Bounding quantum gate error rate based on reported average fidelity

Yuval R. Sanders, Joel J. Wallman, Barry C. Sanders

Research output: Contribution to journalArticlepeer-review

74 Citations (Scopus)
85 Downloads (Pure)


Remarkable experimental advances in quantum computing are exemplified by recent announcements of impressive average gate fidelities exceeding 99.9% for single-qubit gates and 99% for two-qubit gates. Although these high numbers engender optimism that fault-tolerant quantum computing is within reach, the connection of average gate fidelity with fault-tolerance requirements is not direct. Here we use reported average gate fidelity to determine an upper bound on the quantum-gate error rate, which is the appropriate metric for assessing progress towards fault-tolerant quantum computation, and we demonstrate that this bound is asymptotically tight for general noise. Although this bound is unlikely to be saturated by experimental noise, we demonstrate using explicit examples that the bound indicates a realistic deviation between the true error rate and the reported average fidelity. We introduce the Pauli distance as a measure of this deviation, and we show that knowledge of the Pauli distance enables tighter estimates of the error rate of quantum gates.

Original languageEnglish
Article number012002
Pages (from-to)1-13
Number of pages13
JournalNew Journal of Physics
Publication statusPublished - 21 Dec 2015
Externally publishedYes

Bibliographical note

Copyright the Author(s) 2016. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.


  • average fidelity
  • fault-tolerance thresholds
  • quantum computation
  • quantum information
  • randomized benchmarking


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