Lifting topological codes: Three-dimensional subsystem codes from two-dimensional anyon models

• URL: http://arxiv.org/abs/2305.06365v3
• Date: Sat, 18 May 2024 18:20:52 GMT
• Title: Lifting topological codes: Three-dimensional subsystem codes from two-dimensional anyon models
• Authors: Jacob C. Bridgeman, Aleksander Kubica, Michael Vasmer,
• Abstract summary: 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.
• Score: 44.99833362998488
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Topological subsystem codes in three spatial dimensions allow for quantum error correction with no time overhead, even in the presence of measurement noise. The physical origins of this single-shot property remain elusive, in part due to the scarcity of known models. To address this challenge, we provide a systematic construction of a class of topological subsystem 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 [Kubica and Vasmer, Nat. Commun. 13, 6272 (2022)] but also provides a new perspective on several aspects of the original model, including the origin of the Gauss law for gauge flux, and boundary conditions for the code family. We then numerically study the performance of the first few codes in this class against phenomenological noise to verify their single-shot property. Lastly, we discuss Hamiltonians naturally associated with these codes, and argue that they may be gapless.

Related papers

• The Physics of (good) LDPC Codes II. Product constructions [0.03922370499388702]
  We continue the study of classical and quantum low-density parity check (LDPC) codes from a physical perspective. We formulate a general framework for systematically constructing codes with various features on generic Euclidean and non-Euclidean graphs.
  arXiv  Detail & Related papers  (2024-02-26T18:56:46Z)
• Interplay between lattice gauge theory and subsystem codes [0.0]
  In this work, we extend the interplay between quantum information system and gauge-theory model from the view point of subsystem code. We show that $Z$ lattice-Higgs model in (2+1)-dimensions with specific open boundary conditions is noting but a kind of subsystem code. Mixed anomaly of them dictates the existence of boundary zero modes, which is a direct consequence of symmetry-protected topological order in Higgs and confinement phases.
  arXiv  Detail & Related papers  (2023-04-12T09:20:44Z)
• Proofs of network quantum nonlocality aided by machine learning [68.8204255655161]
  We show that the family of quantum triangle distributions of [DOI40103/PhysRevLett.123.140] did not admit triangle-local models in a larger range than the original proof. We produce a large collection of network Bell inequalities for the triangle scenario with binary outcomes, which are of independent interest.
  arXiv  Detail & Related papers  (2022-03-30T18:00:00Z)
• Holography, cellulations and error correcting codes [0.0]
  We study codes associated with holographic geometries in higher dimensions, relating cellulations of the spatial sections of the geometries to stabiliser codes. We construct analogues of the HaPPY code for three-dimensional hyperbolic space (AdS$_4$), using both absolutely maximally entangled (AME) and non-AME codes. We explain how our codes could be applied to interesting classes of holographic dualities based on gravity-scalar theories (such as JT gravity) through toroidal reductions of hyperbolic spaces.
  arXiv  Detail & Related papers  (2021-12-23T11:16:56Z)
• Duality approach to quantum annealing of the 3-XORSAT problem [0.0]
  We study the performance of quantum algorithms for models with a unique ground state on simple hypergraphs. The degeneracy of classical ground state manifold translates into the emergence of an extensive number of $Z$ symmetries. The duality developed in this work provides a practical tool for studies of quantum models with classically degenerate energy manifold.
  arXiv  Detail & Related papers  (2021-06-11T12:30:08Z)
• Quantum anomalous Hall phase in synthetic bilayers via twistless twistronics [58.720142291102135]
  We propose quantum simulators of "twistronic-like" physics based on ultracold atoms and syntheticdimensions. We show that our system exhibits topologicalband structures under appropriate conditions.
  arXiv  Detail & Related papers  (2020-08-06T19:58:05Z)
• State preparation and measurement in a quantum simulation of the O(3) sigma model [65.01359242860215]
  We show that fixed points of the non-linear O(3) sigma model can be reproduced near a quantum phase transition of a spin model with just two qubits per lattice site. We apply Trotter methods to obtain results for the complexity of adiabatic ground state preparation in both the weak-coupling and quantum-critical regimes. We present and analyze a quantum algorithm based on non-unitary randomized simulation methods.
  arXiv  Detail & Related papers  (2020-06-28T23:44:12Z)
• Cellular automaton decoders for topological quantum codes with noisy measurements and beyond [68.8204255655161]
  We propose an error correction procedure based on a cellular automaton, the sweep rule, which is applicable to a broad range of codes beyond topological quantum codes. For simplicity, we focus on the three-dimensional (3D) toric code on the rhombic dodecahedral lattice with boundaries and prove that the resulting local decoder has a non-zero error threshold. We find that this error correction procedure is remarkably robust against measurement errors and is also essentially insensitive to the details of the lattice and noise model.
  arXiv  Detail & Related papers  (2020-04-15T18:00:01Z)
• Dissipative analog of four-dimensional quantum Hall physics [0.0]
  We study a QH system which features a nontrivial configuration of three-dimensional Weyl cones on its boundaries. We propose a three-dimensional analog of this model in the form of a dissipative Weyl semimetal. We find exceptional points with an order that scales with system size.
  arXiv  Detail & Related papers  (2020-03-24T18:01:11Z)
• Probing chiral edge dynamics and bulk topology of a synthetic Hall system [52.77024349608834]
  Quantum Hall systems are characterized by the quantization of the Hall conductance -- a bulk property rooted in the topological structure of the underlying quantum states. Here, we realize a quantum Hall system using ultracold dysprosium atoms, in a two-dimensional geometry formed by one spatial dimension. We demonstrate that the large number of magnetic sublevels leads to distinct bulk and edge behaviors.
  arXiv  Detail & Related papers  (2020-01-06T16:59:08Z)

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.