Memory-Efficient Differentiable Programming for Quantum Optimal Control of Discrete Lattices

TL;DR

This paper introduces a memory-efficient differentiable programming method for quantum optimal control on discrete lattices, enabling the simulation of larger models and longer time spans by reducing memory requirements through invertibility-based recomputation.

Contribution

It presents a novel invertibility-based differentiable programming approach that significantly reduces memory usage in quantum optimal control for discrete lattices.

Findings

Reduces memory requirements for quantum optimal control simulations.

Demonstrates effectiveness on lattice gauge theory models.

Enables larger and longer quantum simulations.

Abstract

Quantum optimal control problems are typically solved by gradient-based algorithms such as GRAPE, which suffer from exponential growth in storage with increasing number of qubits and linear growth in memory requirements with increasing number of time steps. Employing QOC for discrete lattices reveals that these memory requirements are a barrier for simulating large models or long time spans. We employ a nonstandard differentiable programming approach that significantly reduces the memory requirements at the cost of a reasonable amount of recomputation. The approach exploits invertibility properties of the unitary matrices to reverse the computation during back-propagation. We utilize QOC software written in the differentiable programming framework JAX that implements this approach, and demonstrate its effectiveness for lattice gauge theory.