Quantum error correction in a time-dependent transverse field Ising model

TL;DR

This paper introduces a quantum error correction code based on a time-dependent transverse field Ising model, which can be implemented with local operations and protects against multiple error types, demonstrated with ultracold Rydberg atoms.

Contribution

It presents a novel quantum error correcting code using a time-dependent Ising model that is implementable with finite-depth local circuits and protects against both X and Z errors.

Findings

Code can be implemented with 10 ultracold Rydberg atoms.

Finite-depth local unitary circuit realization.

Protection against both X and Z errors for even N ≥ 10.

Abstract

We describe a simple quantum error correcting code built out of a time-dependent transverse field Ising model. The code is similar to a repetition code, but has two advantages: an $N$-qubit code can be implemented with a finite-depth spatially local unitary circuit, and it can subsequently protect against both $X$ and $Z$ errors if $N\ge 10$ is even. We propose an implementation of this code with 10 ultracold Rydberg atoms in optical tweezers, along with further generalizations of the code.