Papers

In quantum machine learning, training a quantum model requires each sample to be prepared as a quantum state by a loading circuit that must be re-executed for every shot at every training step. The total burden therefore scales with both the number of samples and the cost of preparation. Existing approaches reduce the loading cost of individual inputs or distill data and compress their representations before applying a separate quantum encoding. This separation can leave resulting samples costly to prepare or cause additional loss of the information during subsequent compilation into shallow circuits. We propose quantum dataset distillation (QDD), which distills the full dataset directly into a small set of shallow circuits. Each synthetic sample is parameterized as a staircase circuit corresponding to a low-rank tensor network, making the sample and its loading circuit the same object. The circuit parameters are optimized classically with exact gradients using distribution matching under an explicit loading budget, without post-hoc state-preparation synthesis. On MNIST and Fashion-MNIST, only 10 circuits per class ($0.0017\times$ the full dataset size) achieve accuracy comparable to full-data training and outperform selection baselines under matched sample and loading budgets. In finite-shot training, QDD reaches 95% of the full-data accuracy with more than $100\times$ fewer cumulative shots. Additionally, we validate QDD on real quantum hardware, demonstrating its practical deployment potential.

Grover's algorithm is optimal in terms of oracle queries. We can trade accuracy for speed, which gives rise to the quantum partial-search algorithm. The partial-search algorithm is implemented using two kinds of Grover operators, global and local, where the former is the standard Grover operator for full search and the latter has a diffusion operator acting on the search subspace. The global-local-global sequence, also known as the Grover-Radhakrishnan-Korepin (GRK) algorithm, has been proved optimal in the oracle-query metric. In this work, we show that the alternating sequence of global and local Grover operators, formed by repeatedly applying a fixed product of global and local Grover operators, can achieve a lower expected circuit depth than the GRK algorithm. Through systematic analysis, we obtain its exact success probability, expected depth, and asymptotically optimal parameters. We derive the boundary, characterized by the ratio between the depths of the oracle and the global diffusion operator, separating the depth-optimal and oracle-optimal partial-search algorithms. When the depths of the oracle and the global diffusion operator are comparable, our proposed alternating partial-search sequence can reduce the minimum expected circuit depth by more than 20% compared with the GRK algorithm.

A variety of quantum emitters compete in the quest for the best single-photon source for photonic quantum technologies. Consequently, only a consistent approach to analyze the second-order auto correlation function allows comparison of the multi-photon contribution ($g^{(2)}(0)$) of different sources. However, the community employs different and inconsistent methods for blinking sources, leading to incomparable benchmarks of source quality. Here, we use the emission of an inherently non-blinking quantum dot (QD) and apply artificial blinking through two different mechanisms: masking the recorded raw data in post-processing and emulation of a blinking system by gating the laser excitation pulses. We then compare the $g^{(2)}(0)$ values with the non-blinking result. For the analysis, we investigate five estimators of $g^{(2)}(0)$ actively used in the literature. While fitting the envelope of the correlations on long-time scales with the correct blinking model is the best choice, normalizing to the Poisson level gives by far the worst proximity. Furthermore, we test our predictive model to identify the underlying blinking mechanism of a QD in a circular Bragg grating cavity.

We propose a sub-Doppler cooling scheme for trapped-ion crystals in Paul traps. The combination of a hollow tweezer and microwave drive creates an effective two-level system which is cooled through attractive Sisyphus cooling. For ${}^{171}\rm{Yb}^+$ ions, we numerically identify optimal parameters for one- and two-ion crystals, and investigate the cooling rate in ion crystals with up to three ions. Our cooling scheme utilizes a single ion addressed with a tweezer to achieve sub-Doppler cooling of the $N$ axial motional modes perpendicular to the tweezer propagation direction, does not rely on the Lamb-Dicke regime and uses off-resonant light. We reach $1/e$ cooling times for the center of mass mode of $\tau_{\rm com}<2$ ms, and a steady-state excitation number of $\bar{n}_{\rm{com}}\approx 0.7$. Our scheme is well-suited as an intermediate stage between Doppler cooling and ground-state sideband cooling, and can be readily realized in trapped-ion platforms.

In this paper, I address the problem regarding the physicality of Hilbert space in quantum mechanics, a topic brought into focus by Carcassi et al.'s paper "The unphysicality of Hilbert spaces" recently. I argue for the physicality of the Hilbert space in quantum mechanics, and demonstrate that there are inevitable ambiguity and arbitrariness if we want to identify the set of physical states with a proper subset of it. Moreover, I distinguish the ontological and modal reading of physicality from the pragmatic and operational reading of physicality, and then develop what I call the hierarchical view of physicality. According to this view, physicality is not a monolithic concept, but a layered one that admits degrees. I show the connection between the concept of physicality and modal metaphysics, and finally explain how it can be used to address the interpretational problem of quantum field theory brought by the existence of inequivalent representations.

We propose a framework for optimizing pulsed local oscillators (LO) for homodyne detection of multiphoton-number states by exploiting the tensor structure of their joint-spectral amplitude (JSA). We show that finding the optimal LO is equivalent to computing the JSA tensor's leading unitary eigenpair and that the factor matrices of the JSA's Tucker higher-order singular value decomposition (HOSVD) coincide with the Schmidt modes of the photon number state's single-particle reduced density matrix. We use the HOSVD to bound the optimal homodyne visibility and to initialize gradient based optimization. In simulated JSAs, weakly correlated, few-mode states reach near-unity visibility, with the leading HOSVD mode being the optimal LO, while strongly correlated, multimode states require full optimization and saturate below unit visibility even at the true optimum. These results offer a practical route to design LOs for homodyne detection experiments with realistic sources of photon-number states, which contributes to the practical implementation of sources of non-Gaussian quantum states.

We introduce a class of $2d$ quantum spin systems based on a unitary spherical fusion category with a chosen object. These models have frustration-free, reflection positive, but generally non-commuting local interactions, generalizing the Levin-Wen string-net models. Based on the theory developed in arXiv:2510.20662, we explicitly realize the Temperley-Lieb-Jones algebra, and more generally fusion spin chains as their boundary algebras.

Recent advances have revealed an interplay between quantum computing and topological data analysis (TDA). Most quantum TDA has focused on Betti numbers, which characterize the connectivity and “holes” of a dataset. Homology, however, contains additional information in the form of torsion: a nontrivial cycle can become trivial after being repeated finitely, revealing global constraints on how cycles combine and wrap around one another. Beyond applications in biomolecular studies, torsion appears in physical settings including homological quantum rotor codes, discrete charges, and gauge sectors. We study torsion from both classical and quantum perspectives. Given a graph $G$ and its clique complex $K = \mathrm{Cl}(G)$, we first prove that, for fixed $r$ and prime $p$, deciding whether $H_r(K,\mathbb{Z})$ contains $p$-torsion is NP-hard. As a corollary, when a homological rotor code is specified by $G$, deciding whether the code has a finite-dimensional logical sector of a given order is NP-hard. We discuss related problems, including the Bockstein homomorphism, Smith normal form, lattice saturation, and cohomology. Second, for a finite set of primes $P$, we develop a quantum algorithm that serves as a one-sided torsion witness. For fixed $r$, it outputs WITNESS or INCONCLUSIVE, i.e. WITNESS certifies that either $H_r(K,\mathbb{Z})$ or $H_{r-1}(K,\mathbb{Z})$ contains $p$-torsion for some $p\in P$ while INCONCLUSIVE makes no claim about its presence or absence. We identify a regime in which the algorithm achieves a near-quadratic quantum speedup over the corresponding classical algorithm under the same input model. Our NP-hardness result complements recent hardness results for estimating Betti numbers, adding a complexity-theoretic perspective to quantum TDA. Together, these results demonstrate that integral homology, beyond its Betti numbers, can be computationally challenging.

The Purcell effect has emerged as a powerful mechanism for controlling spontaneous emission and dissipation in cavity and nanophotonic systems; however, its realization in dissipative non-Hermitian hybrid platforms remains largely unexplored. In this work, we investigate the Purcell effect in a dissipatively coupled photon-magnon hybrid quantum system consisting of a yttrium iron garnet (YIG) thin film integrated with an inverted octa-ring resonator (IORR) in a planar geometry. To describe the underlying dissipative hybrid dynamics, we develop a quantum theoretical framework based on non-Hermitian coupled-mode theory combined with the input-output formalism. We also analyze the temporal decay dynamics of the photon-magnon system. Full-wave electromagnetic simulations demonstrate that the system can be engineered to operate in the level-attraction regime through dissipative photon-magnon coupling. By systematically tuning the magnon damping, we uncover the emergence of a Purcell regime in which cavity-photon dissipation is selectively enhanced through magnon-mediated loss channels. We further show that the saturation magnetization (Ms) provides an additional degree of control over the onset, tunability, and robustness of the Purcell enhancement. The combined modulation of magnon damping and Ms strongly influences the effective photon-magnon coupling, hybrid-mode evolution, and dissipation landscape, enabling precise control of hybrid quantum states. These findings establish a versatile strategy for engineering magnetization- and dissipation-controlled photon-magnon interactions in planar, chip-compatible architectures, opening new avenues for non-Hermitian cavity magnonics, tunable microwave dissipation engineering, and hybrid quantum information technologies.

Quantum sensing protocols usually presuppose where and when each signal acts, yet this information is unavailable beforehand in experiments such as scattering and radar. We show that causal agnosticity forces a measurement scheme to be interferometric even when only discrete interactions are allowed. Describing the sensing events in the recently developed quantum state over spacetime formalism, we then prove that the Fisher information of an interferometer is bounded by the squared sum of the local generator norms, independently of how the events are ordered. Nonunitary and spatiotemporally correlated signals can be explained as well when their physical dilation has a spacetime state on the enlarged events. Notably, the bound holds without presupposing a background spacetime that orders the events whenever the full collection of target and auxiliary events has a spacetime state. We show that this bound yields the spacetime Heisenberg limit and characterize its saturation through marginals of the spacetime state `dressed' by the signal. The $N^2$ scaling of the Fisher information with $N$ sensing events arises from the coherence of a single reference system shared across spacetime, whereas independently repeated interferometry obeys the standard quantum limit.

Prior work has explored quantum algorithms for topological data analysis (TDA), revealing the possibility of exponential quantum speedups in estimating the ratios of Betti numbers to the dimension of the combinatorial Laplacian. However, this quantity is only non-vanishing and efficient-to-quantumly-estimate when Betti numbers are exponentially large, a case for which concrete examples are rarely known. Furthermore, certain randomized classical algorithms are sometimes efficient in this regime. Thus, the prospect of achieving quantum advantage in conventional TDA appears fairly narrow. Here, we address these challenges to the quantum advantage in TDA by developing quantum algorithms for Mayer homology, which generalize simplicial homology to $N$-nilpotent boundary operators ($\partial^N =0$) and have recently been successfully applied to real-world TDA contexts. We introduce an efficient quantum algorithm for estimating Mayer Betti numbers and their persistent counterparts. We then prove that for high-order simplices, Mayer Betti numbers are often exponentially large in the dense regime, which ameliorates the normalization bottleneck of conventional quantum TDA. In the same regime, we argue that existing dequantization algorithms developed for conventional TDA, when applied to Mayer homology, generally lose theoretical guaranties, facing certain structural barriers that prevent their practical utilities. We also provide logical resource estimates revealing that a quantum computer with roughly a few hundred qubits and sixty million Toffoli gates could solve Mayer homology problems beyond the capabilities of known classical approaches. Finally, we discuss real-world applications of Mayer homology in genomics, supersymmetry, drug discovery, and neuroscience, revealing the potential of our quantum algorithm to deliver real-world impacts via Mayer homology.

A new wavefront sensing framework based on the interference of counter-accelerating Airy beams is presented. An engineered cubic phase function transforms a single Gaussian beam into two coherent Airy beams with opposite transverse accelerations, which self-recombine during free-space propagation to form an interference pattern encoding the aberrated incident wavefront. Numerical simulations demonstrate accurate recovery of the aberrated exit-pupil phase across the aberration sets considered, with a root-mean-square phase reconstruction error below $10^{-6} \mathrm{\;rad}$ for the aberration set shown and consistently low errors for the other sets, while maintaining accurate recovery in the presence of measurement noise. The approach eliminates collection optics and enables a compact wavefront-sensing architecture for applications where conventional interferometric systems are difficult to implement, including electron-optical systems, augmented and virtual reality systems.

For every fixed integers $r \ge 4$ and $2 \le k \le r-2$, we construct $r$-dimensional cubical sheaf complexes whose degree-$k$ CSS codes have positive constant rate, linear distance, and constant soundness, with bounded row and column weights. Taking $r=4$ and $k=2$ gives a family of asymptotically good binary qLTCs. At the core of our construction is a uniform product-expansion theorem for explicit Reed-Solomon codes on norm-one evaluation sets. The key point is that the expansion constant stays bounded away from zero as the local code lengths grow. We place these codes on arithmetic cubical complexes, obtaining constant local expansion for both the resulting sheaf and its dual. Together with the local-to-global framework of Dinur, Lin, and Vidick (FOCS 2024) and sheaf duality, this gives linear distance and constant soundness, while an asymmetric choice of local code dimensions gives positive rate. The resulting codes are explicit and polynomial-time computable.

We establish a sufficient condition under which overlapping PEPS boundary states satisfy the approximate factorization criterion for a spectral gap. The condition is formulated in terms of the boundary response induced by cutting bonds through the center of a rectangular region. We decompose this response into a contribution common to all four associated regions and a remainder measured in the instantaneous boundary metric. A single linear transport absorbs the common contribution and yields compatible factorization operators, with an error controlled solely by the remainder. We apply this framework to Ising PEPS and to the spin-3/2 AKLT model on the hexagonal lattice. For Ising PEPS, the required boundary-response estimate reduces to a Dobrushin-Shlosman-type condition. For the hexagonal AKLT model, a rooted expansion in paths and loops isolates the common response, while a local comparison of boundary states together with a scalar Kotecký-Preiss estimate controls the remaining terms. In both cases, the factorization error decays exponentially with the overlap width, up to a prefactor proportional to the cut length. For AKLT, we establish the corresponding physical projector estimate and obtain a uniform spectral gap. For Ising PEPS, the gap implication additionally requires compatible injective regional contractions, as specified in the paper. More generally, the method provides a systematic route from locality of PEPS boundary response to spectral gaps of two-dimensional parent Hamiltonians.

Which quantum measurement extracts the most classical information from an ensemble? We introduce the posterior algebra, a new canonical operator algebra selected by mutual information. For faithful ensembles, an affine information bound is exact precisely when this algebra is commutative; its joint spectral measurement is then optimal, and every optimal finite POVM refines it. Binary ensembles have one generator; compactness covers singular states, giving a proof of Shor's finite-dimensional binary orthogonal-measurement conjecture. The framework also gives rigidity bounds and a certified posterior-spectral receiver, validated on 408 mixed-state instances.

We introduce cavity Rydberg quantum photonics as a novel platform for generating hybrid entangled states of optical photons. The system achieves world-record sizes of these states and has the potential to produce yet larger states in the future. In the hybrid entangled state produced here, a superposition of two coherent states is entangled with a polarization qubit carried by a photon in another beam path. We perform quantum state tomography of this hybrid entangled state and evaluate various key properties. By optimizing the decoherence we increase the size compared to previous hybrid entangled states, reaching a size of $\alpha^2= 2.4$. Besides the fundamental interest in Schrödinger cat states, this work is interesting because of potential applications in the field of quantum information processing.

Silicon-based spin qubits in Si/SiGe heterostructures are a leading platform for scalable quantum computing, yet bridging the gap between theoretical computer-aided design(CAD) models and experimental reality remains a significant challenge. Standard simulations often fail to capture critical physical phenomena, such as interface dipoles, parasitic charge accumulation, and the magnetic hysteresis of on-chip micromagnets. In this work, we present a comprehensive, experimentally calibrated 3D simulation pipeline for a 6-dot Si/SiGe device. We refine the semiconductor band alignment and introduce a semi-empirical classical charge screening model to accurately capture the formation of parasitic wells and their suppression of gate lever-arms. Furthermore, we apply the Jiles-Atherton model to account for the hysteresis and pre-magnetization of integrated cobalt micromagnets, successfully reproducing the experimental resonant frequencies across all six qubits. By coupling these calibrated electrostatic and magnetic profiles into a time-dependent rotating wave approximation (RWA) Hamiltonian, we reproduce experimental observables, including microwave power chevrons. This framework provides a robust foundation for predicting device behavior, evaluating microwave line losses, and optimizing future scalable spin qubit architectures prior to fabrication.

Finite-shot optimization can make noisy variational quantum eigensolver energies look artificially accurate. We studied six hardware-tractable molecular active spaces on two IBM Heron r3 processors. Seven optimizer-selected values fell below the exact active-space eigenvalue by up to 17.36 mHa. The cell-balanced fraction of the source-observed best-final advantage not retained on later fixed-parameter measurement was 0.989 (approximate 95% session-level interval [0.906, 1.072]); alternative aggregations span 0.892-0.989. Thus little of the selected advantage remained on average. Measurements occurred 5.6-38.4 days later, so parameter-dependent drift remains a competing explanation. Best-observed hardware VQE values require prompt independent confirmation before supporting accuracy claims.

The fixed-angle conjecture for the quantum approximate optimisation algorithm (QAOA) is shown to be false for depth-2 QAOA on 9-regular graphs, and proven to be correct for depth-1 on any regular graph, as well as for any depth on all 2-regular graphs.

We evaluate the Hellinger-distance coherence of the two-flavor neutrino state subject to Lindblad damping of the mass-eigenstate interference term, and obtain a closed expression in terms of the flavor-basis density-matrix elements. In the two-flavor vacuum treatment with negligible wave-packet separation, the undamped state is pure, and the smallest eigenvalue of the damped state grows linearly with $\epsilon=1-\kappa$, where $\kappa=e^{-\Gamma L}$. An expansion about the pure state then yields a nonanalytic $\sqrt{\epsilon}$ correction to the Hellinger coherence, with coefficient $K=2\sqrt{2}\,u\sin2\theta/\sqrt{1-2u}$, whereas the flavor-transition probability, the $l_1$ coherence, the concurrence, the entanglement of formation and the local quantum Fisher information all respond linearly in $\epsilon$. Using representative Daya Bay, KamLAND and MINOS working points together with a current $90\%$ C.L. bound on energy-independent damping, we find fractional changes in the Hellinger coherence of $0.18\%$, $9.40\%$ and $21.51\%$, against $0.0009\%$, $0.43\%$ and $1.81\%$ for the concurrence. The comparison concerns the response of the quantifiers to the damping parameter and carries no implication about experimental resolution. The same mechanism operates, with a different coefficient, for a correlated dephasing channel acting on the flavor coherence, where the non-Markovian regime produces damped revivals.

We use quantum simulation to study how visible neutrino decay modifies the vacuum CP asymmetry in muon-to-electron oscillations within a $3+1$ neutrino scenario. The decay channel preserves CP symmetry, with CP violation arising from phases in the mixing matrix. We track the energy redistribution from visible decay and distinguish how parent attenuation and daughter regeneration modify the CP asymmetry. For the reference benchmark, the regenerated contribution is $4.85\times10^{-4}$, approximately $46\%$ of the total decay-induced shift. The full circuit for an effective two-energy model agrees with independent classical evolution. On an IBM quantum processor, we prepare the daughter state conditioned on decay and restore its physical normalization using fixed source and decay probabilities. After correction for measurement errors, the flavor-probability and coherence measurements both agree with the prediction within one standard error. Null controls test the suppression of the regenerated signal when daughter coherence or the relevant CP-sensitive mixing factor vanishes.

Quantum Rabi model (QRM) is a fundamental model in light-matter interactions (LMIs), whereas this finite-component system manifests infinite physics to be explored and a full understanding has not yet been reached after a hundred years since it was proposed. In the present work we create a geometric perspective for the QRM by mapping to a curved nanowire system, with curvature-induced spin-orbit coupling (SOC) manipulatable by LMI strength and frequency ratio, which is capable of revealing and perceiving the property universality and diversity from the ground state to the whole spectrum in a unified picture. Indeed, we unveil a super university in the adiabatic regime which manifests a universal scaling of spin texture ubiquitously valid for different couplings, different frequencies and different energy levels. The curve frame also facilitates our finding that a direction changeover of tangential spin swing emerges in the non-adiabatic spin texture in association with the quantum phase transition (QPT) in the QRM, which endows a geometric non-adiabaticity interpretation and connotation to the QPT. We also clarify that, among the curvature-induced effects, the SOC accounts for the spectral bifurcation and oscillations. Our method and analysis, readily generalized to other light-matter models, opens a dialogue between geometry and physics, thus paving a novel way to gain deeper insight into LMIs.

We present a unified study of charge and spin qubits encoded in a single interacting quantum dot tunnel-coupled to Rashba fermionic leads. The dot is described by an Anderson impurity Hamiltonian with either repulsive or attractive local interactions and a magnetic field of arbitrary orientation. In the repulsive regime, a spin qubit is encoded in the singly occupied spin sector, whereas in the attractive regime, close to the degeneracy between the empty and doubly occupied configurations, these two states define a charge-qubit subspace. We combine a weak-coupling Lindblad master equation in the Markovian secular limit with numerically controlled matrix-product-state simulations of the full dot-reservoir system. In equilibrium, we identify magnetic pair breaking in the attractive regime and a weak Rashba-induced magnetic anisotropy when the magnetic field is rotated relative to the spin-orbit axis. In the dynamical regime, relaxation and decoherence are controlled by the energetic gap between the logical manifold and nearby leakage states, and are further enhanced by Rashba-dependent tunneling. These findings show that even a minimal Anderson-impurity description captures key ingredients for coherent spin and charge qubits: the energetic structure of leakage states and spin-orbit-dependent dot-lead hybridization.

Gottesman-Kitaev-Preskill (GKP) states are widely studied as a bosonic encoding for fault-tolerant quantum computing because small displacement errors can be identified and corrected through syndrome measurements. However, fault-tolerant operation requires substantially greater GKP squeezing than is currently available in optical platforms. It is therefore important to identify quantum-information tasks that can be realised with finite-squeezing GKP states. Here, we study Bell nonlocality in finite-energy GKP Bell states under experimentally motivated measurement constraints. Although finite-energy GKP Bell states support Bell nonlocality even at low squeezing, logical Pauli measurements alone cannot reveal it. Accessing the maximum CHSH violation supported by the state generally requires logical non-Clifford rotations. We instead show that the required non-Gaussian resource can reside in the measurement itself. Photon-number-resolving detection combined with Gaussian preprocessing and adaptive feed-forward closely approaches the maximum violation of the CHSH Bell inequality without implementing logical non-Clifford gates. The same measurement principle strongly enhances Bell violations for cat-code Bell pairs and entangled coherent states, demonstrating that its usefulness extends beyond the GKP lattice. Our results identify non-Gaussian measurements as a practical route to revealing Bell nonlocality in finite-energy bosonic states.

Accurate measurement of an intended conditional phase does not by itself place a multiqubit phase gate in its declared generalized-gate equivalence class. We cast the diagnosis as structured Hamiltonian learning of the diagonal successful block in a known basis: Ramsey measurements on a connected graph reconstruct a target-relative eigenphase map; a Walsh transform then yields the per-cycle stroboscopic error generator in a selected logarithm branch, whose branch-dependent coefficients alone cannot decide global equivalence. For diagonal Pauli-Z dressing of weight at most m we derive an exact branch-independent criterion from multiplicative Boolean-Mobius invariants, converted at finite shot counts into a pass/fail/unresolved decision under prespecified tolerances and simultaneous confidence, separate from model rejection. For shared-control C^mZ gates a circular target-face contrast isolates each intended conditional phase, yet a support theorem exhibits forbidden interactions invisible to every target face once multiple targets or external spectators are present. We derive a Cramer-Rao bound for arbitrary integer phase contrasts, recovering the 4^m attempted-circuit scaling of a uniform (m+1)-body face, and quantify degradation from visibility loss, heralded survival, readout confusion, and correlated noise, while systematic bias triggers model rejection. Seeded simulations implement the 4M-setting multiplexed acquisition end to end: for M=3,4,5 at a common budget its mean phase-map RMSE is 0.689-0.794 times a separately compiled statewise scan, and a blind-interaction test yields 300/300 global-audit rejections versus 1/300 for target faces. These results estimate the error generator of a diagonal successful block under a specified acquisition model; they are not unknown-basis Hamiltonian identification, arbitrary-channel tomography, or hardware certification.

We propose a new method for measuring several characteristics of a fermion-boson medium formed during deep inelastic particle scattering. This method involves measuring the group and phase velocities of the accompanying wave process. The phase and group velocities of a wave process are related by the Rayleigh differential condition. The refractive index of a medium is determined by the phase velocity, while the group velocity characterises the medium's dispersion properties. In the case of deep inelastic $ep$ scattering under consideration, the wave process in an individual event is understood to be the exchange between an electron and a proton of an effective, non-perturbative mediator of interaction (${\cal B}$) with the quantum numbers of a neutral current. In the first report, we present new data on the group velocity of interaction carriers ${\cal B}$. We extracted the group velocity modulus values, $U_{_{\cal B}}^*$, from the HERA collider data using a formula derived from modified Heisenberg uncertainty relations and applying the indirect measurement method. The HERA data demonstrate that in the selected kinematic domain the speed of the mediator ${\cal B}$ exceeds the speed of light $c$ in free space, $U_{_{\cal B}}^* > c$. To compare with the obtained data on group velocity, we analyse a simplest model of dispersion relation occurring due to the relativistic relationship between the energy, mass and momentum of a particle, supplemented by de Broglie relations.

Color centers in silicon carbide are a promising platform for quantum technologies, offering long-coherence electron and nuclear spins for storing and manipulating quantum information, as well as single-photon emission for quantum communication. Low photon collection efficiency is commonly addressed by integrating color centers into nanophotonic devices. Here, we report a scalable method for the deterministic integration of color centers into silicon carbide nanopillars, using the same nanoscale mask for both implantation of oxygen-related color centers (PL5, PL6) and subsequent nanopillar fabrication via dry etching. This approach solves the issue of low color center creation yield in nanostructures, with figures of merit comparable to bulk samples. We demonstrate count rate enhancements of up to one order of magnitude for PL5 and four times for PL6, while preserving spin coherence times. Our method is directly applicable to other solid-state platforms, offering a scalable route to efficiently integrate color centers into nanostructures.

Highly entangled and highly non-stabilizer quantum states need not be hard to learn. We give efficient algorithms for testing and recovering hidden tensor-product structure in unknown pure state vectors of the form $\lvert\psi\rangle = U_C \bigotimes_i \lvert\psi_i\rangle$, where $U_C$ is an arbitrary unknown Clifford unitary. Although the Clifford can thoroughly scramble the visible product structure, we prove that the Bell distribution retains a characteristic family of quadratic symmetries. By simultaneously block-diagonalising these symmetries, our algorithms linearize the problem and manage to recover both a disentangling Clifford and the hidden partitions with polynomial sample and computational complexity. This may be viewed as an extension of the abelian StateHSP paradigm in which classical post-processing exposes genuinely quadratic structure. Applied to Choi states, the method yields efficient proper learning algorithms for typical $t$-doped Clifford unitaries in regimes containing exponentially more $T$ gates than previously accessible: the required condition fails only for an exponentially small fraction of circuits when $t\sim n$, and continues to hold for a constant fraction even when $t=2n$. Our framework also provides tools for compressing structured many-body Hamiltonians and suggests benchmarking protocols for encoded logical product states in the early fault-tolerant regime.

Universal information extracted from a critical quantum state depends on how the state is probed. Spatial entanglement, participation statistics, and stabilizer Rényi entropy correspond to different replica geometries and need not isolate the same boundary data. We show that the complete distribution of Pauli magnitudes in critical Ising chains carries an exact geometric fingerprint of boundary termination, distinguishing lattice realizations that flow to the same infrared boundary fixed point. This structure is organized by discrete Selberg ensembles associated with the classical root systems $A$, $B$, $C$, and $D$: three open chains sharing the free–free Ising boundary condition retain distinct $B_L$, $C_L$, and $D_L$ trigonometric wall geometries. The standard symmetry-breaking representatives instead produce rectangular, pinned, and character-inserted $C$ ensembles. Their four boundary moments contain exactly two independent multiplicative combinations invariant under local endpoint normalizations. One of these reduces exactly at finite rank to a moment of the fundamental symplectic character and provides a lattice target for a defect–measurement-boundary junction amplitude. A conditional Gaussian-character law predicts its values throughout the unlocked phase, while exact-arithmetic finite-rank results at the $\alpha=4$ transition depart sharply from the Gaussian continuation. These results show that the full Pauli spectrum resolves boundary information invisible to the infrared boundary fixed point alone and provide concrete targets for replicated boundary conformal field theory.

The fate of average symmetry-protected topological (ASPT) states based on the one-dimensional cluster state is investigated by using the Choi mapping, namely, the doubled Hilbert-space formalism. By introducing two effective spins, $\tau$ and $\eta$, on each doubled rung, we obtain a transparent representation of the ASPT parent Hamiltonian and systematically identify the conserved stabilizers and the corresponding orders. We further study symmetry-preserving operations that deform the ASPT by combining qualitative effective-Hamiltonian and systematic parent-Hamiltonian analyses with numerical matrix-product-state filtering calculations. We find that although the ASPT remains robust over a broad range of decoherence strengths, strong-to-weak spontaneous symmetry breaking (SWSSB) becomes exact in the maximal-decoherence limit. In addition, we consider symmetry preserving no-click postselection, which removes the exact conservation law supporting the Rényi-2 string order of the ASPT and drives the system toward weak-symmetry spontaneous symmetry breaking (WSSB). Again, the ASPT remains robust over a broad range of postselection strengths, with WSSB becoming pronounced only near the projective limit and exact at the limit itself.