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.
Highlights
Simulating the dynamics of quantum many-body systems is a central challenge in Physics, Chemistry and the Material Sciences as well as in other areas of science and technology
We propose a novel approach to resource-efficient Hamiltonian dynamics simulations on quantum circuits that we argue offers certain advantages, which directly translate to a shorter algorithm runtime, over state-of-the-art quantum simulation algorithms [1, 2]
We find that its gate and qubit costs are O(Q2 + QM (C∆D0 + kod + log M )) and O(Q), respectively, where C∆D0 is the cost of calculating the change in diagonal energy due to the action of a permutation operator and kod is an upper bound on the ‘off-diagonal locality’, i.e., the locality of the Pi’s [1, 12]
Summary
Simulating the dynamics of quantum many-body systems is a central challenge in Physics, Chemistry and the Material Sciences as well as in other areas of science and technology. We propose a novel approach to resource-efficient Hamiltonian dynamics simulations on quantum circuits that we argue offers certain advantages, which directly translate to a shorter algorithm runtime, over state-of-the-art quantum simulation algorithms [1, 2] (see Sec. 4 for a detailed comparison). We accomplish this by utilizing a series expansion of the quantum time-evolution operator in its off-diagonal elements wherein the operator is expanded around its diagonal component [3,4,5].
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