Polynomial-time additive-error estimation of output probabilities for shallow quantum circuits

Abstract:We give a deterministic classical algorithm that estimates $|\langle x|U|0^n\rangle|^2$ to additive error $\varepsilon$ in $\mathrm{poly}(n, 1/\varepsilon)$ time, where $U$ is a constant-depth quantum circuit comprised of gates with bounded fan-in and arbitrary connectivity, and $x$ is an arbitrary $n$-bit output string. This improves over prior state-of-the-art algorithms that takes $n^{O(log(n))}$ time for the same task, $n^{O(log(log(n))}$ when $U$ is geometrically local, and $n^{O(1)}$ for 2D geometrically-local circuits.

Quantum Physics (quant-ph); Computational Complexity (cs.CC); Data Structures and Algorithms (cs.DS)

arXiv:2610.02146 [quant-ph]

(or arXiv:2610.02146v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2610.02146 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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