Minimum-Time Selective Control of Homonuclear Spins

TL;DR

This paper introduces a numerical algorithm for rapidly controlling two homonuclear spins in NMR quantum computation, significantly reducing control time and effort, especially when resonance frequencies are close.

Contribution

It presents a geometric analysis-based minimum-time estimation method combined with gradient optimization for efficient control of homonuclear spins.

Findings

Reduces control time in simulations and experiments

Effective for small frequency differences

Demonstrated with NMR experiments on carbon spins

Abstract

In NMR (Nuclear Magnetic Resonance) quantum computation, the selective control of multiple homonuclear spins is usually slow because their resonance frequencies are very close to each other. To quickly implement controls against decoherence effects, this paper presents an efficient numerical algorithm fordesigning minimum-time local transformations in two homonuclear spins. We obtain an accurate minimum-time estimation via geometric analysis on the two-timescale decomposition of the dynamics. Such estimation narrows down the range of search for the minimum-time control with a gradient-type optimization algorithm. Numerical simulations show that this method can remarkably reduce the search efforts, especially when the frequency difference is very small and the control field is high. Its effectiveness is further demonstrated by NMR experiments with two homunuclear carbon spins in a trichloroethylene (C2H1Cl3) sample system.