High-Order Hermite Optimization: Fast and Exact Gradient Computation in Open-Loop Quantum Optimal Control using a Discrete Adjoint Approach

TL;DR

The paper presents the High-Order Hermite Optimization (HOHO) method, enabling fast, exact gradient computation in quantum control problems using high-order Hermite Runge-Kutta methods, significantly improving efficiency.

Contribution

It introduces the first efficient discrete adjoint method for quantum control with high-order Hermite integration, implemented in an open-source Julia package.

Findings

Speedups up to 775x in numerical experiments

First exact gradient computation for high-order Hermite methods in quantum control

Open-source implementation available in Julia

Abstract

This work introduces the High-Order Hermite Optimization (HOHO) method, an open-loop discrete adjoint method for quantum optimal control. Our method is the first of its kind to efficiently compute exact (discrete) gradients when using continuous, parameterized control pulses while solving the forward equations (e.g. Schrodinger's equation or the Linblad master equation) with an arbitrarily high-order Hermite Runge-Kutta method. The HOHO method is implemented in QuantumGateDesign$.$jl (https://github.com/leespen1/QuantumGateDesign.jl), an open-source software package for the Julia programming language, which we use to perform numerical experiments comparing the method to Juqbox$.$jl (https://github.com/LLNL/Juqbox.jl). For realistic model problems we observe speedups up to 775x.