2013 IEEE 54th Annual Symposium on Foundations of Computer Science (2006)

Berkeley, California

Oct. 21, 2006 to Oct. 24, 2006

ISSN: 0272-5428

ISBN: 0-7695-2720-5

pp: 411-419

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/FOCS.2006.50

Harry Buhrman , CWI and U of Amsterdam, Netherlands

Falk Unger , CWI, Amsterdam, Netherlands

Alexander Schrijver , CWI and U of Amsterdam, Netherlands

Noah Linden , U of Bristol, UK

Richard Cleve , U of Waterloo and Perimeter Institute, Canada

Monique Laurent , CWI, Amsterdam, Netherlands

ABSTRACT

We show that quantum circuits cannot be made faulttolerant against a depolarizing noise level of \hat \theta = (6 - 2\sqrt 2 )/7 \approx 45%, thereby improving on a previous bound of 50% (due to Razborov [18]). More precisely, the circuit model for which we prove this bound contains perfect gates from the Clifford group (CNOT, Hadamard, S, X, Y , Z) and arbitrary additional one-qubit gates that are subject to depolarizing noise \hat \theta. We prove that this set of gates cannot be universal for arbitrary (even classical) computation, from which the upper bound on the noise threshold for faulttolerant quantum computation follows.

INDEX TERMS

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CITATION

Harry Buhrman,
Falk Unger,
Alexander Schrijver,
Noah Linden,
Richard Cleve,
Monique Laurent,
"New Limits on Fault-Tolerant Quantum Computation",

*2013 IEEE 54th Annual Symposium on Foundations of Computer Science*, vol. 00, no. , pp. 411-419, 2006, doi:10.1109/FOCS.2006.50SEARCH