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Quantum Simulation

Classical simulation of quantum circuits by half Gauss sums

arXiv
Authors: Kaifeng Bu, Dax Enshan Koh

Year

2018

Paper ID

22981

Status

Preprint

Abstract Read

~2 min

Abstract Words

114

Citations

N/A

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}-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.

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  • This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
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  • We give an efficient algorithm to evaluate a certain class of exponential sums, namely the periodic, quadratic, multivariate half Gauss sums.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1812.00224 [2] arXiv https://arxiv.org/abs/1812.00224 [3] Publisher https://arxiv.org/abs/1812.00224

Local Citation Graph (Related-Paper Links)

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