Low-depth Hamiltonian Simulation by Adaptive Product Formula

Understand

Various Hamiltonian simulation algorithms have been proposed to efficiently study the dynamics of quantum systems on a quantum computer.

• The existing algorithms generally approximate the time evolution operators, which may need a deep quantum circuit that is beyond the capability of near-term noisy quantum devices.
• Here, focusing on the time evolution of a fixed input quantum state, we propose an adaptive approach to construct a low-depth time evolution circuit.
• By introducing a measurable quantifier that characterizes the simulation error, we use an adaptive strategy to learn the shallow quantum circuit that minimizes that error.