Direct Collocation for Quantum Optimal Control

TL;DR

This paper introduces PICO, a novel direct collocation method adapted for quantum optimal control, enabling efficient handling of complex constraints and free-time problems, outperforming existing algorithms in simulation and hardware tests.

Contribution

The paper develops PICO, a new direct collocation approach tailored for quantum control, supporting nonlinear constraints and free-time optimization, with improved convergence over traditional methods.

Findings

PICO outperforms GRAPE and CRAB in convergence speed.

PICO successfully optimizes control in hardware experiments.

Supports complex nonlinear constraints and free-time problems.

Abstract

We present an adaptation of direct collocation -- a trajectory optimization method commonly used in robotics and aerospace applications -- to quantum optimal control (QOC); we refer to this method as Pade Integrator COllocation (PICO). This approach supports general nonlinear constraints on the states and controls, takes advantage of state-of-the-art large-scale nonlinear programming solvers, and has superior convergence properties compared to standard approaches like GRAPE and CRAB. PICO also allows for the formulation of novel free-time and minimum-time control problems -- crucial for realizing high-performance quantum computers when the optimal pulse duration is not known a priori. We demonstrate PICO's performance both in simulation and on hardware with a 3D circuit cavity quantum electrodynamics system.