Unitary Gate Synthesis via Polynomial Optimization

TL;DR

This paper introduces a polynomial optimization approach for synthesizing quantum gates using the Magnus expansion, enabling globally optimal solutions with faster convergence and scalability compared to local methods.

Contribution

It formulates a novel polynomial optimization framework for quantum gate synthesis that guarantees global optimality and improves efficiency over existing local methods.

Findings

Achieves high-accuracy gate synthesis with global optimality certificates

Demonstrates faster convergence and scalability in numerical experiments

Outperforms CRAB and GRAPE in accuracy and efficiency

Abstract

Quantum optimal control plays a crucial role in the development of quantum technologies, particularly in the design and implementation of fast and accurate gates for quantum computing. Here, we present a method to synthesize gates using the Magnus expansion. In particular, we formulate a polynomial optimization problem that allows us to find the global solution without resorting to approximations of the exponential. The global method we use provides a certificate of globality and lets us do single-shot optimization, which implies it is generally faster than local methods. By optimizing over Hermitian matrices generating the unitaries, instead of the unitaries themselves, we can reduce the size of the polynomial to optimize, leading to fast convergence and scalability. Numerical experiments comparing our results with CRAB and GRAPE show that we maintain high accuracy while providing globality certificates.