Geometric quantum gates in liquid-state NMR based on a cancellation of dynamical phases

TL;DR

This paper demonstrates a modified double-loop method for implementing geometric quantum gates in liquid-state NMR, successfully eliminating dynamical phases and realizing one-qubit gates with high precision, advancing quantum computing techniques.

Contribution

It introduces a modified double-loop approach using spin echo in NMR to cancel dynamical phases in geometric quantum gates.

Findings

Dynamical phase is effectively eliminated.

One-qubit gates are successfully implemented.

Fidelity of gates is improved but still not optimal.

Abstract

A proposal for applying non-adiabatic geometric phases to quantum computing, called the double-loop method [S.-L. Zhu and Z. D. Wang, Phys. Rev. A {\bf 67}, 022319 (2003)], is demonstrated in a liquid state NMR quantum computer. Using a spin echo technique, the original method is modified so that quantum gates are implemented in a standard high-precision NMR system for chemical analysis. We show that the dynamical phase is successfully eliminated and a one-qubit quantum gate is realized, although the fidelity is not so high.