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

• Published in: New journal of physics Vol. 19; no. 6; pp. 63012 - 63021
• Main Authors: Herold, Michael, Kastoryano, Michael J, Campbell, Earl T, Eisert, Jens
• Format: Journal Article
• Language: English
• Published: Bristol IOP Publishing 01.06.2017
• Subjects: Cellular automata; Data processing; Decoders; Decoding; dissipative dynamics; Error correction; Error correction & detection; Fault tolerance; Liouvillians; Physics; quantum error correction; quantum memory; Quantum phenomena; Qubits (quantum computing); topological order; Topology
• ISSN: 1367-2630; 1367-2630
• DOI: 10.1088/1367-2630/aa7099

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.