Geometric Aspects of Composite Pulses

TL;DR

This paper explores how certain composite pulses in quantum systems can be designed as geometric quantum gates by ensuring they have vanishing dynamical phase, enhancing robustness against control errors.

Contribution

It demonstrates that specific composite pulses for one- and two-qubit systems act as geometric quantum gates with vanishing dynamical phase, linking composite pulse design to geometric quantum computation.

Findings

Composite pulses can be designed as geometric gates.

Vanishing dynamical phase is achievable in composite pulses.

Geometric nature enhances robustness against errors.

Abstract

Unitary operations acting on a quantum system must be robust against systematic errors in control parameters for reliable quantum computing. Composite pulse technique in nuclear magnetic resonance (NMR) realises such a robust operation by employing a sequence of possibly poor quality pulses. In this article, we demonstrate that two kinds of composite pulses, one compensates for a pulse length error in a one-qubit system and the other compensates for a J-coupling error in a twoqubit system, have vanishing dynamical phase and thereby can be seen as geometric quantum gates, which implement unitary gates by the holonomy associated with dynamics of cyclic vectors defined in the text.