Self-dual bivariate bicycle codes with transversal Clifford gates

• URL: http://arxiv.org/abs/2510.05211v1
• Date: Mon, 06 Oct 2025 18:00:35 GMT
• Title: Self-dual bivariate bicycle codes with transversal Clifford gates
• Abstract summary: We introduce a broad family of self-dual bi-dual bicycle codes that achieve higher encoding rates than surface and color codes.<n>In particular, we enumerate weight-8 self-dual bi-dual bicycle codes with up to $n leq 200$ physical qubits, realized on twisted tori that enhance code distance and improve stabilizer locality.
• Score: 5.692499671837265
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Bivariate bicycle codes are promising candidates for high-threshold, low-overhead fault-tolerant quantum memories. Meanwhile, color codes are the most prominent self-dual CSS codes, supporting transversal Clifford gates that have been demonstrated experimentally. In this work, we combine these advantages and introduce a broad family of self-dual bivariate bicycle codes. These codes achieve higher encoding rates than surface and color codes while admitting transversal CNOT, Hadamard, and $S$ gates. In particular, we enumerate weight-8 self-dual bivariate bicycle codes with up to $n \leq 200$ physical qubits, realized on twisted tori that enhance code distance and improve stabilizer locality. Representative examples include codes with parameters $[[n,k,d]]$: $[[16,4,4]]$, $[[40,6,6]]$, $[[56,6,8]]$, $[[64,8,8]]$, $[[120,8,12]]$, $[[152,6,16]]$, and $[[160,8,16]]$.

Related papers

• Quantum bivariate bicycle codes with weight-8 checks surpassing the BB benchmark [0.0]
  BB codes of Bravyi emphet al.citeBravyi2024 are quantum low-density parity-check codes with weight-$6$ checks.<n>We develop the structure theory of BB-type codes with weight-$8$ checks (weight-$4$ generators) and use it to construct and certify new codes.
  arXiv  Detail & Related papers  (2026-09-06T12:34:34Z)
• Quantum Bicycle LDPC Codes with High $kd^2/n$ from Divisor-Driven Search [3.344730946122235]
  Bicycle quantum low-density parity-check (LDPC) codes include some of the best known small quantum codes.<n>We show that in the case the construction collapses into the ring $F[x]/(xl)$: self-orthogonality is automatic.<n>A computer search based on this framework recovers the short codes.
  arXiv  Detail & Related papers  (2026-08-10T04:45:08Z)
• Breaking the bicycle frame: Coset-based quantum LDPC codes [65.96089068176079]
  Generalizing the construction of two-block group algebra (2BGA) codes, we introduce a family of two-block quantum LDPC codes.<n>We identify several new quantum LDPC codes, including weight-6 codes with parameters $[48,8,6]]$, $[96,8,10]]$, and $[224,12,16]]$.<n>Our codes, when decoded using BP-OSD, perform competitively with BB codes, achieving thresholds of $approx0.65%$ for the weight-6 family and $approx0.35%$ for the weight-8 family.
  arXiv  Detail & Related papers  (2026-06-15T20:20:57Z)
• Independent Trivariate Bicycle Codes [0.0]
  We introduce six independent tridimensional bicycle (ITB) codes.<n>We construct four codes including a $[140,6,14]]$ code with $kd2/n = 8.40$.<n>On the superconducting noise model, the $[140,6,14]] code achieves a per-round per-observable rate of $5.6 times 10-5$ at $p = 0.20%$.
  arXiv  Detail & Related papers  (2026-03-18T13:22:40Z)
• Multivariate Multicycle Codes for Complete Single-Shot Decoding [0.0]
  We introduce a new family of quantum error correcting codes.<n>MM codes possess metachecks and high confinement.<n>Our codes surpass all known single-shot decodable quantum CSS codes of practical blocksize.
  arXiv  Detail & Related papers  (2026-01-26T19:00:03Z)
• Quantum error correction beyond $SU(2)$: spin, bosonic, and permutation-invariant codes from convex geometry [48.254879700836376]
  We develop a framework for constructing quantum error-correcting codes and logical gates for three types of spaces.<n>We prove that many codes and their gates in $SU(q)$ can be inter-converted between the three state spaces.<n>We present explicit constructions of codes with shorter length or lower total spin/excitation than known codes with similar parameters.
  arXiv  Detail & Related papers  (2025-09-24T20:21:30Z)
• Planar quantum low-density parity-check codes with open boundaries [7.741302957350027]
  We introduce the first systematic procedure to convert BB codes into fully planar, open-boundary qLDPC codes.<n>We present code families with logical dimensions $6 leq kleq13$, e.g., $[[78, 6, 6]]$, $[[107, 7, 7]]$, $[268, 8, 12]]$, $[405, 9, 15]]$, $[[348, 10, 13]]$, $[[450, 11, 15]]$, $[[386, 12, 12]]$, $[362, 13, 11]]$,
  arXiv  Detail & Related papers  (2025-04-11T18:00:05Z)
• Generalized toric codes on twisted tori for quantum error correction [9.623534315687825]
  Kitaev toric code is widely considered one of the leading candidates for error correction in fault-tolerant quantum computation.<n>Direct methods to increase its logical dimensions, such as lattice surgery or introducing punctures, often incur prohibitive overheads.<n>We introduce a ring-theoretic approach for efficiently analyzing topological CSS codes in two dimensions.
  arXiv  Detail & Related papers  (2025-03-05T19:00:05Z)
• Coxeter codes: Extending the Reed-Muller family [59.90381090395222]
  We introduce a class of binary linear codes that generalizes the RM family by replacing the domain $mathbbZm$ with an arbitrary finite Coxeter group.<n> Coxeter codes also give rise to a family of quantum codes for which closed diagonal $Z$ rotations can perform non-trivial logic.
  arXiv  Detail & Related papers  (2025-02-20T17:16:28Z)
• Targeted Clifford logical gates for hypergraph product codes [54.57204856880369]
  We first derive symplectic matrices for CNOT, CZ, Phase, and Hadamard operators, which together generate the Clifford group.<n>This enables us to design explicit transformations that result in targeted logical gates for arbitrary codes in this family.
  arXiv  Detail & Related papers  (2024-11-26T02:32:44Z)
• SSIP: automated surgery with quantum LDPC codes [55.2480439325792]
  We present Safe Surgery by Identifying Pushouts (SSIP), an open-source lightweight Python package for automating surgery between qubit CSS codes. Under the hood, it performs linear algebra over $mathbbF$ governed by universal constructions in the category of chain complexes. We show that various logical measurements can be performed cheaply by surgery without sacrificing the high code distance.
  arXiv  Detail & Related papers  (2024-07-12T16:50:01Z)
• Code conversion with the quantum Golay code for a universal transversal gate set [0.13597551064547497]
  The $[[7,1,3]]$ Steane code and $[[23,1,7]]$ quantum Golay code have been identified as good candidates for fault-tolerant quantum computing via code concatenation. A crucial ingredient to this procedure is the $[49,1,5]]$ triorthogonal code, which can itself be seen as related to the self-dual $[[17,1,5]]$ 2D color code.
  arXiv  Detail & Related papers  (2023-07-26T18:00:04Z)
• Distance bounds for generalized bicycle codes [0.7513100214864644]
  Generalized bicycle (GB) codes is a class of quantum error-correcting codes constructed from a pair of binary circulant matrices. We have done an exhaustive enumeration of GB codes for certain prime circulant sizes in a family of two-qubit encoding codes with row weights 4, 6, and 8. The observed distance scaling is consistent with $A(w)n1/2+B(w)$, where $n$ is the code length and $A(w)$ is increasing with $w$.
  arXiv  Detail & Related papers  (2022-03-31T17:43:34Z)
• Morphing quantum codes [77.34726150561087]
  We morph the 15-qubit Reed-Muller code to obtain the smallest known stabilizer code with a fault-tolerant logical $T$ gate. We construct a family of hybrid color-toric codes by morphing the color code.
  arXiv  Detail & Related papers  (2021-12-02T17:43:00Z)
• Efficient color code decoders in $d\geq 2$ dimensions from toric code decoders [77.34726150561087]
  We prove that the Restriction Decoder successfully corrects errors in the color code if and only if the corresponding toric code decoding succeeds. We numerically estimate the Restriction Decoder threshold for the color code in two and three dimensions against the bit-flip and phase-flip noise.
  arXiv  Detail & Related papers  (2019-05-17T17:41:50Z)

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.