An upper bound on quantum fault tolerant thresholds

TL;DR

This paper establishes upper bounds on quantum fault tolerance thresholds using optimal recovery and entropy estimates, suggesting a maximum threshold around 6.88% to 6.90%, which aligns with prior empirical findings.

Contribution

It introduces a method to calculate upper bounds on quantum fault tolerance thresholds without overhead restrictions, using entropy and optimal recovery operators.

Findings

Fault tolerance threshold estimated at 6.88% for depolarizing noise.

Conjectured optimal threshold around 6.90%.

Threshold calculations extended to other noise types.

Abstract

In this paper we calculate upper bounds on fault tolerance, without restrictions on the overhead involved. Optimally adaptive recovery operators are used, and the Shannon entropy is used to estimate the thresholds. By allowing for unrealistically high levels of overhead, we find a quantum fault tolerant threshold of 6.88% for the depolarizing noise used by Knill, which compares well to "above 3%" evidenced by Knill. We conjecture that the optimal threshold is 6.90%, based upon the hashing rate. We also perform threshold calculations for types of noise other than that discussed by Knill.