Stairway Codes: Floquetifying Bivariate Bicycle Codes and Beyond

• URL: http://arxiv.org/abs/2603.00228v1
• Date: Fri, 27 Feb 2026 19:00:00 GMT
• Title: Stairway Codes: Floquetifying Bivariate Bicycle Codes and Beyond
• Authors: Shoham Jacoby, Alex Retzker, Fernando Pastawski,
• Abstract summary: Floquet codes define fault-tolerant protocols through periodic measurement sequences.<n>We introduce Stairway codes, a family of high-rate Floquet protocols.<n>We demonstrate logical error rates surpassing those of other Floquet codes at comparable encoding rates.
• Score: 41.99844472131922
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Floquet codes define fault-tolerant protocols through periodic measurement sequences that drive a dynamically evolving stabilizer group. They provide a natural framework for hardware supporting two-qubit parity measurements but no unitary entangling gates. However, few known constructions achieve both high encoding rates and high thresholds. We close this gap by introducing Stairway codes, a family of high-rate Floquet protocols obtained by Floquetifying Abelian two-block group algebra codes, a class that includes the bivariate bicycle codes. By representing the static code as a foliated ZX-calculus network within a $(w{-}1)$-dimensional space-time lattice and rotating the time axis, we decompose its weight-$w$ stabilizers into a periodic sequence of pairwise measurements. This reduces the design of new codes within this family to the selection of favorable periodic boundary conditions. We identify instances with competitive parameters, analyze their distance under circuit-level noise, and demonstrate logical error rates surpassing those of other Floquet codes at comparable encoding rates. Remarkably, our construction requires fewer than 300 physical qubits to match the distance and encoding rate of semi-hyperbolic Floquet codes that use over 1300 qubits.

Related papers

• Single-Shot and Few-Shot Decoding via Stabilizer Redundancy in Bivariate Bicycle Codes [5.685589351789461]
  We prove that $g(z)$ dictates the code's stabilizer redundancy and the structure of the classical emphsyndrome codes required for single-shot decoding.<n>Within the coprime BB ansatz, high quantum rate imposes an upper bound on syndrome distance, limiting single-shot performance.
  arXiv  Detail & Related papers  (2026-01-03T09:49:58Z)
• Logical gates on Floquet codes via folds and twists [45.88028371034407]
  We show how two techniques from static quantum error-correcting codes can be implemented on Floquet codes.<n>First, we present a way of implementing fold-transversal operations on Floquet codes in order to yield logical Hadamard and S gates.<n>Second, we present a way of implementing logical CNOT gates on Floquet codes via Dehn twists.
  arXiv  Detail & Related papers  (2025-12-19T19:00:06Z)
• Hyperbolic Floquet code with graph-edge syndromes [0.0]
  Floquet codes are stabilizer-based codes in which low-weight parity measurements are applied in a time-periodic schedule.<n>Parity measurements in our code consist of the repetitions of six-step measurements on (semi-)hyperbolic three-colorable tilings.<n>Our code on the regular $8,3$ lattice has the following three advantages: (i) parity measurements are weight-2, (ii) for the numbers $k$ and $n$ of logical and physical qubits, respectively, the encoding rate is finite.
  arXiv  Detail & Related papers  (2025-09-28T23:03:17Z)
• Efficient and Universal Neural-Network Decoder for Stabilizer-Based Quantum Error Correction [44.698141103370546]
  GraphQEC is a code-agnostic decoder leveraging machine-learning on the graph structure of stabilizer codes with linear time complexity.<n>Our approach represents the first universal solution for real-time quantum error correction across arbitrary stabilizer codes.
  arXiv  Detail & Related papers  (2025-02-27T10:56:53Z)
• Existence and Characterisation of Bivariate Bicycle Codes [0.0]
  We show that BB codes provide compact quantum memory with low overhead and enhanced error correcting capabilities.<n>We explore these codes by leveraging their ring structure and predict their dimension as well as conditions on their existence.
  arXiv  Detail & Related papers  (2025-02-24T11:04:15Z)
• Simple Construction of Qudit Floquet Codes on a Family of Lattices [0.0]
  We propose a simple, yet general construction of qudit Floquet codes based on a simple set of conditions on the sequence two-body measurements defining the code.<n>We show that this construction includes the existing constructions of both qubit and qudit Floquet codes as special cases.<n>In addition, any qudit Floquet code obtained by our construction achieves a rate of encoded logical qudits over physical qudits approaching $frac12$ as the number of physical qudits in total and on the faces of the lattice grows larger.
  arXiv  Detail & Related papers  (2024-10-02T20:41:43Z)
• Accommodating Fabrication Defects on Floquet Codes with Minimal Hardware Requirements [44.99833362998488]
  Floquet codes provide good fault-tolerant characteristics while benefiting from reduced connectivity requirements in hardware.<n>This is an under-studied issue of crucial importance for running such codes on realistic hardware.<n>We introduce a new method of accommodating defective qubits on a wide range of two-dimensional Floquet codes.
  arXiv  Detail & Related papers  (2024-05-24T18:00:05Z)
• Estimating the Decoding Failure Rate of Binary Regular Codes Using Iterative Decoding [84.0257274213152]
  We propose a new technique to provide accurate estimates of the DFR of a two-iterations (parallel) bit flipping decoder.<n>We validate our results, providing comparisons of the modeled and simulated weight of the syndrome, incorrectly-guessed error bit distribution at the end of the first iteration, and two-itcrypteration Decoding Failure Rates (DFR)
  arXiv  Detail & Related papers  (2024-01-30T11:40:24Z)
• Fault-tolerant hyperbolic Floquet quantum error correcting codes [0.4527817188861902]
  We introduce a family of dynamically generated quantum error correcting codes that we call "hyperbolic Floquet codes"<n>One of our hyperbolic Floquet codes uses 400 physical qubits to encode 52 logical qubits with a code distance of 8, i.e., it is a $[[400,52,8]]$ code.<n>At small error rates, comparable logical error suppression to this code requires 5x as many physical qubits (1924) when using the honeycomb Floquet code with the same noise model and decoder.
  arXiv  Detail & Related papers  (2023-09-18T18:00:02Z)
• Homological Quantum Rotor Codes: Logical Qubits from Torsion [47.52324012811181]
  homological quantum rotor codes allow one to encode both logical rotors and logical qudits in the same block of code.<n>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)
• Finding the disjointness of stabilizer codes is NP-complete [77.34726150561087]
  We show that the problem of calculating the $c-disjointness, or even approximating it to within a constant multiplicative factor, is NP-complete. We provide bounds on the disjointness for various code families, including the CSS codes,$d codes and hypergraph codes. Our results indicate that finding fault-tolerant logical gates for generic quantum error-correcting codes is a computationally challenging task.
  arXiv  Detail & Related papers  (2021-08-10T15:00:20Z)

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.