Between Shor and Steane: A Unifying Construction for Measuring Error Syndromes.

Journal Article (Journal Article)

Fault-tolerant quantum error correction requires the measurement of error syndromes in a way that minimizes correlated errors on the quantum data. Steane and Shor ancilla are two well-known methods for fault-tolerant syndrome extraction. In this Letter, we find a unifying construction that generates a family of ancilla blocks that interpolate between Shor and Steane. This family increases the complexity of ancilla construction in exchange for reducing the rounds of measurement required to fault tolerantly measure the error. We then apply this construction to the toric code of size L×L and find that blocks of size m×m can be used to decode errors in O(L/m) rounds of measurements. Our method can be applied to any Calderbank-Shor-Steane code and presents a new direction for optimizing fault-tolerant quantum computation.

Full Text

Duke Authors

Cited Authors

  • Huang, S; Brown, KR

Published Date

  • August 2021

Published In

Volume / Issue

  • 127 / 9

Start / End Page

  • 090505 -

PubMed ID

  • 34506191

Electronic International Standard Serial Number (EISSN)

  • 1079-7114

International Standard Serial Number (ISSN)

  • 0031-9007

Digital Object Identifier (DOI)

  • 10.1103/physrevlett.127.090505

Language

  • eng