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Doubling the order of approximation via the randomized product formula
Chien-Hung Cho, D. Berry, Min-Hsiu Hsieh·October 20, 2022·DOI: 10.1103/PhysRevA.109.062431
Physics
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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.