Holonomic quantum computation: a scalable adiabatic architecture

TL;DR

This paper introduces a scalable, robust holonomic quantum computing framework using adiabatic gates, with a geometric approach applicable to Rydberg atom experiments.

Contribution

It presents a universal set of holonomic adiabatic gates for scalable quantum computation with a differential geometric analysis of their robustness.

Findings

Gates are inherently robust against classical control errors.

Framework is compatible with recent Rydberg-based quantum platforms.

Geometric nature of gates enhances error resilience.

Abstract

Holonomic quantum computation exploits the geometric evolution of eigenspaces of a degenerate Hamiltonian to implement unitary evolution of computational states. In this work we introduce a framework for performing scalable quantum computation in atom experiments through a universal set of fully holonomic adiabatic gates. Through a detailed differential geometric analysis, we elucidate the geometric nature of these gates and their inherent robustness against classical control errors and other noise sources. The concepts that we introduce here are expected to be widely applicable to the understanding and design of error robustness in generic holonomic protocols. To underscore the practical feasibility of our approach, we contextualize our gate design within recent advancements in Rydberg-based quantum computing and simulation.