The Fibonacci scheme for fault-tolerant quantum computation

TL;DR

This paper rigorously analyzes Knill's Fibonacci scheme for fault-tolerant quantum computing, establishing lower bounds on the fault rate threshold and highlighting its reduced overhead due to efficient postselection.

Contribution

It provides the first rigorous threshold bounds for the Fibonacci scheme and demonstrates its lower overhead compared to similar fault-tolerance methods.

Findings

Threshold fault rate of 0.00067 for adversarial noise

Threshold fault rate of 0.00125 for depolarizing noise

Reduced overhead due to sparing use of postselection

Abstract

We rigorously analyze Knill's Fibonacci scheme for fault-tolerant quantum computation, which is based on the recursive preparation of Bell states protected by a concatenated error-detecting code. We prove lower bounds on the threshold fault rate of .67\times 10^{-3} for adversarial local stochastic noise, and 1.25\times 10^{-3} for independent depolarizing noise. In contrast to other schemes with comparable proved accuracy thresholds, the Fibonacci scheme has a significantly reduced overhead cost because it uses postselection far more sparingly.