TY - JOUR

T1 - Phase-space-simulation method for quantum computation with magic states on qubits

AU - Raussendorf, Robert

AU - Bermejo-Vega, Juani

AU - Tyhurst, Emily

AU - Okay, Cihan

AU - Zurel, Michael

N1 - 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’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754446, and from the UGR Research and Knowledge Transfer Found Athenea3i.

PY - 2020/1/31

Y1 - 2020/1/31

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85079367964&partnerID=8YFLogxK

U2 - 10.48550/arXiv.1905.05374

DO - 10.48550/arXiv.1905.05374

M3 - Article

AN - SCOPUS:85079367964

VL - 101

JO - Physical Review A

JF - Physical Review A

SN - 2469-9926

IS - 1

M1 - 012350

ER -