Classical Simulation of Quantum Circuits by Half Gauss Sums
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Author(s)
Bu, Kaifeng
Koh, Dax E.
Date Issued
January 31, 2022
Publisher
Springer Berlin Heidelberg
Citation
Bu, Kaifeng and Koh, Dax E. 2022. "Classical Simulation of Quantum Circuits by Half Gauss Sums."
Version
Author's final manuscript
Abstract
Abstract
We give an efficient algorithm to evaluate a certain class of exponential sums, namely the periodic, quadratic, multivariate half Gauss sums. We show that these exponential sums become
$$\#{\mathsf {P}}$$
#
P
-hard to compute when we omit either the periodicity or quadraticity condition. We apply our results about these exponential sums to the classical simulation of quantum circuits, and give an alternative proof of the Gottesman–Knill theorem. We also explore a connection between these exponential sums and the Holant framework. In particular, we generalize the existing definition of affine signatures to arbitrary dimensions, and use our results about half Gauss sums to show that the Holant problem for the set of affine signatures is tractable.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s00220-022-04320-1
