Time-optimal Control of Independent Spin-1/2 Systems under Simultaneous Control

TL;DR

This paper presents the first analytical solution and experimental demonstration of time-optimal control for two independent spin-1/2 particles using a common magnetic field, significantly reducing control duration.

Contribution

It introduces a novel symmetry reduction technique combined with Pontryagin Maximum Principle to derive explicit solutions for time-optimal control in quantum spin systems.

Findings

Achieved an average gate error of 1%.

Reduced control duration by 70-80% compared to existing methods.

First analytical and experimental demonstration of such control.

Abstract

We derive the explicit solution of the problem of time-optimal control by a common magnetic fields for two independent spin-$\frac{1}{2}$ particles. Our approach is based on the Pontryagin Maximum Principle and a novel symmetry reduction technique. We experimentally implement the optimal control using zero-field nuclear magnetic resonance. This reveals an average gate error of $1\%$ and a $70 \%$ to $80$ $\%$ decrease in the experiment duration as compared to existing methods. This is the first analytical solution and experimental demonstration of time-optimal control in such a system and it provides a route to achieve time optimal control in more general quantum systems.