arXiv:2509.05044v3 Announce Type: replace-cross
Abstract: This paper provides a complete classification of all subvarieties of pointed Abelian lattice-ordered groups (l-groups), as well as all subquasivarieties that are generated by their totally ordered members. We present two complementary approaches to achieve this classification.
First, using purely l-group-theoretic methods, we analyze the structure of lexicographic products and values to identify all join-irreducible members of the lattice of subvarieties of positively pointed Abelian l-groups. We provide a novel equational basis for each of these subvarieties, leading to a complete description of the entire subvariety lattice. As a direct application, our l-group-theoretic classification yields an alternative, self-contained proof of Komori's classification of subvarieties of MV-algebras.
Second, we explore the connection to MV-algebras via an extended version of Mundici's functor. We prove that this functor preserves universal classes, a result of independent model-theoretic interest. This allows us to lift the classification of universal classes of totally ordered MV-algebras, due to Gispert, to a complete classification of universal classes of totally ordered pointed Abelian l-groups. As a direct consequence, we obtain a complete structural description of the lattice of subquasivarieties that are generated by their totally ordered members.
Science Journals
arXiv:2509.09371v2 Announce Type: replace-cross
Abstract: Distributionally robust optimization (DRO) protects statistical learning against distributional shifts by optimizing the worst-case performance over a set of perturbed distributions. However, standard DRO formulations often treat all feature perturbations equally. This can be unnecessarily conservative when external knowledge suggests that the predictive signal is embedded in a low-dimensional representation of covariates. We propose REpresentation-Aware Distributionally robust estimation (READ), a Wasserstein DRO framework that uses external representations to guide the geometry of robustness. Rather than uniformly perturbing all covariate directions, READ increases the transport cost of perturbations that change representation coordinates, thereby reshaping the dual regularization toward the representation subspace. Meanwhile, it preserves protection against variations orthogonal to the representation. We study READ in two regimes. First, for inference on the current target, we characterize our estimator asymptotically and develop a Wasserstein profile inference approach to construct representation-aligned confidence regions while enabling automatic hyperparameter tuning. Second, for deployment to future populations that differ from the current target but are generated from the same representation-invariant random-coefficient model, we show that the resulting regions achieve higher coverage of future model parameters than standard methods. Simulations and a single-cell multi-omics application demonstrate the advantages of READ in multi-source and multitask transfer learning settings.
arXiv:2311.04455v2 Announce Type: replace-cross
Abstract: We study the weighted average consensus problem for a gossip network of agents with vector-valued states. For a given matrix-weighted graph, the gossip process is described by a sequence of pairs of adjacent agents communicating and updating their states based on the edge matrix weight. Our key contribution is providing conditions for the convergence of this non-homogeneous Markov process as well as the characterization of its limit set. To this end, we introduce the notion of "$w$-holonomy" of a set of stochastic matrices, which enables the characterization of sequences of gossiping pairs resulting in reaching a desired consensus in a decentralized manner. Stated otherwise, our result characterizes the limiting behavior of infinite products of (non-commuting, possibly with absorbing states) stochastic matrices.
arXiv:2601.02129v2 Announce Type: replace-cross
Abstract: Recent asteroseismic observations constitute a great challenge for rotating stellar evolution models, which predict overly fast internal rotation rates when only hydrodynamic processes are included. This suggests the absence of one or several unidentified angular momentum (AM) transport processes in these models. Transport by large-scale and strong magnetic fields in the radiative zone is a promising candidate to explain the observations. While these fields might be characterised by a fossil origin, the Tayler-Spruit dynamo constitutes a primary mechanism to form the necessary magnetic fields. Despite recent numerical studies, this mechanism remains poorly known. Motivated by this scenario, we investigated the Tayler-Spruit dynamo through a new set of 3D numerical simulations. We modelled the radiative zone as a Boussinesq stably stratified fluid whose differential rotation is maintained by a volumetric body force. Here, we report, for the first time, the coexistence of two dynamo solutions, which mainly differ by the magnetic field location (near the equator and the polar axis). While the equatorial dynamo is driven by an instability sharing both characteristics of the magnetorotational and Tayler instabilities, we focus mainly on the newly identified polar dynamo, which is driven by the standard Tayler instability. We show that this dynamo can still operate and transport AM efficiently in a strong stratification regime, with a Brunt-V\"ais\"al\"a frequency that is 130 times larger than the rotation rate. We extracted new scaling laws for the magnetic field, AM transport, and the minimum shear to trigger the dynamo. Finally, we were able to roughly constrain the signature of the generated magnetic fields on asteroseismic modes propagating in main sequence and evolved stars.
arXiv:2601.04543v2 Announce Type: replace-cross
Abstract: Using quantum key distribution (QKD) protocols, a secret key is created between two distant users (transmitter and receiver) at a particular key rate. Quantum technology can facilitate secure communication for cryptographic applications, combining QKD with one-time-pad (OTP) encryption. In order to ensure the continuous operation of QKD in real-world networks, efforts have been concentrated on optimizing the use of experimental components and effective QKD protocols to improve secret key rates and increase the transmission between multiple users. Generally, in experimental implementations, the secret key rates are limited by single-photon detectors, which are used at the receivers of QKD and create a bottleneck due to their limited detection rates (detectors with low detection efficiency and high detector dead-time). We experimentally show that secret key rates can be increased by combining the time-bin information of two such detectors on the data line of the receiver for the coherent-one-way (COW) QKD protocol with a minimal increase in quantum bit error rate (QBER, the proportion of erroneous bits). Further, we implement a point-to-multipoint COW QKD protocol, introducing an additional receiver module. The three users (one transmitter and two receivers) share the secret key in post-processing, relying on OTP encryption. Typically, the dual-receiver extension can improve the combined secret key rates of the system; however, one has to optimise the experimental parameters to achieve this within security margins. These methods are general and can be applied to any implementation of the COW protocol.
arXiv:2102.12081v2 Announce Type: replace
Abstract: As novel applications spring up in future network scenarios, the requirements on network service capabilities for differentiated services or burst services are diverse. Aiming at the research of collaborative computing and resource allocation in edge scenarios, migrating computing tasks to the edge and cloud for computing requires a comprehensive consideration of energy consumption, bandwidth, and delay. Our paper proposes a collaboration mechanism based on computation offloading, which is flexible and customizable to meet the diversified requirements of differentiated networks. This mechanism handles the terminal's differentiated computing tasks by establishing a collaborative computation offloading model between the cloud server and edge server. Experiments show that our method has more significant improvements over regular optimization algorithms, including reducing the execution time of computing tasks, improving the utilization of server resources, and decreasing the terminal's energy consumption.
arXiv:2506.13507v2 Announce Type: replace
Abstract: This letter revisits update ordering in layered belief propagation (LBP) decoding of low-density parity-check (LDPC) codes. The closest probability-based schedule orders layers by check node unsatisfied probabilities estimated only from the channel observations, although these probabilities change once decoding messages are exchanged. We therefore refresh the check node unsatisfied probabilities during decoding and use them as dynamic priorities. The first schedule, Dyn-EBP, selects the most reliable available check node while ensuring that every check node is updated once in each iteration. The second schedule, Dyn-PEBP, adds a linear update-count penalty and allows limited repeated updates without letting a small subset of check nodes dominate the schedule. For 5G new radio LDPC base graph 1 codes with five iterations, the proposed schedules yield small BLER reductions relative to the channel-only probability schedule and remain competitive with LBP, LPHD scheduling, and RD-RBP. The gain is modest, but it shows that probability-based scheduling benefits from message-level refinement.
arXiv:2508.19913v2 Announce Type: replace
Abstract: A well-known result by Kant [Algorithmica, 1996] implies that $n$-vertex outerplane graphs admit embedding-preserving planar straight-line grid drawings where the internal faces are convex polygons in $O(n^{2})$ area. In this paper, we present an algorithm to compute such drawings in $O(n^{1.5})$ area. We also consider outerplanar drawings in which the internal faces are required to be strictly-convex polygons. In this setting, we provide a $\Theta(nk^2)$ area bound for $n$-vertex outerplanar graphs whose weak dual is a path and whose maximum face size is $k$ and a $\Theta(nd^2)$ area bound for $n$-vertex outerplanar graphs whose diameter is bounded by $d$.
arXiv:2607.12704v3 Announce Type: replace
Abstract: Multi-label classification assigns several co-occurring labels to each aerial scene, yet deployed models often encounter data distributions different from their training. Feature-statistics augmentation such as MixStyle, EFDMix, and correlated style uncertainty improves generalization at low cost but perturbs channel statistics globally, treating each image as a single style; one class can then contaminate the augmentation of another. Domain generalization is understudied for multi-label remote sensing; no prior method or multi-source benchmark targets it. A label-decoupled augmentation framework is therefore proposed, confining style perturbation to label-specific regions. Per-label attention, obtained from a learnable module or from gradient class-activation maps, yields per-label feature statistics; these statistics are mixed with cross-domain samples that share present labels, under independent per-label coefficients, and features are recomposed by attention-weighted normalization. Three operators combined with two attention sources produce six variants, evaluated on a leave-one-domain-out benchmark from multi-label UCM, AID, and DFC15 over six shared labels. Averaged over three splits and five seeds, the best variant attains 71.5% mean average precision, exceeding empirical risk minimization by 5.0 points and the strongest global-statistics baseline by 1.3 points, with the largest gain on the hardest transfer (up to 7.7 points). Ablations indicate that spatial attention and refreshed localization maps are most influential. The framework adds at most 0.35% parameters, leaves inference unchanged, and appears to offer a generic, inexpensive upgrade path for multi-label statistics-based domain generalization. Code is available upon acceptance at https://github.com/Alaa-Almouradi/Style-Augmentation-Upgrade.
arXiv:2602.04596v2 Announce Type: replace-cross
Abstract: Bayes-filtered transformers are transformers meta-learned on sequences from a prior predictive distribution to approximate the corresponding posterior predictive distribution. They output total predictive uncertainty in a single forward pass but never explicitly represent a posterior distribution, making the standard route to separating aleatoric from epistemic uncertainty unavailable. We address this challenge through the lens of Bayesian predictive inference (BPI). Our main result is a predictive Central Limit Theorem (CLT) for supervised settings under conditions that are among the weakest known in the BPI literature. The CLT characterises the posterior of the limiting predictive distribution given an observed context as asymptotically Gaussian; the variance of this Gaussian quantifies epistemic uncertainty. We apply the framework to TabPFN, a Bayes-filtered transformer that is a state-of-the-art foundation model for tabular prediction. The resulting credible bands achieve near-nominal frequentist coverage as context length grows, and the decomposition largely matches standard desiderata: epistemic uncertainty shrinks with context length and is highest in sparsely observed regions within the span of the context data, while aleatoric uncertainty dominates near decision boundaries where classes overlap.
arXiv:2602.17923v2 Announce Type: replace-cross
Abstract: Computational models of complex physical systems often rely on simplifying assumptions which inevitably introduce model error, with consequent predictive errors. Given data on model observables, the estimation of parameterized model-error representations, along with other model parameters, would be ideally done while separating the contributions of each of the two sets of parameters, in order to ensure meaningful stand-alone model predictions. This work builds an embedded model error framework using a weight-space representation of Gaussian processes (GPs) to flexibly capture model-error spatiotemporal correlations and enable inference with GP-embedding in non-linear models. To disambiguate model and model-error/bias parameters, we extend an existing orthogonal GP method to the embedded model-error setting and derive appropriate orthogonality constraints. To address the increased dimensionality introduced by the GP representation, we employ the likelihood-informed subspace method. The construction is demonstrated on linear and non-linear examples, where it effectively corrects model predictions to match data trends. Extrapolation beyond the training data recovers the prior predictive distribution, and the orthogonality constraints lead to meaningful stand-alone model predictions and nearly uncorrelated posteriors between model and model-error parameters.
arXiv:2604.15107v2 Announce Type: replace-cross
Abstract: Shapley values provide a flexible framework for attributing feature contributions to model predictions, but they are not naturally suited for feature selection: a feature may receive a positive attribution even when it is redundant given the remaining variables. In this paper, we introduce \textbf{MinShap}, a general framework for identifying \emph{important} or \emph{non-redundant} features through conditional importance functionals $VI_j^S$. Rather than averaging feature contributions across conditioning sets, MinShap aggregates them using the \emph{minimum}, thereby testing whether a feature remains relevant under every conditioning context. We show that, under a simple \emph{null monotonicity} condition, the minimum aggregation exactly characterizes feature redundancy and yields a principled feature selection criterion. This perspective provides a unified framework for statistical feature selection and representation-based interpretability while retaining the stability advantages of Shapley-style aggregation. We develop scalable algorithms with statistical guarantees, establish connections to multiple-testing procedures, and demonstrate through theory and experiments that MinShap produces more accurate and stable feature selection than existing model-agnostic approaches.
arXiv:2606.24768v2 Announce Type: replace-cross
Abstract: This paper presents general strong duality results when testing hypotheses by betting against them. A bet is an e-variable for a composite null hypothesis $\Pcal$: a nonnegative random variable $X$ whose expected value is at most one under every $P \in \mathcal P$. Following Kelly, Breiman, Cover, Shafer, and Grunwald et al. (2024), we study a natural minimax \emph{log-optimality} criterion: given a composite alternative $\Qcal$, we characterize the ``GROW value'' $\sup_{X} \inf_{Q} \E_{Q}[\log X]$. This paper generalizes the results of Larsson et al. (2025) from (arbitrary $\mathcal P$ and) simple $\mathcal Q$ to arbitrary $\mathcal Q$. We prove that there always exists a minimizing information-projection pair between the weak-$*$ closures of the convex hulls of arbitrary $\mathcal P$ and $\mathcal Q$, and show that the GROW value for \emph{bounded} e-variables always equals their relative entropy. We also prove a similarly general strong duality for the REGROW criterion with bounded e-variables and arbitrary bounded offsets. Under various assumptions our results extend to unbounded e-variables, and examples show that without any assumptions such extensions fail. Our results are analogous to those in Larsson et al. (2026), swapping tests for bounded e-variables, minimax risk for the GROW criterion, and total variation for relative entropy.
arXiv:2607.01741v2 Announce Type: replace-cross
Abstract: Reinforcement Learning (RL) is a sequential decision-making framework in which an agent learns optimal policies through interaction with an environment by maximizing cumulative rewards. Among RL methods, Bayesian Reinforcement Learning (BRL) addresses common practical challenges related to data scarcity by leveraging prior knowledge about the environment and sequential belief updates. However, most BRL approaches require an explicit likelihood function, which is frequently inaccessible or intractable in real-world settings.
We propose Likelihood-Free Iterated Batch Importance Sampling (LF-IBIS), a novel algorithm for BRL that updates the agent's beliefs online as new interactions become available. By combining Approximate Bayesian Computation with Iterated Batch Importance Sampling, LF-IBIS enables full Bayesian inference in settings where the environment dynamics are not described by an explicit or tractable likelihood. The method yields approximate posterior distributions over both environment parameters and optimal policies, providing a quantification of policy uncertainty useful for a Bayesian treatment of the exploration-exploitation trade-off. We test the method on a simulation study in response-adaptive randomization in clinical trials, where closed-form posteriors enable validation. Additional experiments address settings where the posterior has no closed form and illustrate online policy updating based on the posterior distribution of the optimal policy.
arXiv:2607.02947v2 Announce Type: replace-cross
Abstract: Public official-information request records contain process signals. They can support research, workflow review, and analyst-led assessment. Yet they also mix observed correspondence, platform states, inferred events, and legal outcomes. FOI-O is a reusable process-modelling method and verification infrastructure for Freedom of Information administration. It is a global model that began with the New Zealand Official Information Act and has since iterated through the Australian Commonwealth and New South Wales settings. The NZ package remains the mature reference implementation; the Australian work remains provisional pending empirical evaluation and jurisdiction-specific legal validation. FOI-O models request records, observed correspondence, controlled vocabularies, provenance, review queues, release metadata, and bounded analysis rules. Legally meaningful outcomes require certification by an authorised decision-maker. Its typed operational and semantic contracts are supported by deterministic examples, process models, fixture-only process-mining exports, quality gates, and tests. This article describes the motivation, architecture, ontology-development method, its versioned extraction and review protocol, how related repositories share data and evidence, and how the method may be adapted for Australia, validation evidence, and implementation boundaries. The project is not legal advice, is not an official government publication, and does not certify release, refusal, redaction, charging, extension, transfer, complaint, or publication outcomes.
arXiv:2607.08793v3 Announce Type: replace-cross
Abstract: Sepsis is a leading cause of mortality, yet optimal treatment policies remain contested. Existing reinforcement learning (RL) approaches learn fixed strategies for sepsis treatment, limiting adaptability to changing clinical objectives during inference. We propose EHRMPC, a framework that decouples learning patient dynamics from optimizing treatment by training a patient digital twin in the form of a generative electronic health record (EHR) model. The digital twin predicts clinical trajectories under interventions and enables model predictive control (MPC) to optimize treatments via inference-time planning over simulations. We evaluate EHR-MPC on a multicenter ICU sepsis cohort spanning 8 hospitals in the Mass General Brigham health system using both off-policy importance sampling and on-policy simulation-based evaluation. Relative to RL baselines, EHR-MPC achieves comparable off-policy performance and improved simulation performance. Unlike RL, this work frames sepsis treatment optimization as inference-time control over learned patient dynamics, establishing a general framework for decision making with generative clinical models.
arXiv:2607.11135v3 Announce Type: replace-cross
Abstract: The tryptophan residues in tubulin $\alpha\beta$-dimers form an ordered aromatic network that has been proposed to support quantum exciton transport even under physiological environmental noise. Existing studies of this system mostly assume white-noise dephasing, but the statistical properties of the protein-solvent bath coupled to tryptophan sites remain uncharacterised under physiological conditions. Here we characterise this fluctuation bath via all-atom molecular dynamics simulations of a solvated tubulin dimer at 310 K, combining high-frequency and long-time trajectories with 10 fs and 10 ps sampling intervals. The resulting autocorrelation of the site-energy fluctuations is tri-exponential, with three well-separated decay modes: sub-100-fs and picosecond fluctuations driven by water dynamics, and a nanosecond mode originating from protein conformational rearrangements. All three modes fall deep within the non-Markovian regime. We further demonstrate that the slow protein mode introduces strong quasi-static disorder, which results in Anderson localisation, while the two fast water modes frequently tune chromophore pairs through resonance, enabling environment-assisted quantum transport (ENAQT). On the full eight-site network, the coloured-noise bath confines excitons predominantly to strongly coupled proximal tryptophan pairs, in marked contrast to the more uniform delocalisation predicted by the standard white-noise Haken-Strobl model. Our workflow generalises to other pigment-protein systems with solvent-exposed chromophores.
arXiv:2607.13291v2 Announce Type: replace-cross
Abstract: Quantum networking testbeds lack a distinct plane for coordinating distributed measurements and collecting experimental data across heterogeneous devices. To address this gap, we present the Measurement Plane, a dedicated plane that complements the data, control, and management planes rather than replacing or extending their pipelines. The contribution is presented as a distributed framework that organizes measurement functions into four layers: application, experiment coordination, capability, and resource agents. Our design separates user workflows from device-specific control.
We implemented the framework as containerized microservices connected through publish--subscribe messaging, and validated it on a two-node quantum networking setup connected by an optical network. The framework successfully coordinated remote nodes to execute coincidence measurement and polarization entanglement distribution experiments with visibility interference of up to 98 percent. This evaluation demonstrated the effectiveness of the framework for supporting complex, distributed quantum experiments, enabling online measurement and feedback, and significantly reducing manual configuration and execution effort.
arXiv:2601.08056v4 Announce Type: replace-cross
Abstract: Animal behavior reflects interactions between the nervous system, body, and environment. Therefore, biomechanics and environmental context must be considered to understand algorithms for behavioral control. Computational models that embed artificial neural controllers within body models in simulated environments are a powerful tool for this purpose. Here, we review advances in biorealistic neuromechanical models while also highlighting emerging opportunities ahead. We first show how these models enable inference of biophysical variables that are difficult to measure experimentally. Through systematic perturbations, one can generate new experimentally testable hypotheses using these models. We then examine how neuromechanical models facilitate the exchange among neuroscience, robotics, and machine learning, and showcase their applications in healthcare. We envision that coupling experimental studies with active probing of their neuromechanical surrogates will significantly accelerate progress in neuroscience.
arXiv:2607.14087v2 Announce Type: replace-cross
Abstract: We prove a stochastic comparison for Gaussian maxima. Let $R$ be an $m\times m$ correlation matrix satisfying $R-\mathbf{1} \mathbf{1}^{\mathsf T}/m\succeq0$, let $X\sim\mathcal{N}(0,R)$, and let $Z_1,\ldots,Z_m$ be independent standard Gaussian random variables. Then $\max_{1\leq i\leq m}X_i \leq_{\mathrm{st}} \max_{1\leq i\leq m}Z_i$, or equivalently, $\mathbb{P}\{X_i\leq c\text{ for every }i\}\geq\Phi(c)^m$ for every $c\in\mathbb{R}$. This comparison resolves the Weak Simplex Conjecture: among $d+1$ equiprobable equal-energy signals in $\mathbb{R}^d$ transmitted over an additive white Gaussian noise channel, the regular simplex maximizes the probability of correct maximum-likelihood decoding at every signal-to-noise ratio. It also proves the inequality asserted by the Simplex Mean Width Conjecture and gives an exact formula for the largest number of equiprobable messages that can be sent at prescribed energy and error probability by a deterministic no-feedback AWGN code under a per-codeword energy constraint. The proof combines a Gaussian product inequality for log-concave functions with an adaptive tilting argument that makes the inequality applicable to the one-sided threshold events defining the maximum. A lean formalization of this argument is available at https://github.com/abhmul/weak-simplex-conjecture-lean.
arXiv:2607.14089v2 Announce Type: replace-cross
Abstract: Strained membrane resonators have emerged as a promising platform for optomechanical accelerometry; however, the desired combination of low frequency and high $Q$-mass product requires a rethinking of their dissipation dilution engineering. Applying Bayesian optimization to a Si$_3$N$_4$ membrane, we discover a class of sail-like trampoline resonators in which the frequency is decreased by an order of magnitude while preserving the $Q$-mass product. We demonstrate centimeter-scale sails with kHz frequencies, $Q\sim10^7$ and $Q\times\text{mass}\sim$ 10 g. Vertically integrating a 7 kHz device with a nanoribbon, we realize a monolithic cavity optomechanical accelerometer with a room temperature thermal noise of $40\;\text{n}g_0/\sqrt{\text{Hz}}$, sufficient to resolve $\mu g_0/\sqrt{\text{Hz}}$ ambient vibration over a bandwidth of 4 kHz with a displacement imprecision of $10^{-14}\;\text{m}/\sqrt{\text{Hz}}$. Cryogenic arrays of sail membranes may be attractive for new physics searches and distributed quantum sensing experiments.
arXiv:2607.14637v2 Announce Type: replace-cross
Abstract: For close binaries and star-planet systems, tidal interactions mediate the energy transfer between the orbital motion and the internal flows of the bodies involved, thus playing a central role in their evolution. For equilibrium tides, the associated energy transfer is commonly modeled through an effective viscosity acting on the tidal flow. However, the scaling of viscous dissipation efficiency with tidal frequency $\omega_\text{T}$ remains debated, particularly when $\omega_\text{T}$ greatly exceeds the convective eddy turnover frequency $\omega_\text{c}$. Previous numerical studies have addressed this issue by subjecting a turbulent convective flow to an oscillating background shear mimicking equilibrium tides. In this work, we adopt a novel three-layered convective box -- designed to represent a stellar convection zone sandwiched between two stable layers -- driven by an external periodic forcing. We quantify tidal dissipation efficiency by the forcing power on the flow in steady state. Our results yield a shallower scaling of tidal power per unit mass with $\omega_\text{T}$ than reported in earlier shear-flow simulations. This scaling is consistent with the prediction by \cite{Terquem2021}, suggesting that the effective turbulent viscosity depends only weakly on $\omega_\text{T}$, although our simulations are restricted to $\omega_\text{T}\lesssim 10\omega_\text{c}$. Moreover, we find no evidence of inverse energy transfer (or ``negative viscosity''), a phenomenon observed in some prior shear-flow simulations. We further investigate the influence of rotation within the same local framework. Slow rotation ($\Omega\lesssim \omega_\text{T}$) tends to enhance the tidal power, whereas fast rotation ($\Omega\gtrsim\omega_\text{T}$) significantly suppresses it. We discuss the limitations of our approach and the broader implications of our findings.
arXiv:2607.15159v2 Announce Type: replace-cross
Abstract: We construct a new family of Calderbank-Shor-Steane (CSS) codes using the generator and parity-check matrices of Low-Density Generator Matrix (LDGM) codes, with row operations applied to both matrices in order to achieve the desired quantum rate. Decoding is performed in an iterative manner, by applying message passing over the associated graph, and discrete Density Evolution (DDE) is used to optimize performance in the depolarizing channel. The proposed construction offers high flexibility and easiness in the design, producing quantum codes that possess excellent error correction capabilities. By properly designing the structure of the code, we are able to control and bound the weight of the stabilizer generators to a small value, which results in codes particularly well suited for fault-tolerant quantum computation. At the same time, these codes achieve very good performance in terms of error correction capability.
arXiv:2607.15700v2 Announce Type: replace-cross
Abstract: Quartet correlations in neutron-rich Te isotopes are investigated within the quartet Bardeen-Cooper-Schrieffer (BCS) framework. Taking $^{100}$Sn as an inert core, we consider two valence protons and valence neutrons occupying the $2d_{5/2} \oplus 1g_{7/2}$ model space, and solve the quartet BCS variational equations with a charge-independent isovector pairing interaction. The effective pairing strength is constrained from empirical neutron pairing gaps in the Te isotopic chain. We find that the valence quartet number increases as the valence neutron number is enlarged from $N_{\rm val}=2$ to $14$. The same increasing behavior is also found for the condensed quartet component. The proton occupation of the $1g_{7/2}$ orbit is strongly enhanced relative to the conventional like-particle BCS reference and is driven close to the degeneracy-weighted limit. These results suggest that additional valence neutrons enhance the quartet admixture in the correlated quartet BCS state, while redistributing the fixed proton weight from pair-like configurations to quartet configurations.
arXiv:2607.16114v2 Announce Type: replace-cross
Abstract: It is well-known that combinatorial circuits are modeled mathematically by string diagrams in monoidal categories. Given a gate set $\Sigma$, the circuits over $\Sigma$ can be thought of as string diagrams in the free monoidal category generated by $\Sigma$. In this model, circuit semantics are then given by monoidal functors out of this free category. For quantum circuits, this functor is often valued in the category of unitary matrices. This model suffices for concrete quantum circuits, but fails to describe parameterized families of quantum circuits, such as those which arise in the analysis of ansatz circuits. In this paper, we introduce an approach to parameterized circuit semantics, which is based on enriched category theory. We first introduce an abstract categorical construction, and use this to gain new insights on controlled operations and quantum communication. We then study the special cases of Cartesian monoidal parameters and monoidal closed parameters, both endowing the parameterized semantics with useful constructions. We conclude by showing that the monoidal closed case can be used to unify two perspectives on quantum control.