Intrinsic Heralding and Optimal Decoders for Non-Abelian Topological Order

• URL: http://arxiv.org/abs/2507.23765v1
• Date: Thu, 31 Jul 2025 17:52:03 GMT
• Title: Intrinsic Heralding and Optimal Decoders for Non-Abelian Topological Order
• Authors: Dian Jing, Pablo Sala, Liang Jiang, Ruben Verresen,
• Abstract summary: We exploit the non-deterministic fusion of non-Abelian anyons to inform active error correction and design decoders.<n>This intrinsic heralding enhances thresholds over those of Abelian counterparts when noise is dominated by a single non-Abelian anyon type.
• Score: 1.7635061227370266
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Topological order (TO) provides a natural platform for storing and manipulating quantum information. However, its stability to noise has only been systematically understood for Abelian TOs. In this work, we exploit the non-deterministic fusion of non-Abelian anyons to inform active error correction and design decoders where the fusion products, instead of flag qubits, herald the noise. This intrinsic heralding enhances thresholds over those of Abelian counterparts when noise is dominated by a single non-Abelian anyon type. Furthermore, we present an approach for determining the optimal threshold for non-Abelian TOs with perfect anyon syndromes for any noise model, formulated as a statistical mechanics model using Bayesian inference. We numerically illustrate these results for $D_4 \cong \mathbb Z_4 \rtimes \mathbb Z_2$ TO. In particular, for non-Abelian charge noise and perfect syndrome measurement, we find an optimal threshold $p_c=0.218(1)$, whereas an intrinsically heralded minimal-weight perfect-matching (MWPM) decoder already gives $p_c=0.20842(2)$, outperforming standard MWPM with $p_c = 0.15860(1)$. Our work highlights how non-Abelian properties can enhance stability, rather than reduce it, and discusses potential generalizations for achieving fault tolerance.

Related papers

• Stochastic Weakly Convex Optimization Under Heavy-Tailed Noises [55.43924214633558]
  In this paper, we focus on two types of noises: one is sub-Weibull noises, and the other is SsBC noises.<n>Under these two noise assumptions, the in-expectation and high-probability convergence of SFOMs have been studied in the contexts of convex optimization and smooth optimization.
  arXiv  Detail & Related papers  (2025-07-17T16:48:45Z)
• Optimal High-probability Convergence of Nonlinear SGD under Heavy-tailed Noise via Symmetrization [50.49466204159458]
  We propose two novel estimators based on the idea of noise symmetrization.<n>We provide a sharper analysis and improved rates.<n>Compared to works assuming symmetric noise with moments, we provide a sharper analysis and improved rates.
  arXiv  Detail & Related papers  (2025-07-12T00:31:13Z)
• Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness [74.18546828528298]
  We show that SignSGD with Majority Voting can robustly work on the whole range of complexity with $kappakappakappakappa-1right, kappakappakappa-1right, kappakappakappa-1right, kappakappakappa-1right, kappakappakappa-1right, kappakappakappa-1right, kappakappakappa-1right, kappa
  arXiv  Detail & Related papers  (2025-02-11T19:54:11Z)
• Decoherence and wavefunction deformation of $D_4$ non-Abelian topological order [0.0]
  We show that certain non-Abelian TOs can be analyzed and understood to a similar degree, despite being significantly richer.<n>By identifying the corresponding local statistical mechanical spin or rotor model with $D_4$ symmetry, we find a remarkable stability against proliferating non-Abelian anyons.
  arXiv  Detail & Related papers  (2024-09-19T17:56:21Z)
• Stability and Loop Models from Decohering Non-Abelian Topological Order [0.0]
  We identify relevant statistical mechanical models for decohering non-Abelian TO.<n>We find a remarkable stability to quantum channels which proliferate non-Abelian anyons with large quantum dimension.<n>Our work opens up the possibility of non-Abelian TO being robust against maximally proliferating certain anyons.
  arXiv  Detail & Related papers  (2024-09-18T18:00:01Z)
• Information limits and Thouless-Anderson-Palmer equations for spiked matrix models with structured noise [19.496063739638924]
  We consider a saturate problem of Bayesian inference for a structured spiked model. We show how to predict the statistical limits using an efficient algorithm inspired by the theory of adaptive Thouless-Anderson-Palmer equations.
  arXiv  Detail & Related papers  (2024-05-31T16:38:35Z)
• Improving Quantum Approximate Optimization by Noise-Directed Adaptive Remapping [3.47862118034022]
  Noise-Directed Remapping (NDAR) is a algorithm for approximately solving binary optimization problems by leveraging certain types of noise. We consider access to a noisy quantum processor with dynamics that features a global attractor state. Our algorithm bootstraps the noise attractor state by iteratively gauge-transforming the cost-function Hamiltonian in a way that transforms the noise attractor into higher-quality solutions.
  arXiv  Detail & Related papers  (2024-04-01T18:28:57Z)
• High-probability Convergence Bounds for Nonlinear Stochastic Gradient Descent Under Heavy-tailed Noise [59.25598762373543]
  We show that wetailed high-prob convergence guarantees of learning on streaming data in the presence of heavy-tailed noise. We demonstrate analytically and that $ta$ can be used to the preferred choice of setting for a given problem.
  arXiv  Detail & Related papers  (2023-10-28T18:53:41Z)
• Efficient Active Learning Halfspaces with Tsybakov Noise: A Non-convex Optimization Approach [28.518140532315776]
  We study the problem of computationally label efficient active learning. In this paper, we prove any approximate. first-order stationary light point of a structured un-labeled data set.
  arXiv  Detail & Related papers  (2023-10-23T23:55:28Z)
• Extra-Newton: A First Approach to Noise-Adaptive Accelerated Second-Order Methods [57.050204432302195]
  This work proposes a universal and adaptive second-order method for minimizing second-order smooth, convex functions. Our algorithm achieves $O(sigma / sqrtT)$ convergence when the oracle feedback is with variance $sigma2$, and improves its convergence to $O( 1 / T3)$ with deterministic oracles.
  arXiv  Detail & Related papers  (2022-11-03T14:12:51Z)
• Stochastic Linear Bandits Robust to Adversarial Attacks [117.665995707568]
  We provide two variants of a Robust Phased Elimination algorithm, one that knows $C$ and one that does not. We show that both variants attain near-optimal regret in the non-corrupted case $C = 0$, while incurring additional additive terms respectively. In a contextual setting, we show that a simple greedy algorithm is provably robust with a near-optimal additive regret term, despite performing no explicit exploration and not knowing $C$.
  arXiv  Detail & Related papers  (2020-07-07T09:00:57Z)
• Attribute-Efficient Learning of Halfspaces with Malicious Noise: Near-Optimal Label Complexity and Noise Tolerance [21.76197397540397]
  This paper is concerned with computationally efficient learning of homogeneous sparse halfspaces in $mathbbRd$ under noise. We show that the sample complexity is $tildeObig(frac 1 epsilon s2 log5 d big)$ which also enjoys the attribute efficiency.
  arXiv  Detail & Related papers  (2020-06-06T04:57:39Z)
• Contextual Linear Bandits under Noisy Features: Towards Bayesian Oracles [65.9694455739978]
  We study contextual linear bandit problems under feature uncertainty, where the features are noisy and have missing entries. Our analysis reveals that the optimal hypothesis can significantly deviate from the underlying realizability function, depending on the noise characteristics. This implies that classical approaches cannot guarantee a non-trivial regret bound.
  arXiv  Detail & Related papers  (2017-03-03T21:39:56Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.