TY - JOUR

T1 - Simulating Quantum Computation

T2 - How Many "Bits" for "It"?

AU - Zurel, Michael

AU - Okay, Cihan

AU - Raussendorf, Robert

N1 - Publisher Copyright: © 2024 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

PY - 2024/9/3

Y1 - 2024/9/3

N2 - A recently introduced classical simulation method for universal quantum computation with magic states operates by repeated sampling from probability functions [M. Zurel et al. PRL 260404 (2020)]. This method is closely related to sampling algorithms based on Wigner functions, with the important distinction that Wigner functions can take negative values obstructing the sampling. Indeed, negativity in Wigner functions has been identified as a precondition for a quantum speed-up. However, in the present method of classical simulation, negativity of quasiprobability functions never arises. This model remains probabilistic for all quantum computations. In this paper, we analyze the amount of classical data that the simulation procedure must track. We find that this amount is small. Specifically, for any number n of magic states, the number of bits that describe the quantum system at any given time is 2n2+O(n).

AB - A recently introduced classical simulation method for universal quantum computation with magic states operates by repeated sampling from probability functions [M. Zurel et al. PRL 260404 (2020)]. This method is closely related to sampling algorithms based on Wigner functions, with the important distinction that Wigner functions can take negative values obstructing the sampling. Indeed, negativity in Wigner functions has been identified as a precondition for a quantum speed-up. However, in the present method of classical simulation, negativity of quasiprobability functions never arises. This model remains probabilistic for all quantum computations. In this paper, we analyze the amount of classical data that the simulation procedure must track. We find that this amount is small. Specifically, for any number n of magic states, the number of bits that describe the quantum system at any given time is 2n2+O(n).

UR - http://www.scopus.com/inward/record.url?scp=85203602745&partnerID=8YFLogxK

U2 - 10.48550/arXiv.2305.17287

DO - 10.48550/arXiv.2305.17287

M3 - Article

AN - SCOPUS:85203602745

VL - 5

JO - PRX Quantum

JF - PRX Quantum

IS - 3

M1 - 030343

ER -