2017/08/31 by Christopher Chamberland, Michael E. Beverland · 2 citations
Computer Science · Physics and Astronomy · #Code (set theory) #Error detection and correction #Flag (linear algebra) #Low-density parity-check code #Parity bit #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum error correction #Quantum-Dot Cellular Automata #Qubit #Set (abstract data type) #quant-ph
paper · pdf · doi:10.22331/q-2018-02-08-53
published as Quantum 2, 53 (2018) · 29 pages (18 pages main text), 22 figures, 7 tables. Comments welcome! V3 represents the version accepted to quantum
openalex created_date 2017/08/17 · arxiv created 2018/01/31 · openalex publication_date 2018/02/08 · arxiv updated 2018/02/09 · openalex updated_date 2026/08/05
In this paper we introduce a general fault-tolerant quantum error correction protocol using flag circuits for measuring stabilizers of arbitrary distance codes. In addition to extending flag error correction beyond distance-three codes for the first time, our protocol also applies to a broader class of distance-three codes than was previously known. Flag circuits use extra ancilla qubits to signal when errors resulting from<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>v</mml:mi></mml:math>faults in the circuit have weight greater than<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>v</mml:mi></mml:math>. The flag error correction protocol is applicable to stabilizer codes of arbitrary distance which satisfy a set of conditions and uses fewer qubits than other schemes such as Shor, Steane and Knill error correction. We give examples of infinite code families which satisfy these conditions and analyze the behaviour of distance-three and -five examples numerically. Requiring fewer resources than Shor error correction, flag error correction could potentially be used in low-overhead fault-tolerant error correction protocols using low density parity check quantum codes of large code length.