Geometric phase and gauge theory structure in quantum computing

TL;DR

This paper explores the geometric phase and gauge structure in quantum computing, revealing that the time evolution operator acts as a free energy operator instead of the Hamiltonian.

Contribution

It introduces a gauge-theoretic perspective on qubit evolution, highlighting the role of geometric phases and redefining the evolution operator in quantum computing.

Findings

Identification of geometric phase in qubit evolution

Revealing the time evolution operator as a free energy operator

Implications for gauge theory in quantum computation

Abstract

We discuss the presence of a geometrical phase in the evolution of a qubit state and its gauge structure. The time evolution operator is found to be the free energy operator, rather than the Hamiltonian operator.