Single-Shot Quantum Error Correction in Intertwined Toric Codes

TL;DR

This paper introduces the intertwined toric code, a 3D subsystem code that enables single-shot quantum error correction with a clear physical basis, simple logical operators, and a well-understood phase diagram, advancing quantum error correction methods.

Contribution

The paper presents a new 3D subsystem code called the intertwined toric code that demonstrates single-shot error correction with a physically motivated and geometrically straightforward structure.

Findings

The ITC code exhibits single-shot error correction capabilities.

The phase diagram of ITC includes phases similar to previous models.

Decoding schemes from Kubica and Vasmer are applicable to ITC.

Abstract

We construct a new subsystem code in three dimensions that exhibits single-shot error correction in a user-friendly and transparent way. As this code is a subsystem version of coupled toric codes, we call it the intertwined toric code (ITC). Although previous codes share the property of single-shot error correction, the ITC is distinguished by its physically motivated origin, geometrically straightforward logical operators and errors, and a simple phase diagram. The code arises from 3d stabilizer toric codes in a way that emphasizes the physical origin of the single-shot property. In particular, starting with two copies of the 3d toric code, we add check operators that provide for the confinement of pointlike excitations without condensing the loop excitations. Geometrically, the bare and dressed logical operators in the ITC derive from logical operators in the underlying toric codes, creating a clear relationship between errors and measurement outcomes. The syndromes of the ITC resemble the syndromes of the single-shot code by Kubica and Vasmer, allowing us to use their decoding schemes. We also extract the phase diagram corresponding to ITC and show that it contains the phases found in the Kubica-Vasmer code. Finally, we suggest various connections to Walker-Wang models and measurement-based quantum computation.