Abstract

Hamiltonian simulation is both a fundamental subcomponent of many quantum algorithms and one of the first problems where quantum advantage is expected to be realised. A key challenge in Hamiltonian simulation is efficiently approximating the matrix exponential for time evolution. In this talk, I will provide an overview of classical algorithms for approximating the matrix exponential and discuss their application to non-autonomous and non-linear Hamiltonian simulation. I will highlight methods that enable the use of long time-steps, drawing on techniques from approximation theory, machine learning, and adaptive ODE solvers.

I will then explore potential applicability and consequences for Hamiltonian simulation on near-term quantum devices, including a specialised algorithm for Hamiltonian simulation of spin systems. Since longer time-steps reduce circuit depth, algorithms that allow long time-steps could be especially valuable for near-term quantum devices, where deeper circuits exacerbate noise accumulation.