Quantum accuracy threshold for concatenated distance-3 codes

TL;DR

This paper establishes a rigorous lower bound on the quantum accuracy threshold for concatenated distance-3 codes, accommodating correlated noise and higher-distance codes, using a novel proof approach and computer-assisted analysis.

Contribution

It introduces a new quantum threshold theorem applicable to concatenated codes and correlated noise, providing the best proven lower bound on the threshold to date.

Findings

Lower bound on quantum threshold epsilon_0 > 2.73 x 10^{-5}

Applicable to correlated noise models

Extends to higher-distance codes

Abstract

We prove a new version of the quantum threshold theorem that applies to concatenation of a quantum code that corrects only one error, and we use this theorem to derive a rigorous lower bound on the quantum accuracy threshold epsilon_0. Our proof also applies to concatenation of higher-distance codes, and to noise models that allow faults to be correlated in space and in time. The proof uses new criteria for assessing the accuracy of fault-tolerant circuits, which are particularly conducive to the inductive analysis of recursive simulations. Our lower bound on the threshold, epsilon_0 > 2.73 \times 10^{-5} for an adversarial independent stochastic noise model, is derived from a computer-assisted combinatorial analysis; it is the best lower bound that has been rigorously proven so far.