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Trapped Ion Quantum Computing

Learning quantum states prepared by shallow circuits in polynomial time

arXiv
Authors: Zeph Landau, Yunchao Liu

Year

2024

Paper ID

37415

Status

Preprint

Abstract Read

~2 min

Abstract Words

112

Citations

N/A

Abstract

We give a polynomial time algorithm that, given copies of an unknown quantum state vertψrangle=Uvert 0nrangle that is prepared by an unknown constant depth circuit U on a finite-dimensional lattice, learns a constant depth quantum circuit that prepares vertψrangle. The algorithm extends to the case when the depth of U is polylog(n), with a quasi-polynomial run-time. The key new idea is a simple and general procedure that efficiently reconstructs the global state vertψrangle from its local reduced density matrices. As an application, we give an efficient algorithm to test whether an unknown quantum state on a lattice has low or high quantum circuit complexity.

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  • This paper contributes to the Trapped-Ion Quantum Computing research area in the Quantum Articles archive.
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  • We give a polynomial time algorithm that, given copies of an unknown quantum state vertψrangle=Uvert 0^nrangle that is prepared by an unknown constant depth circuit U on a...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2410.23618 [2] arXiv https://arxiv.org/abs/2410.23618 [3] Publisher https://arxiv.org/abs/2410.23618

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