Cellular automaton decoders of topological quantum memories in the fault tolerant setting

TL;DR

This paper introduces a cellular automaton-based passive error decoder for topological quantum memories, demonstrating significantly extended qubit survival times through local dissipative processes in a fault-tolerant setting.

Contribution

It proposes a novel discrete-time cellular automaton decoder for passive error correction in topological quantum codes, with numerical evidence of improved qubit lifetime.

Findings

Logical qubit survival time extended by orders of magnitude

Cellular automaton decoding acts as a fully dissipative quantum memory

Resource analysis shows polylogarithmic overhead

Abstract

Active error decoding and correction of topological quantum codes - in particular the toric code - remains one of the most viable routes to large scale quantum information processing. In contrast, passive error correction relies on the natural physical dynamics of a system to protect encoded quantum information. However, the search is ongoing for a completely satisfactory passive scheme applicable to locally-interacting two-dimensional systems. Here, we investigate dynamical decoders that provide passive error correction by embedding the decoding process into local dynamics. We propose a specific discrete time cellular-automaton decoder in the fault tolerant setting and provide numerical evidence showing that the logical qubit has a survival time extended by several orders of magnitude over that of a bare unencoded qubit. We stress that (asynchronous) dynamical decoding gives rise to a Markovian dissipative process. We hence equate cellular-automaton decoding to a fully dissipative topological quantum memory, which removes errors continuously. In this sense, uncontrolled and unwanted local noise can be corrected for by a controlled local dissipative process. We analyze the required resources, commenting on additional polylogarithmic factors beyond those incurred by an ideal constant resource dynamical decoder.