Upper bounds on the noise threshold for fault-tolerant quantum computing

Julia Kempe, Oded Regev, Falk Unger, Ronald De Wolf

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We prove new upper bounds on the tolerable level of noise in a quantum circuit. Our circuits consist of unitary k-qubit gates each of whose input wires is subject to depolarizing noise of strength p, and arbitrary one-qubit gates that are essentially noise-free. We assume the output of the circuit is the result of measuring some designated qubit in the final state. Our main result is that for p > 1 - Θ(1/√k), the output of any such circuit of large enough depth is essentially independent of its input, thereby making the circuit useless. For the important special case of k = 2, our bound is p > 35.7%. Moreover, if the only gate on more than one qubit is the CNOT, then our bound becomes 29.3%. These bounds on p are notably better than previous bounds, yet incomparable because of the somewhat different circuit model that we are using. Our main technique is a Pauli basis decomposition, which we believe should lead to further progress in deriving such bounds.

Original languageEnglish (US)
Title of host publicationAutomata, Languages and Programming - 35th International Colloquium, ICALP 2008, Proceedings
Pages845-856
Number of pages12
EditionPART 1
DOIs
StatePublished - 2008
Event35th International Colloquium on Automata, Languages and Programming, ICALP 2008 - Reykjavik, Iceland
Duration: Jul 7 2008Jul 11 2008

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 1
Volume5125 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other35th International Colloquium on Automata, Languages and Programming, ICALP 2008
CountryIceland
CityReykjavik
Period7/7/087/11/08

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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