Quantum Computation by Geometrical Means

TL;DR

This paper introduces a geometrical framework for quantum computation using non-abelian connections to implement holonomic gates, providing a new approach to universal quantum computing with degenerate states.

Contribution

It presents a novel geometrical method employing non-abelian connections to realize universal quantum gates via holonomies in degenerate systems.

Findings

Explicit construction of a universal set of holonomic quantum gates

Demonstration of holonomies acting on degenerate states for quantum computation

A simple geometrical model illustrating the approach

Abstract

A geometrical approach to quantum computation is presented, where a non-abelian connection is introduced in order to rewrite the evolution operator of an energy degenerate system as a holonomic unitary. For a simple geometrical model we present an explicit construction of a universal set of gates, represented by holonomies acting on degenerate states.