Comparing Experiments to the Fault-Tolerance Threshold.
Achieving error rates that meet or exceed the fault-tolerance threshold is a central goal for quantum computing experiments, and measuring these error rates using randomized benchmarking is now routine. However, direct comparison between measured error rates and thresholds is complicated by the fact that benchmarking estimates average error rates while thresholds reflect worst-case behavior when a gate is used as part of a large computation. These two measures of error can differ by orders of magnitude in the regime of interest. Here we facilitate comparison between the experimentally accessible average error rates and the worst-case quantities that arise in current threshold theorems by deriving relations between the two for a variety of physical noise sources. Our results indicate that it is coherent errors that lead to an enormous mismatch between average and worst case, and we quantify how well these errors must be controlled to ensure fair comparison between average error probabilities and fault-tolerance thresholds.
Centre for Engineered Quantum Systems, School of Physics, University of Sydney, Sydney, 2006 New South Wales, Australia.|Institute for Theoretical Physics, University of Cologne, D-50937 Cologne, Germany.|Institute for Physics and FDM, University of Freiburg, D-79104 Freiburg, Germany.
Richard
R
Kueng
Centre for Engineered Quantum Systems, School of Physics, University of Sydney, Sydney, 2006 New South Wales, Australia.
David M
DM
Long
Centre for Engineered Quantum Systems, School of Physics, University of Sydney, Sydney, 2006 New South Wales, Australia.
Andrew C
AC
Doherty
Centre for Engineered Quantum Systems, School of Physics, University of Sydney, Sydney, 2006 New South Wales, Australia.
Steven T
ST
Flammia