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1967
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L. Vandenberghe and S. Boyd, SIAM Rev. 38
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I. L. Chuang and M. A. Nielsen, J. Mod. Opt. 44
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M. Horodecki, P. Horodecki, and R. Horodecki, Phys. Rev. A 60
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2015

Comparing Experiments to the Fault-Tolerance Threshold

Kueng, Richard, Long, David M., Doherty, Andrew C. et al.

Understand

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.

Built on

C. W. Helstrom, Information and Control 10
1967
Earlier work this paper cites.
L. Vandenberghe and S. Boyd, SIAM Rev. 38
1996
Earlier work this paper cites.
A. Y. Kitaev, Russian Math. Surv. 52
1997
Earlier work this paper cites.
D. Aharonov and M. Ben-Or, in 29th ACM Symp. on Theory of Computing (STOC) (New York, 1997) pp. 176–188, arXiv:quant-ph/9906129
1997
Earlier work this paper cites.
I. L. Chuang and M. A. Nielsen, J. Mod. Opt. 44
1997
Earlier work this paper cites.
E. Knill, R. Laflamme, and W. H. Zurek, Proc. R. Soc. A 454
1998
Earlier work this paper cites.
M. Horodecki, P. Horodecki, and R. Horodecki, Phys. Rev. A 60
1999
Earlier work this paper cites.
M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, New York, 2000)
2000
Earlier work this paper cites.
M. A. Nielsen, Phys. Lett. A 303
2002
Earlier work this paper cites.
A. Barvinok, A Course in Convexity , Vol. 54 (American Mathematical Society, Providence, 2002)
2002
Earlier work this paper cites.
S. Boyd and L. Vandenberghe, Convex Optimization (Cambridge University Press, New York, 2004)
2004
Earlier work this paper cites.
J. Emerson, R. Alicki, and K. Życzkowski, J. Opt. B 7
2005
Earlier work this paper cites.
A. Gilchrist, N. K. Langford, and M. A. Nielsen, Phys. Rev. A 71
2005
Earlier work this paper cites.
P. Aliferis, D. Gottesman, and J. Preskill, Quant. Inf. Comput. 6
2006
Earlier work this paper cites.
P. Aliferis and A. W. Cross, Phys. Rev. Lett. 98
2007
Earlier work this paper cites.