Exact solutions for time-optimal control of spin I=1 by NMR

TL;DR

This paper derives exact time-optimal control solutions for a spin I=1 system in NMR, using nonselective pulses and Cartan decomposition, revealing phase-dependent gate times and providing analytical and numerical results.

Contribution

It introduces a novel approach for time-optimal control of spin I=1 nuclei using nonselective pulses and Cartan decomposition, with explicit solutions for key quantum gates.

Findings

Minimum gate times depend strongly on the global phase.

Analytical solutions match numerical data.

Partial solutions for single-qutrit gates are obtained.

Abstract

We consider the problem of time-optimal control of quadrupole nucleus with the spin I=1 by NMR. In contrast to the conventional methods based on selective pulses, the control is implemented using nonselective pulses separated by free evolution intervals. Using the Cartan decomposition, the system of equations is obtained for finding parameters of a control field. Partial time-optimal solutions for the important single-qutrit gates (selective rotations and quantum Fourier transform) are found. The strong dependence of minimum gate implementation times on global phase of the gate is observed. The analytical values of minimum times are consistent with the numerical data.