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Two-qubit Stabilizer Circuits with Recovery II: Analysis

Authors Wim van Dam , Raymond Wong

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Author Details

Wim van Dam
  • Department of Computer Science, Department of Physics, University of California, Santa Barbara, CA, USA
Raymond Wong
  • Department of Computer Science, University of California, Santa Barbara, CA, USA

Funding

This material is based upon work supported by the National Science Foundation under Grants No. 0917244 and 1719118.

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Wim van Dam and Raymond Wong. Two-qubit Stabilizer Circuits with Recovery II: Analysis. In 13th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 111, pp. 8:1-8:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/LIPIcs.TQC.2018.8

Abstract

We study stabilizer circuits that use non-stabilizer qubits and Z-measurements to produce other non-stabilizer qubits. These productions are successful when the correct measurement outcome occurs, but when the opposite outcome is observed, the non-stabilizer input qubit is potentially destroyed. In preceding work [arXiv:1803.06081 (2018)] we introduced protocols able to recreate the expensive non-stabilizer input qubit when the two-qubit stabilizer circuit has an unsuccessful measurement outcome. Such protocols potentially allow a deep computation to recover from such failed measurements without the need to repeat the whole prior computation. Possible complications arise when the recovery protocol itself suffers from a failed measurement. To deal with this, we need to use nested recovery protocols. Here we give a precise analysis of the potential advantage of such recovery protocols as we examine its optimal nesting depth. We show that if the expensive input qubit has cost d, then typically a depth O(log d) recovery protocol is optimal, while a certain special case has optimal depth O(sqrt{d}). We also show that the recovery protocol can achieve a cost reduction by a factor of at most two over circuits that do not use recovery.

Subject Classification

ACM Subject Classification
  • Theory of computation → Quantum computation theory
Keywords
  • stabilizer circuit
  • recovery circuit
  • magic state

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