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

Understand

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.