Cellular-automaton decoders for topological quantum memories

TL;DR

This paper proposes a novel cellular automaton-based framework for topological quantum memories, enabling error correction through local, simple rules inspired by classical field theories, achieving thresholds above 6%.

Contribution

It introduces a new cellular automaton approach for quantum error correction that does not rely on complex algorithms or global operations.

Findings

Error correction threshold above 6.1% for 3D automaton with 2D toric code

Threshold above 8.2% with a more complex 2D automaton

Framework offers a passive, dissipative quantum memory solution

Abstract

We introduce a new framework for constructing topological quantum memories, by recasting error recovery as a dynamical process on a field generating cellular automaton. We envisage quantum systems controlled by a classical hardware composed of small local memories, communicating with neighbours, and repeatedly performing identical simple update rules. This approach does not require any global operations or complex decoding algorithms. Our cellular automata draw inspiration from classical field theories, with a Coulomb-like potential naturally emerging from the local dynamics. For a 3D automaton coupled to a 2D toric code, we present evidence of an error correction threshold above 6.1% for uncorrelated noise. A 2D automaton equipped with a more complex update rule yields a threshold above 8.2%. Our framework provides decisive new tools in the quest for realising a passive dissipative quantum memory.