4 research outputs found
Flag fault-tolerant error correction with arbitrary distance codes
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 faults in the circuit have
weight greater than . 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.Comment: 29 pages (18 pages main text), 22 figures, 7 tables. Comments
welcome! V3 represents the version accepted to quantu