Threshold Estimate for Fault Tolerant Quantum Computation

TL;DR

This paper estimates the error threshold for fault-tolerant quantum computing using concatenated codes, suggesting a gate error threshold around 10^{-3} and a memory error threshold around 10^{-4}.

Contribution

It provides a rough estimate of the accuracy thresholds for fault-tolerant quantum computation with concatenated codes, focusing on gate and memory errors.

Findings

Gate error threshold approximately 10^{-3}.

Memory error threshold approximately 10^{-4}.

Simulation supports these threshold estimates.

Abstract

I make a rough estimate of the accuracy threshold for fault tolerant quantum computing with concatenated codes. First I consider only gate errors and use the depolarizing channel error model. I will follow P.Shor (quant-ph/9505011) for fault tolerant error correction (FTEC) and the fault tolerant implementation of elementary operations on states encoded by the 7-qubit code. A simple computer simulation suggests a threshold for gate errors of the order \epsilon \approx 10^{-3} or better. I also give a simple argument that the threshold for memory errors is about 10 times smaller, thus \epsilon \approx 10^{-4}.