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Title: Unbiased simulation of near-Clifford quantum circuits

Abstract

Modeling and simulation are essential for predicting and verifying the behavior of fabricated quantum circuits, but existing simulation methods are either impractically costly or require an unrealistic simplification of error processes. In this paper, we present a method of simulating noisy Clifford circuits that is both accurate and practical in experimentally relevant regimes. In particular, the cost is weakly exponential in the size and the degree of non-Cliffordness of the circuit. Our approach is based on the construction of exact representations of quantum channels as quasiprobability distributions over stabilizer operations, which are then sampled, simulated, and weighted to yield unbiased statistical estimates of circuit outputs and other observables. As a demonstration of these techniques, we simulate a Steane [[7,1,3]]-encoded logical operation with non-Clifford errors and compute its fault tolerance error threshold. Finally, we expect that the method presented here will enable studies of much larger and more realistic quantum circuits than was previously possible.

Authors:
 [1];  [1];  [1];  [1];  [1];  [1];  [1]
  1. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Quantum Computing Inst.
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE; Intelligence Advanced Research Projects Activity (IARPA) (United States)
OSTI Identifier:
1376419
Grant/Contract Number:
AC05-00OR22725
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Physical Review A
Additional Journal Information:
Journal Volume: 95; Journal Issue: 6; Journal ID: ISSN 2469-9926
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; quantum algorithms; quantum computation; quantum simulation; quantum information

Citation Formats

Bennink, Ryan S., Ferragut, Erik M., Humble, Travis S., Laska, Jason A., Nutaro, James J., Pleszkoch, Mark G., and Pooser, Raphael C.. Unbiased simulation of near-Clifford quantum circuits. United States: N. p., 2017. Web. doi:10.1103/PhysRevA.95.062337.
Bennink, Ryan S., Ferragut, Erik M., Humble, Travis S., Laska, Jason A., Nutaro, James J., Pleszkoch, Mark G., & Pooser, Raphael C.. Unbiased simulation of near-Clifford quantum circuits. United States. doi:10.1103/PhysRevA.95.062337.
Bennink, Ryan S., Ferragut, Erik M., Humble, Travis S., Laska, Jason A., Nutaro, James J., Pleszkoch, Mark G., and Pooser, Raphael C.. 2017. "Unbiased simulation of near-Clifford quantum circuits". United States. doi:10.1103/PhysRevA.95.062337.
@article{osti_1376419,
title = {Unbiased simulation of near-Clifford quantum circuits},
author = {Bennink, Ryan S. and Ferragut, Erik M. and Humble, Travis S. and Laska, Jason A. and Nutaro, James J. and Pleszkoch, Mark G. and Pooser, Raphael C.},
abstractNote = {Modeling and simulation are essential for predicting and verifying the behavior of fabricated quantum circuits, but existing simulation methods are either impractically costly or require an unrealistic simplification of error processes. In this paper, we present a method of simulating noisy Clifford circuits that is both accurate and practical in experimentally relevant regimes. In particular, the cost is weakly exponential in the size and the degree of non-Cliffordness of the circuit. Our approach is based on the construction of exact representations of quantum channels as quasiprobability distributions over stabilizer operations, which are then sampled, simulated, and weighted to yield unbiased statistical estimates of circuit outputs and other observables. As a demonstration of these techniques, we simulate a Steane [[7,1,3]]-encoded logical operation with non-Clifford errors and compute its fault tolerance error threshold. Finally, we expect that the method presented here will enable studies of much larger and more realistic quantum circuits than was previously possible.},
doi = {10.1103/PhysRevA.95.062337},
journal = {Physical Review A},
number = 6,
volume = 95,
place = {United States},
year = 2017,
month = 6
}

Journal Article:
Free Publicly Available Full Text
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  • Modeling and simulation are essential for predicting and verifying the behavior of fabricated quantum circuits, but existing simulation methods are either impractically costly or require an unrealistic simplification of error processes. We present a method of simulating noisy Clifford circuits that is both accurate and practical in experimentally relevant regimes. In particular, the cost is weakly exponential in the size and the degree of non-Cliffordness of the circuit. Our approach is based on the construction of exact representations of quantum channels as quasiprobability distributions over stabilizer operations, which are then sampled, simulated, and weighted to yield unbiased statistical estimates ofmore » circuit outputs and other observables. As a demonstration of these techniques, we simulate a Steane [[7,1,3]]-encoded logical operation with non-Clifford errors and compute its fault tolerance error threshold. We expect that the method presented here will enable studies of much larger and more realistic quantum circuits than was previously possible.« less
  • Abstract not provided.
  • A general theory of quantum Clifford algebras is presented, based on a quantum generalization of the Cartan theory of spinors. We concentrate on the case when it is possible to apply the quantum-group formalism of bicovariant bimodules. The general theory is then singularized to the quantum SL({ital n},{bold C}) group case, to generate explicit forms for the whole class of braidings required. The corresponding spinor representations are introduced and investigated. Starting from our Clifford algebras we introduce the quantum-Euclidean underlying spaces compatible with different choices of {asterisk}-structures from where the analogues of Dirac and Laplace operators are built. Using themore » formalism developed, quantum Spin({ital n}) groups are defined. {copyright} {ital 1996 American Institute of Physics.}« less