2018/04/03 by Muyuan Li, Daniel Miller, Kenneth R. Brown
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Block code #Code (set theory) #Computer science #Constant-weight code #Decoding methods #Discrete mathematics #Error detection and correction #Lattice (music) #Linear code #Mathematics #Physics #Programming language #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum and electron transport phenomena #Quantum computer #Quantum error correction #Quantum mechanics #Qubit #Toric code #quant-ph
paper · pdf · doi:10.1103/physreva.98.050301
published as Phys. Rev. A 98, 050301 (2018)
arxiv created 2018/04/03 · openalex publication_date 2018/11/06 · arxiv updated 2018/11/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
A Bacon-Shor code is a subsystem quantum error-correcting code on an L\ifmmode×\else\texttimes\fiL lattice where the 2(L\ensuremath-1) weight-2L stabilizers are usually inferred from the measurements of 2L(L\ensuremath-1) weight-2 gauge operators. Here, we show that the stabilizers can be measured directly and fault tolerantly with bare ancillary qubits by constructing circuits that follow the pattern of gauge operators. We then examine the implications of this method for small quantum error-correcting codes by comparing distance-3 versions of the rotated surface code and the Bacon-Shor code with the standard depolarizing model and in the context of a trapped-ion quantum computer. We find that for a simple circuit of prepare, error correct, and measure, the Bacon-Shor code outperforms the surface code by requiring fewer qubits, taking less time, and having a lower error rate.