Papers › Optimised Trotter Decompositions for Classical and Quantum Computing
Optimised Trotter Decompositions for Classical and Quantum Computing
Johann Ostmeyer
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Suzuki-Trotter decompositions of exponential operators like exp(Ht) 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 Aₖ, 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.
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