Quantum Algorithm for Simulating Hamiltonian Dynamics with an Off-diagonal Series Expansion

Abstract

We propose an efficient quantum algorithm for simulating the dynamics of general Hamiltonian systems. Our technique is based on a power series expansion of the time-evolution operator in its off-diagonal terms. The expansion decouples the dynamics due to the diagonal component of the Hamiltonian from the dynamics generated by its off-diagonal part, which we encode using the linear combination of unitaries technique. Our method has an optimal dependence on the desired precision and, as we illustrate, generally requires considerably fewer resources than the current state-of-the-art. We provide an analysis of resource costs for several sample models.

24 pages, 8 figures. Minor corrections included

References in corpus (3)

• Simulating Hamiltonian dynamics with a truncated Taylor series
• Synthesis of Quantum Logic Circuits
• Calculating the divided differences of the exponential function by addition and removal of inputs

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