Geometric phases in dressed state quantum computation

TL;DR

This paper explores how geometric phases naturally occur in dressed state quantum gates and demonstrates how to utilize these phases to perform quantum operations with arbitrary Hamiltonians.

Contribution

It introduces a method to identify dressed states that enable quantum gates to be executed up to a phase, combining dynamical and geometric phases, for any Hamiltonian and time.

Findings

Existence of dressed states for arbitrary Hamiltonians and times

Quantum gates can be performed up to a phase combining dynamical and geometric components

Illustrations provided for several quantum systems

Abstract

Geometric phases arise naturally in a variety of quantum systems with observable consequences. They also arise in quantum computations when dressed states are used in gating operations. Here we show how they arise in these gating operations and how one may take advantage of the dressed states producing them. Specifically, we show that that for a given, but arbitrary Hamiltonian, and at an arbitrary time {\tau}, there always exists a set of dressed states such that a given gate operation can be performed by the Hamiltonian up to a phase {\phi}. The phase is a sum of a dynamical phase and a geometric phase. We illustrate the new phase for several systems.