Com­plex Quantum Sys­tems Sem­in­ar: Guan­nan Chen (Bath Uni­ver­sity) "Al­gorithms for Hamilto­ni­an Sim­u­la­tion and Op­tim­al Con­trol"

Title: Algorithms for Hamiltonian Simulation and Optimal Control

Abstract: The precision and efficiency of quantum simulations and controls are vital for the advancement of quantum technologies. This talk presents three recent developments in algorithms for quantum spin systems and broader Hamiltonian systems. Firstly, we introduce a fourth-order Magnus-based algorithm for simulating many-body systems under the presence of highly-oscillatory time-dependent pulses. These integrators achieve high accuracy despite taking large time-steps, which corresponds to faster computation on classical computers and shorter circuit depths on quantum computers, making our algorithm a suitable candidate on near-term quantum devices.  Secondly, we introduce a method for optimal control of spins utilizing analytical first derivatives and approximation of second derivative using Gauss–Newton method, facilitating efficient quantum gate design. Finally, we discuss a novel iterative linearization approach for solving nonlinear dispersive equations, ensuring the preservation of structural properties such as the L2 norm, momentum, and Hamiltonian energy.