Phases of Floquet code under local decoherence

• URL: http://arxiv.org/abs/2504.19041v1
• Date: Sat, 26 Apr 2025 22:28:20 GMT
• Title: Phases of Floquet code under local decoherence
• Authors: Yuchen Tang, Yimu Bao,
• Abstract summary: Floquet code is a dynamical quantum memory with a periodically evolving logical space.<n>We show that below the decoherence threshold, the code is in a robust phase characterized by the anyon automorphism.<n>We analytically show that this diagnostic distinguishes the Floquet code from the toric code under repeated syndrome measurements.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Floquet code is a dynamical quantum memory with a periodically evolving logical space. As a defining feature, the code exhibits an anyon automorphism after each period, giving rise to a non-trivial evolution of each logical state. In this paper, we study the Floquet code under local decoherence and demonstrate that below the decoherence threshold, the code is in a robust phase characterized by the anyon automorphism. We first derive the 3D statistical mechanics model for the maximum likelihood decoder of the 2D Floquet code under local Pauli decoherence. We identify a class of two-qubit Pauli channels under which the 3D statistical mechanics model becomes decoupled 2D models and obtain the threshold for such decoherence channels. We then propose a diagnostic of the anyon automorphism in the presence of local decoherence. We analytically show that this diagnostic distinguishes the Floquet code from the toric code under repeated syndrome measurements and undergoes a phase transition at the threshold.

Related papers

• XYZ ruby code: Making a case for a three-colored graphical calculus for quantum error correction in spacetime [1.453022747359034]
  We present a formalism based on tensor networks to capture the logical action and error-correcting capabilities of any Clifford circuit with Pauli measurements. We apply our method to our new family of dynamical codes which are in the same topological phase as the 2+1d color code. We benchmark the performance of the XYZ ruby code on a torus by performing both memory and stability experiments.
  arXiv  Detail & Related papers  (2024-07-11T14:56:26Z)
• Understanding Stabilizer Codes Under Local Decoherence Through a General Statistical Mechanics Mapping [0.0]
  We construct a mapping from the $n$th moment of the decohered ground state density matrix to a classical statistical mechanics model. We analyze the 3D toric code and X-cube model, deriving bounds on their optimal decoding thresholds.
  arXiv  Detail & Related papers  (2024-03-06T18:59:00Z)
• NCoder -- A Quantum Field Theory approach to encoding data [44.99833362998488]
  We present a novel approach to interpretable AI inspired by Quantum Field Theory (QFT) which we call the NCoder. The NCoder is a modified autoencoder neural network whose latent layer is prescribed to be a subset of $n$-point correlation functions.
  arXiv  Detail & Related papers  (2024-02-01T19:00:55Z)
• Cross-cap defects and fault-tolerant logical gates in the surface code and the honeycomb Floquet code [0.0]
  Non-orientable geometry provides a new way the emergent symmetry acts on the code space. We find that the dynamics of the honeycomb Floquet code is precisely described by a condensation operator of the $mathbbZ$ gauge theory.
  arXiv  Detail & Related papers  (2023-10-10T18:12:56Z)
• Engineering 3D Floquet codes by rewinding [0.0]
  Floquet codes are quantum error-correcting codes with dynamically generated logical qubits. We utilize the interpretation of measurements in terms of condensation of topological excitations. We show that rewinding is advantageous for obtaining a desired set of instantaneous stabilizer groups.
  arXiv  Detail & Related papers  (2023-07-25T17:27:40Z)
• Lifting topological codes: Three-dimensional subsystem codes from two-dimensional anyon models [44.99833362998488]
  Topological subsystem codes allow for quantum error correction with no time overhead, even in the presence of measurement noise. We provide a systematic construction of a class of codes in three dimensions built from abelian quantum double models in one fewer dimension. Our construction not only generalizes the recently introduced subsystem toric code, but also provides a new perspective on several aspects of the original model.
  arXiv  Detail & Related papers  (2023-05-10T18:00:01Z)
• Holographic Codes from Hyperinvariant Tensor Networks [70.31754291849292]
  We show that a new class of exact holographic codes, extending the previously proposed hyperinvariant tensor networks into quantum codes, produce the correct boundary correlation functions. This approach yields a dictionary between logical states in the bulk and the critical renormalization group flow of boundary states.
  arXiv  Detail & Related papers  (2023-04-05T20:28:04Z)
• Topological error correcting processes from fixed-point path integrals [0.7873629568804646]
  We analyze and construct topological quantum error correcting codes as dynamical circuits of geometrically local channels and measurements. We derive two new error-correcting codes, namely a Floquet version of the $3+1$-dimensional toric code using only 2-body measurements, and a dynamic code based on the double-semion string-net path integral.
  arXiv  Detail & Related papers  (2023-03-29T02:32:18Z)
• 3D Mitochondria Instance Segmentation with Spatio-Temporal Transformers [101.44668514239959]
  We propose a hybrid encoder-decoder framework that efficiently computes spatial and temporal attentions in parallel. We also introduce a semantic clutter-background adversarial loss during training that aids in the region of mitochondria instances from the background.
  arXiv  Detail & Related papers  (2023-03-21T17:58:49Z)
• Third quantization of open quantum systems: new dissipative symmetries and connections to phase-space and Keldysh field theory formulations [77.34726150561087]
  We reformulate the technique of third quantization in a way that explicitly connects all three methods. We first show that our formulation reveals a fundamental dissipative symmetry present in all quadratic bosonic or fermionic Lindbladians. For bosons, we then show that the Wigner function and the characteristic function can be thought of as ''wavefunctions'' of the density matrix.
  arXiv  Detail & Related papers  (2023-02-27T18:56:40Z)
• Dual-Stream Pyramid Registration Network [34.65021683954268]
  We propose a Dual-Stream Pyramid Registration Network (referred as Dual-PRNet) for unsupervised 3D medical image registration. We design a two-stream architecture able to compute multi-scale registration fields from convolutional feature pyramids. The proposed Dual-PRNet is evaluated on two standard benchmarks for brain MRI registration.
  arXiv  Detail & Related papers  (2019-09-26T08:17:01Z)

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.