Doubling the order of approximation via the randomized product formula

• URL: http://arxiv.org/abs/2210.11281v1
• Date: Thu, 20 Oct 2022 13:59:29 GMT
• Title: Doubling the order of approximation via the randomized product formula
• Authors: Chien Hung Cho and Dominic W. Berry and Min-Hsiu Hsieh
• Abstract summary: We show that by applying randomized corrections, it is possible to more than double the order to 4k + 1. In practice, applying the corrections in a quantum algorithm requires some structure to the Hamiltonian.
• Score: 12.547444644243544
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Randomization has been applied to Hamiltonian simulation in a number of ways to improve the accuracy or efficiency of product formulas. Deterministic product formulas are often constructed in a symmetric way to provide accuracy of even order 2k. We show that by applying randomized corrections, it is possible to more than double the order to 4k + 1 (corresponding to a doubling of the order of the error). In practice, applying the corrections in a quantum algorithm requires some structure to the Hamiltonian, for example the Pauli strings as are used in the simulation of quantum chemistry.

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