Cellular automaton decoders of topological quantum memories in the fault tolerant setting
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 inf...
Saved in:
Published in | New journal of physics Vol. 19; no. 6; pp. 63012 - 63021 |
---|---|
Main Authors | , , , |
Format | Journal Article |
Language | English |
Published |
Bristol
IOP Publishing
01.06.2017
|
Subjects | |
Online Access | Get full text |
Cover
Loading…
Summary: | 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. |
---|---|
Bibliography: | NJP-106374.R1 |
ISSN: | 1367-2630 1367-2630 |
DOI: | 10.1088/1367-2630/aa7099 |