Robust and efficient algorithms for high-dimensional black-box quantum optimization

TL;DR

This paper introduces new black-box optimization algorithms for high-dimensional quantum systems that improve convergence speed and precision, demonstrated on tuning high-fidelity quantum gates.

Contribution

The paper develops AdamSPSA and AdamRSGF algorithms combining randomized perturbation and adaptive momentum, with proven convergence and superior performance in quantum control tasks.

Findings

Accelerated convergence rate compared to existing algorithms

Reduced variance in loss trajectories

Successfully tuned high-fidelity quantum gates with twenty variables

Abstract

Hybrid quantum-classical optimization using near-term quantum technology is an emerging direction for exploring quantum advantage in high-dimensional systems. However, precise characterization of all experimental parameters is often impractical and challenging. A viable approach is to use algorithms that rely only on black-box inference rather than analytical gradients. Here, we combine randomized perturbation gradient estimation with adaptive momentum gradient updates to create the AdamSPSA and AdamRSGF algorithms. We prove the asymptotic convergence of our algorithms in a convex setting, and we benchmark them against other gradient-based optimization algorithms on non-convex optimal control tasks. Our results show that these new algorithms accelerate the convergence rate, decrease the variance of loss trajectories, and efficiently tune up high-fidelity (above 99.9\%) Hann-window single-qubit gates from trivial initial conditions with twenty variables.