Phase-space-simulation method for quantum computation with magic states on qubits

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  • University of British Columbia
  • Freie Universität Berlin (FU Berlin)
  • University of Toronto
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Original languageEnglish
Article number012350
JournalPhysical Review A
Volume101
Issue number1
Publication statusPublished - 31 Jan 2020
Externally publishedYes

Abstract

We propose a method for classical simulation of finite-dimensional quantum systems, based on sampling from a quasiprobability distribution, i.e., a generalized Wigner function. Our construction applies to all finite dimensions, with the most interesting case being that of qubits. For multiple qubits, we find that quantum computation by Clifford gates and Pauli measurements on magic states can be efficiently classically simulated if the quasiprobability distribution of the magic states is non-negative. This provides the so far missing qubit counterpart of the corresponding result [V. Veitch et al., New J. Phys. 14, 113011 (2012)NJOPFM1367-263010.1088/1367-2630/14/11/113011] applying only to odd dimension. Our approach is more general than previous ones based on mixtures of stabilizer states. Namely, all mixtures of stabilizer states can be efficiently simulated, but for any number of qubits there also exist efficiently simulable states outside the stabilizer polytope. Further, our simulation method extends to negative quasiprobability distributions, where it provides probability estimation. The simulation cost is then proportional to a robustness measure squared. For all quantum states, this robustness is smaller than or equal to robustness of magic.

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Phase-space-simulation method for quantum computation with magic states on qubits. / Raussendorf, Robert; Bermejo-Vega, Juani; Tyhurst, Emily et al.
In: Physical Review A, Vol. 101, No. 1, 012350, 31.01.2020.

Research output: Contribution to journalArticleResearchpeer review

Raussendorf R, Bermejo-Vega J, Tyhurst E, Okay C, Zurel M. Phase-space-simulation method for quantum computation with magic states on qubits. Physical Review A. 2020 Jan 31;101(1):012350. doi: 10.48550/arXiv.1905.05374, 10.1103/PhysRevA.101.012350, 10.1103/PhysRevA.105.039902
Raussendorf, Robert ; Bermejo-Vega, Juani ; Tyhurst, Emily et al. / Phase-space-simulation method for quantum computation with magic states on qubits. In: Physical Review A. 2020 ; Vol. 101, No. 1.
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abstract = "We propose a method for classical simulation of finite-dimensional quantum systems, based on sampling from a quasiprobability distribution, i.e., a generalized Wigner function. Our construction applies to all finite dimensions, with the most interesting case being that of qubits. For multiple qubits, we find that quantum computation by Clifford gates and Pauli measurements on magic states can be efficiently classically simulated if the quasiprobability distribution of the magic states is non-negative. This provides the so far missing qubit counterpart of the corresponding result [V. Veitch et al., New J. Phys. 14, 113011 (2012)NJOPFM1367-263010.1088/1367-2630/14/11/113011] applying only to odd dimension. Our approach is more general than previous ones based on mixtures of stabilizer states. Namely, all mixtures of stabilizer states can be efficiently simulated, but for any number of qubits there also exist efficiently simulable states outside the stabilizer polytope. Further, our simulation method extends to negative quasiprobability distributions, where it provides probability estimation. The simulation cost is then proportional to a robustness measure squared. For all quantum states, this robustness is smaller than or equal to robustness of magic.",
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note = "Funding Information: We thank Piers Lillystone (J.B.-V., C.O., R.R., E.T.) and Shane Mansfield (J.B.-V.) for discussion. C.O., R.R., E.T., M.Z. are funded by NSERC, and R.R. acknowledges funding from Cifar. J.B.V. acknowledges funding from the ERC (TAQ 307498) project and the European Union{\textquoteright}s Horizon 2020 research and innovation programme under the Marie Sk{\l}odowska-Curie Grant Agreement No. 754446, and from the UGR Research and Knowledge Transfer Found Athenea3i. ",
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