Adiabatic topological quantum computing

TL;DR

This paper investigates adiabatic processes in topological quantum computing, demonstrating protocols that enable universal quantum computation while maintaining system stability and error resistance.

Contribution

It introduces analytical protocols for adiabatic topological quantum computing that preserve energy gaps and utilize simple local Hamiltonians for universal computation.

Findings

Protocols for adiabatic code deformations maintaining constant energy gap

Analytical tools for understanding adiabatic topological processes

Feasibility of holonomic quantum computing with topological codes

Abstract

Topological quantum computing promises error-resistant quantum computation without active error correction. However, there is a worry that during the process of executing quantum gates by braiding anyons around each other, extra anyonic excitations will be created that will disorder the encoded quantum information. Here we explore this question in detail by studying adiabatic code deformations on Hamiltonians based on topological codes, notably Kitaev's surface codes and the more recently discovered color codes. We develop protocols that enable universal quantum computing by adiabatic evolution in a way that keeps the energy gap of the system constant with respect to the computation size and introduces only simple local Hamiltonian interactions. This allows one to perform holonomic quantum computing with these topological quantum computing systems. The tools we develop allow one to go beyond numerical simulations and understand these processes analytically.