Papers

We extend a perturbative Dyson-type treatment and discrete-symmetry constraints from the Schrödinger and von Neumann equations to a dephasing Lindblad framework. This work develops further the odd-symmetric formulation involving dual temporal conditions from general dynamical considerations to specific tools of quantum mechanics. Applying the resulting scaling relations to published single- and double-diffractive data in $pp$ and $p\bar{p}$ collisions (ISR, UA4, UA5, CDF, D0, ALICE, and E710), we show that single-diffraction cross sections are well described by a three-parameter fit with a relative RMS deviation of $\sim 4\%$, substantially improving upon conventional approximations that neglect decoherence. The extracted decoherence factor is consistently $\phi \approx 0.89$, in agreement across SD, DD, and E710-based (direct) estimates, and is naturally interpreted as $\phi =1$ for CP-invariant dephasing but $\phi <1$ for CPT-invariant dephasing, favouring the latter.

In contrast to eigenvalue-based approaches, we formulate the bulk-boundary correspondence for two-dimensional non-Hermitian quadratic lattice Hamiltonians in terms of Toeplitz operators and singular values, which correctly capture the stability, localization, and scaling of edge and corner modes. We show that singular values, rather than eigenvalues, provide the only stable foundation for topological protection in non-Hermitian systems because they remain robust under translational-symmetry-breaking perturbations that destabilize the eigenvalue spectrum, rendering it unsuitable for topological classification. Building on Toeplitz operator theory, we establish general results for non-Hermitian Hamiltonians defined on half and quarter planes, relating the topological indices of the associated Toeplitz operators to the number of finite-size singular values that are separated from the bulk singular-value spectrum and vanish in the thermodynamic limit. This yields a precise bulk-boundary correspondence for edge and corner modes, including higher-order topological phases, without requiring crystalline symmetries. We illustrate our general results with detailed examples exhibiting topologically protected families of edge states, coexisting edge and corner modes, and phases with both gapped bulk and edges supporting only stable corner modes. The latter is exemplified by a non-Hermitian generalization of the Benalcazar-Bernevig-Hughes model.

One-dimensional chains of coupled spins are minimal models of strongly correlated quantum matter, and have been proposed as wires for transporting quantum information. In liquids, rapid molecular tumbling averages anisotropic dipolar couplings and leaves effective isotropic scalar $J$-coupling Hamiltonians. At zero- to ultralow-field (ZULF) conditions, differences in frequency between nuclear spins of different types are quenched and the internal Hamiltonians can be closely approximated by an isotropic Heisenberg model. In this work, we present [U-$^{13}$C,$^{15}$N]-butyronitrile as a chemically engineered nuclear spin chain whose full spin-spin coupling network can be determined and validated by combining high-field NMR detection with evolution at ultralow fields. Starting from high-field (16.4 T) NMR spectra of $^1$H, $^{13}$C, and $^{15}$N nuclei, we extract all relevant $J$-couplings within a 12-spin network (four $^{13}$C, one $^{15}$N, and seven $^1$H). We then employ a mechanical field-cycling apparatus to prepolarize the spins at high field, shuttle them into a magnetically shielded region for evolution at <50 nT, and detect signals after returning to high field. Fourier analysis of the ultralow-field evolution yields indirect $J$-spectra that are conceptually analogous to ZULF NMR spectra but measured by a high-field NMR spectrometer. We observe clear spectral features at $J$, 1.5$J$, and 2$J$, in good agreement with simulations using the extracted coupling matrix. Finally, we demonstrate 2D experiments that correlate high-field chemical shifts and, thus, fully map interactions within the molecular spin chain. Our results establish [U-$^{13}$C,$^{15}$N]-butyronitrile as an extremely well-characterized spin chain model system and provide a quantitative Hamiltonian benchmark for future hyperpolarization and quantum-control studies.

Rydberg blockade gates are the most experimentally mature entangling operations in neutral-atom quantum processors, combining fast gate times with simple control, but their performance degrades at larger interatomic separations and remains sensitive to motional and technical noise. Non-blockade gate schemes, such as dark state and geometric protocols, offer complementary robustness but typically rely on complex and experimentally demanding control. Here we show that quantum optimal control enables non-blockade gate schemes to be implemented using the experimentally established pulse-shaping techniques developed for blockade-based gates. Focusing on the dark state gate, we construct non-adiabatic implementations that preserve the intrinsic robustness of adiabatic dark state protocols while achieving gate times comparable to time-optimal blockade gates using only smooth, experimentally feasible pulses. The resulting gates exhibit enhanced resilience to motional coupling, laser noise, and interaction inhomogeneity, particularly near and beyond the blockade radius. This work establishes a practical route to fast, robust non-blockade-based two-qubit gates without increased experimental complexity.

These notes introduce quantum computation and quantum error correction, emphasising the importance of stabilisers and the mathematical foundations in basic Lie theory. We begin by using the double cover map $\mathrm{SU}_2 \rightarrow \mathrm{SO}_3(\mathbb{R})$ to illustrate the distinction between states and measurements for a single qubit. We then discuss entanglement and CNOT gates, the Deutsch–Jozsa Problem, and finally quantum error correction, using the Steane $[[7,1,3]]$-code as the main example. The necessary background physics of unitary evolution and Born rule measurements is developed as needed. The circuit model is used throughout.

Near-field force measurements at submicron separations can probe Casimir effects and hypothetical short-range interactions, but require cryogenic operation and stable, in situ control of separation-dependent backgrounds. We propose a self-calibrating quantum force-gradient sensor in which a ferromagnetic microsphere is Meissner-levitated above a type-I superconducting plane, while a bias magnetic field reproducibly tunes the equilibrium gap for in situ separation scans without mechanical approach. The force gradient is encoded as a resonance-frequency shift tracked by a phase-locked loop, and the motion is read out with a SQUID-coupled, flux-tunable microwave resonator that provides adjustable measurement strength without optical heating. Using the input–output formalism, we derive the conditions for reaching the standard quantum limit (SQL) and identify a counterintuitive scaling law: because displacement-to-flux transduction increases with microsphere size, larger microspheres require fewer photons to reach the SQL, enabling a pathway to macroscopic quantum metrology. We quantify the trade-off between suppression of electrostatic patch potentials (via Au coating) and eddy-current dissipation, project force sensitivities of $\sim 10^{-19}\,\rm{N\,Hz^{-1/2}}$ at millikelvin temperatures, and outline protocols to extract Casimir pressure and constrain Yukawa-type deviations from Newtonian gravity over $0.1$–$10\,\mu\mathrm{m}$.

A long-standing goal of nuclear theory is to explain how the structure and dynamics of atomic nuclei and neutron-star matter emerge from the underlying interactions among protons and neutrons. Achieving this goal requires solving the nuclear quantum many-body problem with high accuracy across a wide range of length scales and density regimes. In this review, we discuss how artificial neural network representations of the nuclear many-body wave function have significantly extended the capabilities of continuum quantum Monte Carlo methods. In particular, neural network quantum states enable calculations of larger systems than were previously accessible and provide a flexible framework for capturing phenomena that challenge conventional approaches, including the emergence of nuclear clusters and superfluid phases in dense matter. We highlight recent applications to finite nuclei, infinite nuclear and neutron matter, and dynamical processes relevant to lepton-nucleus and nucleus-nucleus scattering. We also discuss conceptual and methodological connections with condensed matter physics, emphasizing developments in neural network quantum states that bridge strongly correlated systems across disciplines. Together, these developments demonstrate how neural-network methods open new avenues toward unified and accurate descriptions of nuclear structure, matter, and reactions.

Aharonov-Bohm (AB) caging is a complete localization phenomenon in two-dimensional lattices due to destructive interference induced by the background gauge fields. However, current investigations of AB caging are mostly restricted to the Abelian gauge field case, and the observation of AB caging under non-Abelian gauge fields in a quantum system still remains elusive. Here, we report experimental realization of tunable synthetic non-Abelian SU(2) gauge fields in a rhombic lattice, engineered within the synthetic dimensions of a vibrating trapped ion with multiple levels. We realize AB caging under both Abelian and non-Abelian gauge fields and systematically investigate the distinctive transport properties of the non-Abelian case. In particular, we observe typical emergent quantum dynamics unique to non-Abelian AB caging, including initial-state-dependent dynamics, second-order effects, and asymmetric caging behavior. These observations demonstrate the trapped ion system as a powerful platform for simulating emergent phenomena in high-dimensional quantum systems with exotic synthetic gauge fields.

In this work, we compute the defect relative entropy between topological defects in the symmetric product orbifold CFT $\mathrm{Sym}^N(M) = M^{\otimes N}/S_N$. Our analysis covers two distinct classes of defects: universal defects, which realize the $\mathrm{Rep}(S_N)$ non-invertible symmetry, and non-universal defects. We show that the defect relative entropy reduces to a Kullback–Leibler (KL) divergence. The resulting expression decomposes naturally into two contributions: one governed by characters of the symmetric group $S_N$, and the other controlled by modular $S$-matrix elements of the seed RCFT. Remarkably, both sets of data appear as probability distributions, yielding an information-theoretic interpretation of permutation group data and modular data within the symmetric orbifold. The structure of the divergence depends sensitively on the defect class. For universal defects, only the permutation group data contributes; for maximally fractional defects, both permutation and modular data enter and together define the relevant probability distributions. This feature suggests that the maximally fractional defect can be understood as a kind of product of the RCFT defect and the symmetric orbifold defect.

Synthetic frequency dimension offers a powerful approach to simulate lattice models and control photon dynamics. However, extending this concept into the quantum regime, particularly at the single-photon level, has remained challenging in photonic platforms. Here, we demonstrate quantum-state initialization and detection of single-photon evolutions within a synthetic frequency lattice by integrating a superconducting qubit with a 16-meter aluminum coaxial cable. A tunable superconducting quantum interference device (SQUID)-based modulator is employed to synthesize lattice couplings and artificial gauge fields. We observe single-photon quantum random walks and Bloch oscillations, as well as nonadiabatic, unidirectional frequency conversion under rapid temporal modulation of the lattice Hamiltonian, together with band-structure measurements. The lattice connectivity can be readily reconfigured to construct higher-dimensional lattices using multiple drive tones. Our results establish superconducting quantum circuits as a versatile platform for programmable Hamiltonians and extensible synthetic lattices with flexible single-photon control.

This paper introduces a group-theoretic framework to analyze the algebraic structure of the Grover walk on a complete graph with self-loops. We construct a group generated by the Grover matrix and a diagonal matrix whose entries are powers of a complex root of unity. We then characterize the resulting quotient group, which is defined using a subgroup formed by commutators involving these matrices. We show that this quotient group is isomorphic to a finite cyclic group whose structure depends on the parity of the number of vertices. This group-theoretic characterization reveals underlying symmetries in the time evolution of the Grover walk and provides an algebraic framework for understanding its periodic behavior.

Bridging quantum optics and strong-field physics provides a pathway to explore how quantum light shapes extreme nonlinear light-matter interactions. However, direct characterization of non-classical light at damage-threshold intensities remains an open question. Here, we theoretically investigate the impact of photon-number fluctuations of squeezed light on strong-field photoelectron holography using a quantum-optical strong-field approximation. We identify a mechanism, ponderomotive dephasing, whereby the inherent quantum fluctuations of the driving field dictate the stability of the electron's semiclassical action. While amplitude-squeezed light stabilizes the action to enhance holographic contrast, phase-squeezed light amplifies photon-number noise, causing a rapid collapse of fringe visibility. This quantum-optical sensitivity follows a steep quartic wavelength scaling, rendering mid-infrared drivers uniquely sensitive to the field's underlying quantum nature. Crucially, we show that the collapse of holographic contrast is not a loss of information but a metrological gain. By evaluating the Classical Fisher Information, we identify a "dark-port" mechanism in the tunneling tail that enables the estimation of field quadrature noise beyond the Standard Quantum Limit. This fundamental trade-off between structural imaging fidelity and statistical sensitivity establishes the framework for Attosecond Quantum Tomography: an in-situ, reference-free protocol to reconstruct the Wigner distribution of intense quantum light. Our results identify strong-field ionization as a nonlinear quantum transducer, bridging attosecond electron dynamics with quantum information science.

We show that the claim in Ref. [PRL 131, 200202 (2023)], that the quantum time evolution always can be written as a product of a holonomy operator and a dynamic operator, is false, as it is based on a circular use of the time evolution operator.

We present for the first time a general theory of error correction for permutation invariant (PI) codes. Using representation theory of the symmetric group we construct efficient algorithms that can correct any correctible error on any PI code. These algorithms involve measurements of total angular momentum, quantum Schur transforms or logical state teleportations, and geometric phase gates. For erasure errors, or more generally deletion errors, on certain PI codes, we give a simpler quantum error correction algorithm.

We derive the Ward-Takahashi identity and establish the gauge-invariant response theory for open quantum systems described by Lindbladians to show that particle-number conservation is not necessary to satisfy gauge invariance. We construct an observable which can be used to test the gauge invariance in the absence of particle-number conservation. We derive the low-energy collective modes that emerge as a consequence of gauge invariance in open quantum systems, and find that two-body loss induces diffusive modes in dissipative Bardeen-Cooper-Schrieffer (BCS) superconductivity. Possible experimental situations for testing gauge invariance in open quantum systems are also discussed.

We discuss a scheme to generate large Fock states. The scheme involves repeatedly applying an experimentally feasible unitary transformation to convert a semiclassical state into a Fock state. The transformation combines Kerr interaction, which is a non-Gaussian operation, and pulsed coherent drives. We identify suitable parameter values (Kerr strength, pulse timings, displacement amplitude) for the physical processes to implement the transformation and generate large Fock states with near-unity fidelity. The feasibility of implementing the scheme in circuit QED architectures is discussed. The method is also suitable for generating Fock states of cavity fields.

In this paper, we develop a theoretical framework that extends single-reference (SR) coupled-cluster (CC) theory beyond its conventional role of describing a single electronic state-typically the lowest-energy state within the symmetry sector defined by the reference determinant. Rather than viewing the SR-CC cluster operator solely as a device for reproducing one target state, we consider more general constructions in which different components of the cluster operator play distinct roles, ranging from encoding states of different symmetry than the reference to enabling SR-CC Ansatz to describe multiple states simultaneously. These developments lead to a new class of SR-CC downfolding formalisms in which the resulting active-space effective Hamiltonians are capable of concurrently representing multiple correlated states nonorthogonal to the reference function. We establish three theorems that formalize this extension and demonstrate that standard CC downfolding emerges as a special case of the proposed framework. Finally, we introduce a Hermitian variant based on a unitary CC representation, which enables realistic simulations of ground and excited states while reducing the quantum resources required.

We present a digitized implementation of rapid adiabatic passage based on a train of weak, frequency-varying ultrafast pulses. Analytic conditions on the subpulse Rabi frequencies and detunings are derived to reproduce the continuous-time population dynamics of a conventional long-pulse excitation. We find that the reproduced dynamics achieves high fidelity even for pulse trains with a small number of subpulses, provided that each subpulse remains within the perturbative regime. The subpulses act as discrete samples of the underlying continuous evolution; consequently, more complex population dynamics, characterized by multiple oscillations prior to the onset of adiabaticity, require a larger number of subpulses for accurate reproduction. In addition, we demonstrate how the sidebands of a frequency comb can be exploited for resonant excitation at large carrier detuning and for the precise preparation of superposition states.

This letter presents a model system for controllable two-magnon interference in the time domain. This two-magnon interference, i.e., a magnonic analog to the photonic Hong-Ou-Mandel effect, is supported by a tunable magnonic beamsplitter operation formed in a hybrid cavity magnonic system comprising a pair of mutually coupled magnon modes. By applying a time-dependent magnetic field, magnons can be excited independently in each mode and subsequently brought into interaction, shifting from independent to collective oscillations, to realize a controllable magnonic beamsplitter. When the beamsplitter operation is applied to an initially unentangled two-magnon state, a maximally entangled magnonic $N00N$ state with tunable phase sensitivity is produced. These findings suggest that two-magnon interference in hybrid cavity magnonic systems may enable novel quantum metrological devices to study fundamental magnon dynamics and contribute to developing hybrid magnonic quantum computing architectures.

We propose a flux-pumped superconducting parametric amplifier based on symmetrically threaded superconducting quantum interference devices (SQUIDs) that achieves a Kerr-free operating point under suitable drive conditions. Eliminating the Kerr nonlinearity is advantageous for quantum-limited amplification, as it mitigates unwanted distortions in squeezing and prevents degradation of both gain and quantum efficiency in the high-gain strong drive regime. By replacing the central junction in the symmetrically threaded SQUIDs (STS) configuration with a linear inductor, we find that the Kerr-nonlinearity can be eliminated and the effective Hamiltonian reduces to that of a degenerate parametric amplifier (DPA), up to higher-order corrections in the zero-point fluctuations of the superconducting phase operator. We show that the deviations from ideal DPA behavior introduced by these higher-order terms are significantly weaker than those associated with a Kerr nonlinearity. Consequently, the STS design can be driven strongly while maintaining near-quantum-limited performance at the Kerr-free point. Our analysis predicts phase-preserving gain and efficiency approaching the quantum limit, with robust operation demonstrated up to 25 dB of gain.

Entanglement is a central resource in quantum information science, and it is therefore important to design local discrimination protocols that minimize entanglement cost. In this paper, we propose several entanglement-assisted discrimination schemes for the local discrimination of a representative strongly nonlocal unextendible product basis (UPB) in a \(3\otimes 3\otimes 3\) system. By exploiting the structure of the UPB and the properties of maximally entangled resources, we generalize the protocols to a family of strongly nonlocal UPBs in \(d\otimes d\otimes d\) systems. In particular, we show that these UPBs can be perfectly distinguished using two bipartite maximally entangled states, distributed between different pairs of parties, without employing quantum teleportation. We further compare the total supplied and average consumed entanglement under a clearly specified accounting convention. The results demonstrate that avoiding teleportation can reduce the required entanglement in suitable resource-allocation scenarios and clarify the operational role of low-dimensional maximally entangled resources.

Quantum reservoir computing offers a promising route for time series learning by modelling sequential data via rich quantum dynamics while the only training required happens at the level of a lightweight classical readout. However, studies featuring efficient and implementable quantum reservoir architectures along with model learning guarantees remain scarce in the literature. To close this gap, we introduce QuaRK, an end-to-end framework that couples a hardware-realistic quantum reservoir featurizer with a kernel-based readout scheme. Given a sequence of sample points, the reservoir injects the points one after the other to yield a compact feature vector from efficiently measured k-local observables using classical shadow tomography, after which a classical kernel-based readout learns the target mapping with explicit regularization and fast optimization. The resulting pipeline exposes clear computational knobs – circuit width and depth as well as the measurement budget – while preserving the flexibility of kernel methods to model nonlinear temporal functionals and being scalable to high-dimensional data. We further provide learning-theoretic generalization guarantees for dependent temporal data, linking design and resource choices to finite-sample performance, thereby offering principled guidance for building reliable temporal learners. Empirical experiments validate QuaRK and illustrate the predicted interpolation and generalization behaviours on synthetic beta-mixing time series tasks.

Integer Linear Programs (ILPs) are a flexible and ubiquitous model for discrete optimization problems. Solving ILPs is NP-Hard yet of great practical importance. Super-quadratic quantum speedups for ILPs have been difficult to obtain because classical algorithms for many-constraint ILPs are global and exhaustive, whereas quantum frameworks that offer super-quadratic speedup exploit local structure of the objective and feasible set. We address this via quantum algorithms for Gomory's group relaxation. The group relaxation of an ILP is obtained by dropping nonnegativity on variables that are positive in the optimal solution of the linear programming (LP) relaxation, while retaining integrality of the decision variables. We present a competitive feasibility-preserving classical local-search algorithm for the group relaxation, and a corresponding quantum algorithm that, under reasonable technical conditions, achieves a super-quadratic speedup. When the group relaxation satisfies a nondegeneracy condition analogous to, but stronger than, LP non-degeneracy, our approach yields the optimal solution to the original ILP. Otherwise, the group relaxation tightens bounds on the optimal objective value of the ILP, and can improve downstream branch-and-cut by reducing the integrality gap; we numerically observe this on several practically relevant ILPs. To achieve these results, we derive efficiently constructible constraint-preserving mixers for the group relaxation with favorable spectral properties, which are of independent interest.

The Discrete Fourier Transform (DFT) is central to the analysis of uniformly sampled signals, yet many practical applications involve non-uniform sampling, requiring the Non-Uniform Discrete Fourier Transform (NUDFT). While quantum algorithms for the standard DFT are well established, a corresponding framework for the non-uniform case remains underdeveloped. This work introduces a quantum algorithm for the Non-Uniform Quantum Fourier Transform (NUQFT) based on a low-rank factorization of the NUDFT matrix. The factorization is translated into an explicit quantum construction using block encodings, Quantum Signal Processing, and the Linear Combination of Unitaries framework, yielding an $\epsilon$-accurate block encoding of the NUDFT matrix with controlled approximation error from both classical truncation and quantum implementation. Under standard oracle access assumptions for non-uniform sampling points, we derive explicit, non-asymptotic gate-level resource estimates. The resulting complexity scales polylogarithmically with target precision, quadratically with the number of qubits through the quantum Fourier transform, and logarithmically with a geometry-dependent conditioning parameter induced by the non-uniform grid. This establishes a concrete and resource-efficient quantum analogue of the NUDFT and provides a foundation for quantum algorithms on irregularly sampled data.

We report a hidden density-wave instability in the trimer-based ruthenate Ba4Ru3O10, previously regarded as a pure antiferromagnet with a phase transition at TA=100 K. This transition is manifested in lattice parameters, transport, thermodynamics, and magnetic susceptibility, yet remains remarkably insensitive to magnetic fields up to at least 14 T, indicating an electronically driven reconstruction. At much lower temperatures T*= 20 K, charge transport becomes strongly nonlinear, exhibiting distinct depinning thresholds, negative differential resistance, pronounced current- and frequency-dependence, and slow collective dynamics in the Hertz range. While each feature is characteristic of density-wave transport, their simultaneous occurrence in an antiferromagnetic oxide is unprecedented. All nonlinear signatures vanish upon only 3% Ir substitution, which preserves the crystal structure and insulating state, ruling out Joule heating or extrinsic artifacts. The wide separation between the electronic reconstruction at TA and the emergence of nonlinear dynamics at T* identifies Ba4Ru3O10 as a rare correlated system hosting a strongly pinned collective electronic state intertwined with antiferromagnetism.

We present a quantum algorithmic framework for simulating phase-contrast transmission electron microscopy (CTEM) image formation using a fault-tolerant, gate-based quantum circuit model. The electron wavefield on an $N\times N$ grid is amplitude-encoded into a $2\log_2 N$-qubit register. Free-space propagation and objective-lens aberrations are implemented via two-dimensional quantum Fourier transforms (QFTs) and diagonal phase operators in reciprocal space, while specimen interaction is modeled under the weak phase object approximation (WPOA) as a position-dependent phase grating. We validate projected potentials, contrast transfer function (CTF) behavior, and image contrast trends against classical multislice simulations for MoS$_2$ over experimentally relevant parameters, and provide resource estimates and key assumptions that determine end-to-end runtime. While extracting complete $N\times N$ intensity images requires $O(N^2/\epsilon^2)$ measurements that preclude advantage for full-image reconstruction, the framework enables quantum advantage for tasks requiring Fourier-space queries, global image statistics, or phase-coherent observables inaccessible to classical intensity-only detection. This framework provides a physics-grounded mapping from CTEM theory to quantum circuits and establishes a baseline for extending toward full multislice and inelastic scattering models.

In a previous work we developed a field theoretical approach to open quantum systems using condensed matter methods. In the Born approximation we derived the Redfield equation on the basis of a multi-oscillator bath, a Dyson equation, a diagrammatic expansion and a quasi-particle approximation. In addition applying a rotating wave approximation we obtained the Lindblad equation describing a proper quantum map. The issue regarding the additional rotating wave approximation was left as an open problem. The present work addresses the open problem and presents new results. We identify a discrepancy in the popular and standard Redfield equation. The discrepancy is associated with the well-known fact that the Redfield equation does not represent a proper quantum map. The discrepancy is related to the diagrammatic expansion and a consistency requirement in the quasi-particle approximation. The explicit resolution of this discrepancy is obtained by imposing energy conservation on the Born level. As a result we obtain formal equivalence between the energy-conserving Redfield equation and the Lindblad equation without invoking the rotating wave approximation. We provide a detailed mapping of the field theoretical approach to the standard microscopic derivation in the theory of open quantum systems.

Quantum error correction offers a promising path to suppress errors in quantum processors, but the resources required to protect logical operations from noise, especially non-Clifford operations, pose a substantial challenge to achieve practical quantum advantage in the early fault-tolerant quantum computing (EFTQC) era. In this work, we develop a systematic scheme to encode exponential maps of the form $\exp(-i\theta P)$ into stabilizer codes with simple circuit structures and low qubit overhead. We provide encoded circuits with small first-order logical error rate after postselection for the [[n, n-2, 2]] quantum error-detecting codes and the [[5, 1, 3]], [[7, 1, 3]], and [[15, 7, 3]] quantum error-correcting codes. Detailed analysis shows that under the level of physical noise of current devices, our encoding scheme is 4–7 times less noisy than the unencoded operation, while at most 3% of runs need to be discarded.

Identifying stabilizer codes that admit fault-tolerant implementations of the full logical Clifford group would significantly advance fault-tolerant quantum computation. Motivated by this goal, we study several classes of fault-tolerant gadget constructions consisting of Clifford gates acting on the physical qubits, including transversal gadgets, code automorphisms, and fold-transversal gadgets. While stabilizer codes encoding a single logical qubit, most notably the [[7,1,3]] Steane code, are known to admit transversal implementations of the full logical Clifford group, no analogous examples are known for codes encoding multiple logical qubits. In this work, we prove a no-go theorem establishing that no stabilizer code admits a fully transversal implementation of the Clifford group on more than one logical qubit. We further strengthen this result by showing that fold-transversal implementations of the full logical Clifford group are impossible for stabilizer codes encoding more than two logical qubits. More generally, we introduce the notion of k-fold transversal gadgets and prove that implementing the full Clifford group on k logical qubits requires at least k-fold transversal gadgets at the physical level. In addition, we analyze code-automorphism based constructions and demonstrate that they also fail to realize the full Clifford group on multiple logical qubits for any stabilizer code. Together, these results place fundamental constraints on fault-tolerant Clifford gadget design and show that stabilizer codes supporting the full logical Clifford group on multiple logical qubits via these architectures do not exist. Since the Clifford group is a core component of universal gate sets, our findings imply that quantum computing with codes encoding multiple logical qubits within a single code block necessarily entails more complex constructions for fault tolerance.

Metastability, i.e., partial relaxation to long-lived, quasi-stationary states before true asymptotic equilibrium sets in, emerges ubiquitously in classical and quantum dynamical systems as a result of timescales separation. In open quantum systems, an intrinsically nonequilibrium analogue, dynamical metastability, can originate from the spectral geometry of a non-Hermitian operator. In noninteracting models, this mechanism produces boundary-sensitive anomalous relaxation, transient amplification, and topologically mandated long-lived edge modes, all of which are enhanced as system size grows. Here we extend dynamical metastability into the nonlinear, interacting regime and identify magnetic heterostructures as a natural platform for its exploration. We introduce an interacting spin Lindbladian whose linearized magnon dynamics map onto a dynamically metastable Hatano-Nelson chain, and show that dynamical metastability in the noninteracting limit seeds genuinely nonlinear phenomena, including size-dependent spin dipping and anomalous attraction to unstable equilibria. Long-lived edge states associated to topologically mandated Dirac bosons persist under nonlinearities and disorder. We further analyze the magnetization dynamics in magnetic multilayers within the classical Landau-Lifshitz-Gilbert-Slonczewski framework, identifying Dzyaloshinskii-Moriya interaction, nonlocal damping, and spin-transfer torque as control parameters governing bulk-boundary stability mismatch and band topology. While all the distinctive dynamical phenomena previously identified reappear in this experimentally relevant setting, the LLGS framework also supports multistability and limit cycles that are absent in the quantum model. Our results constitute the first systematic study of dynamical metastability in nonlinear dynamics, directly relevant to spin-torque oscillator arrays, magnonic devices, and beyond.