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- W2896548375 abstract "One of the lowest-order corrections to Gaussian quantum mechanics in infinite-dimensional Hilbert spaces are Airy functions: a uniformization of the stationary phase method applied in the path integral perspective. We introduce a periodized stationary phase method to discrete Wigner functions of systems with odd prime dimension and show that the $frac{pi}{8}$ gate is the discrete analog of the Airy function. We then establish a relationship between the stabilizer rank of states and the number of quadratic Gauss sums necessary in the periodized stationary phase method. This allows us to develop a classical strong simulation of a single qutrit marginal on $t$ qutrit $frac{pi}{8}$ gates that are followed by Clifford evolution, and show that this only requires $3^{frac{t}{2}+1}$ quadratic Gauss sums. This outperforms the best alternative qutrit algorithm (based on Wigner negativity and scaling as $simhspace{-3pt} 3^{0.8 t}$ for $10^{-2}$ precision) for any number of $frac{pi}{8}$ gates to full precision." @default.
- W2896548375 created "2018-10-26" @default.
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- W2896548375 date "2021-07-05" @default.
- W2896548375 modified "2023-10-03" @default.
- W2896548375 title "Stationary Phase Method in Discrete Wigner Functions and Classical Simulation of Quantum Circuits" @default.
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- W2896548375 doi "https://doi.org/10.22331/q-2021-07-05-494" @default.
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