Neural Decoder for Topological Codes

Torlai, Giacomo; Melko, Roger G.

doi:10.1103/physrevlett.119.030501

Cited by 172 publications

(157 citation statements)

References 48 publications

(52 reference statements)

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“…This kind of restricted structure makes the neural network easier to train and therefore has been extensively investigated and used. [26,27,29,31,38,39,[56][57][58][59][60][61] The RBM can approximate every discrete probability distribution. [64,65] The BM is most notably a stochastic recurrent neural network whereas the perceptron and the logistic neural network are feedforward neural networks.…”

Section: Boltzmann Machinementioning

confidence: 99%

Quantum Neural Network States: A Brief Review of Methods and Applications

et al. 2019

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One of the main challenges of quantum many‐body physics is the exponential growth in the dimensionality of the Hilbert space with system size. This growth makes solving the Schrödinger equation of the system extremely difficult. Nonetheless, many physical systems have a simplified internal structure that typically makes the parameters needed to characterize their ground states exponentially smaller. Many numerical methods then become available to capture the physics of the system. Among modern numerical techniques, neural networks, which show great power in approximating functions and extracting features of big data, are now attracting much interest. In this work, the progress in using artificial neural networks to build quantum many‐body states is reviewed. The Boltzmann machine representation is taken as a prototypical example to illustrate various aspects of the neural network states. The classical neural networks are also briefly reviewed, and it is illustrated how to use neural networks to represent quantum states and density operators. Some physical properties of the neural network states are discussed. For applications, the progress in many‐body calculations based on neural network states, the neural network state approach to tomography, and the classical simulation of quantum computing based on Boltzmann machine states are briefly reviewed.

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Section: Boltzmann Machinementioning

confidence: 99%

Quantum Neural Network States: A Brief Review of Methods and Applications

et al. 2019

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“…However, optimal decoding for topological codes is known to be a computationally hard problem [9]. Various decoders [10][11][12][13][14] have been proposed that achieve approximately optimal error thresholds instead. Due to several constraints (e.g.…”

Section: Introductionmentioning

confidence: 99%

Neural ensemble decoding for topological quantum error-correcting codes

2020

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Topological quantum error-correcting codes are a promising candidate for building fault-tolerant quantum computers. Decoding topological codes optimally, however, is known to be a computationally hard problem. Various decoders have been proposed that achieve approximately optimal error thresholds. Due to practical constraints, it is not known if there exists an obvious choice for a decoder. In this paper, we introduce a framework which can combine arbitrary decoders for any given code to significantly reduce the logical error rates. We rely on the crucial observation that two different decoding techniques, while possibly having similar logical error rates, can perform differently on the same error syndrome. We use machine learning techniques to assign a given error syndrome to the decoder which is likely to decode it correctly. We apply our framework to an ensemble of Minimum-Weight Perfect Matching (MWPM) and Hard-Decision Re-normalization Group (HDRG) decoders for the surface code in the depolarizing noise model. Our simulations show an improvement of 38.4%, 14.6%, and 7.1% over the pseudo-threshold of MWPM in the instance of distance 5, 7, and 9 codes, respectively. Lastly, we discuss the advantages and limitations of our framework and applicability to other error-correcting codes. Our framework can provide a significant boost to error correction by combining the strengths of various decoders. In particular, it may allow for combining very fast decoders with moderate error-correcting capability to create a very fast ensemble decoder with high error-correcting capability.

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“…Quantum neural network states are currently subject to intense research and represents a new direction for efficiently calculating ground states and unitary evolutions of many-body quantum systems. These researches stimulate an explosion of results to apply machine learning methods to investigate condensed matter physics, like distinguishing phases [37], quantum control [38], error-correcting of topological codes [39], etc. The interplay between machine learning and quantum physics has given birth to a new discipline, now known as quantum machine learning.…”

Section: Introductionmentioning

confidence: 99%

Entanglement area law for shallow and deep quantum neural network states

Jia

et al. 2020

New J. Phys.

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A study of the artificial neural network representation of quantum many-body states is presented. The locality and entanglement properties of states for shallow and deep quantum neural networks are investigated in detail. By introducing the notion of local quasi-product states, for which the locally connected shallow feed-forward neural network states and restricted Boltzmann machine states are special cases, we show that Rényi entanglement entropies of all these states obey the entanglement area law. Besides, we also investigate the entanglement features of deep Boltzmann machine states and show that locality constraints imposed on the neural networks make the states obey the entanglement area law. Finally, as an application, we apply the notion of Rényi entanglement entropy to understand the power of neural networks, and show that image classification problems can be efficiently solved must obey the area law.

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Neural Decoder for Topological Codes

Cited by 172 publications

References 48 publications

Quantum Neural Network States: A Brief Review of Methods and Applications

Quantum Neural Network States: A Brief Review of Methods and Applications

Neural ensemble decoding for topological quantum error-correcting codes

Entanglement area law for shallow and deep quantum neural network states

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