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Berkeley, CA

Oct. 21, 2006 to Oct. 24, 2006

ISBN: 0-7695-2720-5

pp: 411-419

Harry Buhrman , CWI and U of Amsterdam, Netherlands

Richard Cleve , U of Waterloo and Perimeter Institute, Canada

Monique Laurent , CWI, Amsterdam, Netherlands

Noah Linden , U of Bristol, UK

Alexander Schrijver , CWI and U of Amsterdam, Netherlands

Falk Unger , CWI, Amsterdam, Netherlands

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

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

*FOCS*, 2006, 2006 47th Annual IEEE Conference on Foundations of Computer Science, 2006 47th Annual IEEE Conference on Foundations of Computer Science 2006, pp. 411-419, doi:10.1109/FOCS.2006.50