ square lattice. We work in the magnetic basis with a neural-network representation of the gauge wavefunction. The fermions are described by a gauge-covariant Gaussian fermionic correction built on a fixed Néel reference state where, for each sampled gauge configuration $\mathbf{U}$, the correction is generated by a Hermitian operator. This operator is constructed from short Wilson lines and the eigenvectors of the mass–hopping Hamiltonian, with number of variational parameters polynomial in the system size. This Gaussian structure also gives analytical expressions for all fermionic contributions to the energy and related observables in terms of the fermion occupation matrix. The results are validated against strong-coupling perturbation theory, where they recover the expected effective antiferromagnetic spin Hamiltonian. Using this framework, we map a coarse ground state phase diagram in the plane of independent electric and magnetic couplings $(g^2, \lambda)$ and show that a hysteresis analysis can identify the existence of phase transitions. Restoring the physical relation $\lambda=4/g^2$, we characterize how increasing the system size and changing the electric coupling $g^2$ move the state away from the reference Néel state, for lattice sizes $L=4,6,8$. More broadly, the method offers a sign-problem-free variational framework for continuous non-Abelian gauge groups with dynamical matter that should extend to other matter content and higher-dimensional lattices.