Proposals for 3D self-correcting quantum memory

TL;DR

This paper proposes two new 3D self-correcting quantum memory constructions, extending existing codes and exploring fractal-based designs, addressing a key open question in quantum error correction.

Contribution

It introduces two novel 3D quantum memory models, expanding the possibilities for passive error correction in quantum computing.

Findings

First construction extends Haah's code with translation invariance

Second construction uses fractals for flexible design

Existing 3D codes are likely not self-correcting

Abstract

A self-correcting quantum memory is a type of quantum error correcting code that can correct errors passively through cooling. A major open question in the field is whether self-correcting quantum memories can exist in 3D. In this work, we propose two candidate constructions for 3D self-correcting quantum memories. The first construction is an extension of Haah's code, which retains translation invariance. The second construction is based on fractals with greater flexibility in its design. Additionally, we review existing 3D quantum codes and suggest that they are not self-correcting.