Optimal control methods for fast time-varying Hamiltonians

TL;DR

This paper introduces a numerical method for optimizing control pulses in quantum systems that explicitly accounts for the different timescales of control variation and Hamiltonian dynamics, improving physical relevance.

Contribution

The method uniquely separates the timescales of control input and Hamiltonian evolution, enhancing optimization accuracy for filtered or fast-carrier signals.

Findings

Efficient optimization with reduced search space.

Accurate simulation of fast Hamiltonian variations.

Improved physical relevance of control pulses.

Abstract

In this article, we develop a numerical method to find optimal control pulses that accounts for the separation of timescales between the variation of the input control fields and the applied Hamiltonian. In traditional numerical optimization methods, these timescales are treated as being the same. While this approximation has had much success, in applications where the input controls are filtered substantially or mixed with a fast carrier, the resulting optimized pulses have little relation to the applied physical fields. Our technique remains numerically efficient in that the dimension of our search space is only dependent on the variation of the input control fields, while our simulation of the quantum evolution is accurate on the timescale of the fast variation in the applied Hamiltonian.