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

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.