Quantum computing with anyons is fault tolerant

TL;DR

This paper presents an error-correction scheme for topological quantum computing with anyons, enabling fault-tolerant universal quantum computation on noisy hardware by actively correcting errors during braiding operations.

Contribution

The authors develop a novel error-correction method that allows fault-tolerant topological quantum computation with anyons on realistic noisy quantum devices.

Findings

The scheme achieves arbitrarily low failure rates below a certain noise threshold.

It enables universal quantum computation using topological methods on current quantum hardware.

The approach is robust against local perturbations and noise in quantum circuit elements.

Abstract

In seminal work (arxiv:quant-ph/9707021) Alexei Kitaev proposed topological quantum computing (arXiv:cond-mat/0010440, arxiv:quant-ph/9707021, arXiv:quant-ph/0001108, arXiv:0707.1889), whereby logic gates of a quantum computer are conducted by creating, braiding and fusing anyonic particles on a two-dimensional plane. Furthermore, he showed the proposal is inherently robust to local perturbations (arXiv:cond-mat/0010440, arxiv:quant-ph/9707021, arXiv:1001.0344, arXiv:1001.4363) when anyons are created as quasiparticle excitations of a topologically ordered lattice model prepared at zero temperature. Over the decades following this proposal there have been considerable technological developments towards the construction of a fault-tolerant quantum computer. Rather than maintaining some target ground state at zero temperature, a modern approach is to actively correct the errors a target state experiences, where we use noisy quantum circuit elements to identify and subsequently correct for deviations from the ideal state. We present an error-correction scheme that enables us to carry out robust universal quantum computation by braiding anyons. We show that our scheme can be carried out on a suitably large device with an arbitrarily small failure rate assuming circuit elements are below some threshold level of local noise. The error-corrected scheme we have developed therefore enables us to carry out fault-tolerant topological quantum computation using modern quantum hardware that is now under development.