Upper Bounds on the Noise Threshold for Fault-Tolerant Quantum Computing

  • Julia Kempe
  • Oded Regev
  • Falk Unger
  • Ronald de Wolf
Conference paper

DOI: 10.1007/978-3-540-70575-8_69

Part of the Lecture Notes in Computer Science book series (LNCS, volume 5125)
Cite this paper as:
Kempe J., Regev O., Unger F., de Wolf R. (2008) Upper Bounds on the Noise Threshold for Fault-Tolerant Quantum Computing. In: Aceto L., Damgård I., Goldberg L.A., Halldórsson M.M., Ingólfsdóttir A., Walukiewicz I. (eds) Automata, Languages and Programming. ICALP 2008. Lecture Notes in Computer Science, vol 5125. Springer, Berlin, Heidelberg

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 \(p>1-{\it \Theta}(1/\sqrt{k})\), 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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Julia Kempe
    • 1
  • Oded Regev
    • 1
  • Falk Unger
    • 2
  • Ronald de Wolf
    • 2
  1. 1.Department of Computer ScienceTel-Aviv UniversityTel-AvivIsrael
  2. 2.CWIAmsterdamThe Netherlands

Personalised recommendations