Single-Shot Quantum Error Correction in Intertwined Toric Codes

• URL: http://arxiv.org/abs/2307.08118v2
• Date: Tue, 27 Aug 2024 23:07:34 GMT
• Title: Single-Shot Quantum Error Correction in Intertwined Toric Codes
• Authors: Charles Stahl,
• Abstract summary: We construct a new subsystem code that exhibits single-shot error correction in a user-friendly and transparent way. Although previous codes share the property of single-shot error correction, the ITC is distinguished by its physically motivated origin. The syndromes of the ITC resemble the syndromes of the single-shot code by Kubica and Vasmer.
• Score: 0.14833692070415452
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We construct a new subsystem code in three dimensions that exhibits single-shot error correction in a user-friendly and transparent way. As this code is a subsystem version of coupled toric codes, we call it the intertwined toric code (ITC). Although previous codes share the property of single-shot error correction, the ITC is distinguished by its physically motivated origin, geometrically straightforward logical operators and errors, and a simple phase diagram. The code arises from 3d stabilizer toric codes in a way that emphasizes the physical origin of the single-shot property. In particular, starting with two copies of the 3d toric code, we add check operators that provide for the confinement of pointlike excitations without condensing the loop excitations. Geometrically, the bare and dressed logical operators in the ITC derive from logical operators in the underlying toric codes, creating a clear relationship between errors and measurement outcomes. The syndromes of the ITC resemble the syndromes of the single-shot code by Kubica and Vasmer, allowing us to use their decoding schemes. We also extract the phase diagram corresponding to ITC and show that it contains the phases found in the Kubica-Vasmer code. Finally, we suggest various connections to Walker-Wang models and measurement-based quantum computation.

Related papers

• Geometric structure and transversal logic of quantum Reed-Muller codes [51.11215560140181]
  In this paper, we aim to characterize the gates of quantum Reed-Muller (RM) codes by exploiting the well-studied properties of their classical counterparts. A set of stabilizer generators for a RM code can be described via $X$ and $Z$ operators acting on subcubes of particular dimensions.
  arXiv  Detail & Related papers  (2024-10-10T04:07:24Z)
• A blindness property of the Min-Sum decoding for the toric code [3.543432625843538]
  Kitaev's toric code is one of the most prominent models for fault-tolerant quantum computation. Recent efforts have been devoted to improving the error correction performance of the toric code under message-passing decoding.
  arXiv  Detail & Related papers  (2024-06-21T08:28:31Z)
• Concatenating quantum error-correcting codes with decoherence-free subspaces and vice versa [0.0]
  Quantum error-correcting codes (QECCs) and decoherence-free subspace (DFS) codes provide active and passive means to address certain types of errors. The concatenation of a QECC and a DFS code results in a degenerate code that splits into actively and passively correcting parts. We show that for sufficiently strongly correlated errors, the concatenation with the DFS as the inner code provides better entanglement fidelity.
  arXiv  Detail & Related papers  (2023-12-13T17:48:12Z)
• Testing the Accuracy of Surface Code Decoders [55.616364225463066]
  Large-scale, fault-tolerant quantum computations will be enabled by quantum error-correcting codes (QECC) This work presents the first systematic technique to test the accuracy and effectiveness of different QECC decoding schemes.
  arXiv  Detail & Related papers  (2023-11-21T10:22:08Z)
• 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)
• Fault-Tolerant Computing with Single Qudit Encoding [49.89725935672549]
  We discuss stabilizer quantum-error correction codes implemented in a single multi-level qudit. These codes can be customized to the specific physical errors on the qudit, effectively suppressing them. We demonstrate a Fault-Tolerant implementation on molecular spin qudits, showcasing nearly exponential error suppression with only linear qudit size growth.
  arXiv  Detail & Related papers  (2023-07-20T10:51:23Z)
• Homological Quantum Rotor Codes: Logical Qubits from Torsion [51.9157257936691]
  homological quantum rotor codes allow one to encode both logical rotors and logical qudits in the same block of code. We show that the $0$-$pi$-qubit as well as Kitaev's current-mirror qubit are indeed small examples of such codes.
  arXiv  Detail & Related papers  (2023-03-24T00:29:15Z)
• Deep Quantum Error Correction [73.54643419792453]
  Quantum error correction codes (QECC) are a key component for realizing the potential of quantum computing. In this work, we efficiently train novel emphend-to-end deep quantum error decoders. The proposed method demonstrates the power of neural decoders for QECC by achieving state-of-the-art accuracy.
  arXiv  Detail & Related papers  (2023-01-27T08:16:26Z)
• Quantum Lego: Building Quantum Error Correction Codes from Tensor Networks [0.0]
  We represent complex code constructions as tensor networks built from the tensors of simple codes or states. The framework endows a network geometry to any code it builds and is valid for constructing stabilizer codes. We lay out some examples where we glue together simple stabilizer codes to construct non-trivial codes.
  arXiv  Detail & Related papers  (2021-09-16T18:00:00Z)
• Single-shot quantum error correction with the three-dimensional subsystem toric code [77.34726150561087]
  We introduce a new topological quantum code, the three-dimensional subsystem toric code (3D STC) The 3D STC can be realized by measuring geometrically-local parity checks of weight at most three on the cubic lattice with open boundary conditions.
  arXiv  Detail & Related papers  (2021-06-04T17:35:00Z)
• Trapping Sets of Quantum LDPC Codes [9.482750811734565]
  We identify and classify quantum trapping sets (QTSs) according to their topological structure and decoder used. We show that the knowledge of QTSs can be used to design better QLDPC codes and decoders.
  arXiv  Detail & Related papers  (2020-12-30T19:35:17Z)

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.