Optimised Trotter decompositions for classical and quantum computing

doi:10.1088/1751-8121/acde7a

Optimised Trotter decompositions for classical and quantum computing

2023-06-26

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DOI：10.1088/1751-8121/acde7a

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Abstract Suzuki–Trotter decompositions of exponential operators like exp ( H t ) are required in almost every branch of numerical physics. Often the exponent under consideration has to be split into more than two operators H = ∑ k A k , for instance as local gates on quantum computers. We demonstrate how highly optimised schemes originally derived for exactly two operators A 1 , 2 can be applied to such generic Suzuki–Trotter decompositions, providing a formal proof of correctness as well as numerical evidence of efficiency. A comprehensive review of existing symmetric decomposition schemes up to order n ⩽ 4 is presented and complemented by a number of novel schemes, including both real and complex coefficients. We derive the theoretically most efficient unitary and non-unitary 4th order decompositions. The list is augmented by several exceptionally efficient schemes of higher order n ⩽ 8 . Furthermore we show how Taylor expansions can be used on classical devices to reach machine precision at a computational effort at which state of the art Trotterization schemes do not surpass a relative precision of 10−4. Finally, a short and easily understandable summary explains how to choose the optimal decomposition in any given scenario.

Optimised Trotter decompositions for classical and quantum computing

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