Holonomic quantum computing in symmetry-protected ground states of spin chains

TL;DR

This paper proposes a simplified architecture for holonomic quantum computing using symmetry-protected ground states of spin chains, offering robustness against noise and disorder with minimal control requirements.

Contribution

It introduces a novel, simpler approach to topologically inspired quantum computing leveraging symmetry-protected states in spin-1 chains.

Findings

Quantum information stored in ground states of spin chains.

Quantum gates implemented via adiabatic non-Abelian holonomies.

Protection from noise due to symmetry-based ground state degeneracy.

Abstract

While solid-state devices offer naturally reliable hardware for modern classical computers, thus far quantum information processors resemble vacuum tube computers in being neither reliable nor scalable. Strongly correlated many body states stabilized in topologically ordered matter offer the possibility of naturally fault tolerant computing, but are both challenging to engineer and coherently control and cannot be easily adapted to different physical platforms. We propose an architecture which achieves some of the robustness properties of topological models but with a drastically simpler construction. Quantum information is stored in the symmetry-protected degenerate ground states of spin-1 chains, while quantum gates are performed by adiabatic non-Abelian holonomies using only single-site fields and nearest-neighbor couplings. Gate operations respect the symmetry, and so inherit some protection from noise and disorder from the symmetry-protected ground states.