Low-valency scalable quantum error correction with a dynamic compass code

TL;DR

The paper introduces the dynamic compass code, a practical quantum error-correcting code with a threshold, optimized measurement schedules, and potential for fault-tolerant quantum computation on the heavy-hex lattice.

Contribution

It presents a novel measurement schedule for the heavy-hex subsystem code, enabling a scalable, low-valency quantum error correction with demonstrated thresholds and fault-tolerance features.

Findings

The dynamic compass code demonstrates a threshold for stability.

Different measurement schedules trade off protection in X vs Z basis.

Lattice surgery is feasible between code patches.

Abstract

The ongoing development of hardware that is capable of reliably executing general quantum algorithms requires quantum error-correcting codes that are both practical for realisation and rapidly reduce logical error rates as they are scaled up. Here we introduce the dynamic compass code, a code that can be implemented with a modest footprint on the heavy-hex lattice while also demonstrating a threshold. The dynamic code is obtained by choosing a novel measurement schedule for the syndrome extraction circuit of the heavy-hex subsystem code. We numerically evaluate its performance and observe that different choices of schedule can provide a trade-off in protection against logical errors in the $X$ vs $Z$ basis. We also demonstrate that this new measurement schedule provides the code with a threshold for stability experiments. We finally show how the dynamic compass code could be used for fault-tolerant logic by illustrating lattice surgery between code patches.