Fault-Tolerant Quantum Walks

TL;DR

This paper introduces a systematic method for implementing fault-tolerant discrete-time quantum walks on complex graphs, utilizing quantum error correction with the Steane code and universal fault-tolerant operations.

Contribution

It presents the first comprehensive approach to fault-tolerant quantum walks, addressing errors in physical implementations with quantum error correction techniques.

Findings

Demonstrates encoding quantum states with the Steane code

Develops universal fault-tolerant matrix operations for quantum walks

Provides a framework for reliable quantum walk implementations

Abstract

Quantum walks are expected to serve important modelling and algorithmic applications in many areas of science and mathematics. Although quantum walks have been successfully implemented physically in recent times, no major efforts have been made to combat the error associated with these physical implementations in a fault-tolerant manner. In this paper, we propose a systematic method to implement fault-tolerant quantum walks in discrete time on arbitrarily complex graphs, using quantum states encoded with the Steane code and a set of universal fault tolerant matrix operations.