Cellular-automaton decoders for topological quantum memories

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. A new error correction method for quantum computing memories is based on local computing elements. Michael Herold from the Freie Universität Berlin in Germany, with colleagues in Germany, Denmark and the UK, sought to address the challenge of maintaining information stored in topological quantum memories. Without a stable memory, delicate quantum states can decay quickly, introducing errors in stored information. Error correction is an important process in stabilizing topological memories, but was previously conceived as a system-wide process. The proposed practical error correction mechanism relies on parallel cellular operations within the topological quantum memory, so that the local operations replace the need for a complex system-wide scheme. The concept has the further benefit of being compatible with classical hardware, and it is easily scalable.