Efficient Markov chain Monte Carlo algorithm for the surface code

Hutter, Adrian; Wootton, James R.; Loss, Daniel

doi:10.1103/physreva.89.022326

Cited by 72 publications

(72 citation statements)

References 32 publications

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“…Given reliable snapshots of error syndromes, decoding algorithms can be independently applied to each time slice [12]. Decoders exist using notions of minimum-weight perfect matching [13,14], renormalization [15,16], and simulated annealing [17,18], which is highly problematic for 2D architectures, where on chip wiring becomes cumbersome beyond nine physical qubits. However, parallelized decoding is also possible with cellular-automaton decoders that locally store syndrome information, communicating with only nearest neighbors.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2017

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Active error decoding and correction of topological quantum codes-in particular the toric coderemains 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.

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Section: Introductionmentioning

confidence: 99%

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

et al. 2017

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“…The toric code [16] is among the most extensively studied of this family of codes, revealing much insight into related topologically ordered systems. A great deal of work has concentrated on calculating thresholds for various error models [17][18][19], and on the discovery and implementation of new classical decoding algorithms [19][20][21][22][23][24][25]. The toric code performs well, with high thresholds for some commonly studied noise models.…”

Section: Introductionmentioning

confidence: 99%

Logical error rate scaling of the toric code

Watson

Barrett

2014

New J. Phys.

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To date, a great deal of attention has focused on characterizing the performance of quantum error correcting codes via their thresholds, the maximum correctable physical error rate for a given noise model and decoding strategy. Practical quantum computers will necessarily operate below these thresholds meaning that other performance indicators become important. In this work we consider the scaling of the logical error rate of the toric code and demonstrate how, in turn, this may be used to calculate a key performance indicator. We use a perfect matching decoding algorithm to find the scaling of the logical error rate and find two distinct operating regimes. The first regime admits a universal scaling analysis due to a mapping to a statistical physics model. The second regime characterizes the behaviour in the limit of small physical error rate and can be understood by counting the error configurations leading to the failure of the decoder. We present a conjecture for the ranges of validity of these two regimes and use them to quantify the overhead-the total number of physical qubits required to perform error correction.

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“…Nevertheless, the main disadvantage of the MWPMA is that it is not suitable for qudit surface codes with d > 2. For these reasons, the development of alternative decoding algorithms is currently a very active research area [14,15,[22][23][24][25][26][27].…”

Section: Overviewmentioning

confidence: 99%

Fast fault-tolerant decoder for qubit and qudit surface codes

2015

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The surface code is one of the most promising candidates for combating errors in large scale fault-tolerant quantum computation. A fault-tolerant decoder is a vital part of the error correction process-it is the algorithm which computes the operations needed to correct or compensate for the errors according to the measured syndrome, even when the measurement itself is error prone. Previously decoders based on minimum-weight perfect matching have been studied. However, these are not immediately generalizable from qubit to qudit codes. In this work, we develop a fault-tolerant decoder for the surface code, capable of efficient operation for qubits and qudits of any dimension, generalizing the decoder first introduced by Bravyi and Haah [Phys. Rev. Lett. 111, 200501 (2013)]. We study its performance when both the physical qudits and the syndromes measurements are subject to generalized uncorrelated bit-flip noise (and the higher-dimensional equivalent). We show that, with appropriate enhancements to the decoder and a high enough qudit dimension, a threshold at an error rate of more than 8% can be achieved. I. OVERVIEWTopological quantum codes built from qubits [twodimensional (2D) quantum systems] play a central role in architectures for fault-tolerant quantum computing at the forefront of current research [1][2][3][4]. The surface code [5] and the related toric code [6,7] are prominent examples of such codes. Compared with other quantum error correcting codes, they posses the key experimental benefit of requiring only local interactions and yet, under realistic noise models, they have been shown to achieve the highest reported fault-tolerant thresholds [8,9].Recent developments have shown that employing ddimensional quantum systems, or qudits, as the building blocks for fault-tolerant schemes may offer some important advantages. For example, an integral part of many faulttolerant schemes is the distillation of magic states [10]-a procedure necessary to achieve universal computation-where generalization to higher dimensions has resulted in improved distillation thresholds and lower overheads in the number of qudit magic states [11][12][13]. Moreover, threshold investigations of the qudit toric code with noise-free syndrome measurements have shown that, for a standard independent noise model, the error correction threshold increases significantly with increasing qudit dimension [14][15][16], although we caution that it is difficult to fairly compare noise rates between systems of different dimensions. Although it is more challenging to realize qudit quantum systems experimentally, recent work has demonstrated the ability to coherently control and perform operations in single 16-dimensional atomic systems with high fidelity [17,18], with the implementation of high-fidelity multiqudit interactions still to be achieved.A surface code is a stabilizer code with local stabilizer generators. Qudits are associated with the edges of a 2D square lattice. In order to store the encoded information for * fern.watson10@imperial...

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Efficient Markov chain Monte Carlo algorithm for the surface code

Cited by 72 publications

References 32 publications

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

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

Logical error rate scaling of the toric code

Fast fault-tolerant decoder for qubit and qudit surface codes

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