A proposal for self-correcting stabilizer quantum memories in 3 dimensions (or slightly less)

TL;DR

This paper introduces a family of local CSS stabilizer codes inspired by fractal classical memories, aiming to realize self-correcting quantum memories in 3D or similar dimensions, with phase transition evidence supporting their robustness.

Contribution

It proposes new fractal-inspired 3D stabilizer codes for quantum memory with potential self-correction properties, expanding the design space beyond traditional models.

Findings

Existence of finite temperature phase transitions in the models.

Models are defined on fractal subsets of 4D lattices.

Potential for robust quantum information storage at finite temperature.

Abstract

We propose a family of local CSS stabilizer codes as possible candidates for self-correcting quantum memories in 3D. The construction is inspired by the classical Ising model on a Sierpinski carpet fractal, which acts as a classical self-correcting memory. Our models are naturally defined on fractal subsets of a 4D hypercubic lattice with Hausdorff dimension less than 3. Though this does not imply that these models can be realised with local interactions in 3D Euclidean space, we also discuss this possibility. The X and Z sectors of the code are dual to one another, and we show that there exists a finite temperature phase transition associated with each of these sectors, providing evidence that the system may robustly store quantum information at finite temperature.