Fault-tolerant quantum computation with asymmetric Bacon-Shor codes

TL;DR

This paper introduces a fault-tolerant quantum computing scheme using asymmetric Bacon-Shor codes optimized for noise biased towards dephasing, with detailed analysis of error rates and resource overhead.

Contribution

It presents a novel fault-tolerance scheme tailored for biased noise environments, optimizing code parameters and demonstrating compatibility with local 2D hardware.

Findings

Optimal code size depends on noise bias and strength.

Logical error rates are minimized with the proposed scheme.

Resource overhead is quantified for different noise conditions.

Abstract

We develop a scheme for fault-tolerant quantum computation based on asymmetric Bacon-Shor codes, which works effectively against highly biased noise dominated by dephasing. We find the optimal Bacon-Shor block size as a function of the noise strength and the noise bias, and estimate the logical error rate and overhead cost achieved by this optimal code. Our fault-tolerant gadgets, based on gate teleportation, are well suited for hardware platforms with geometrically local gates in two dimensions.