Efficient simulation for time-dependent Hamiltonians #

Guannan Chen, Pranav Singh, Mohammadali Foroozandeh, Chris Budd

14:50 Monday in 4Q04.

Part of the Numerical methods session.

Abstract #

Quantum computation of Hamiltonian simulation is seen as one of the most promising applications for quantum computers. However, there is still a lack of research on simulating time-dependent Hamiltonians. To address this, we use Magnus expansion to develop quantum simulation algorithms for many-body problems with a time-dependent Hamiltonian H(t). Our method exploits the symmetries of the Hamiltonian and achieves a surprising reduction in the expansion and can simulate the time-dependent Hamiltonian at a cost that is no higher than required for a time-independent Hamiltonian. The overall scheme in this work achieves fourth-order convergence rates with small error constants and substantially short circuit depth compared to a second-order method, which makes our algorithm a suitable candidate for near-term quantum computers.