Determination of the semion code threshold using neural decoders

Varona, Santiago; Martín-Delgado, M. A.

doi:10.1103/physreva.102.032411

“…A first step in this direction has been taken in Ref. [32] using a neural network decoder for their semion code. Although they did not find substantial evidence of increased performance compared to the toric code, it is far from clear whether there does not exist a better decoder tailored to the exotic string operators and what can be achieved with Stabilizer codes implementing other topological orders -like the twisted color code introduced in Sec.…”

Section: Discussionmentioning

confidence: 99%

Non-Pauli topological stabilizer codes from twisted quantum doubles

Fuente

¹

,

Tarantino

²

,

Eisert

³

2021

Quantum

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It has long been known that long-ranged entangled topological phases can be exploited to protect quantum information against unwanted local errors. Indeed, conditions for intrinsic topological order are reminiscent of criteria for faithful quantum error correction. At the same time, the promise of using general topological orders for practical error correction remains largely unfulfilled to date. In this work, we significantly contribute to establishing such a connection by showing that Abelian twisted quantum double models can be used for quantum error correction. By exploiting the group cohomological data sitting at the heart of these lattice models, we transmute the terms of these Hamiltonians into full-rank, pairwise commuting operators, defining commuting stabilizers. The resulting codes are defined by non-Pauli commuting stabilizers, with local systems that can either be qubits or higher dimensional quantum systems. Thus, this work establishes a new connection between condensed matter physics and quantum information theory, and constructs tools to systematically devise new topological quantum error correcting codes beyond toric or surface code models.

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“…which can get c(Z P ) [35]. For logical quantum state | G E 〉, suppose G is represented as a logical subspace, g is represented as an eigenvalue, and the eigenvalue is divided into +1 and −1, +1 represents a vertex operator, and −1 represents a plaquette operator, when X b acts on the logical quantum state | G E 〉:…”

Section: Detect and Correct Errorsmentioning

confidence: 99%

Quantum Teleportation Error Suppression Algorithm Based on Convolutional Neural Networks and Quantum Topological Semion Codes

Cao

¹

,

Wang

²

,

Qu

³

et al. 2022

Quantum Engineering

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Quantum error correction (QEC) is a key technique for building scalable quantum computers that can be used to mitigate the effects of errors on physical quantum bits. Since quantum states are more or less affected by noise, errors are inevitable. Traditional QEC codes face huge challenges. Therefore, designing an error suppression algorithm based on neural networks (NN) and quantum topological error correction (QTEC) codes is particularly important for quantum teleportation. In this paper, QTEC codes: semion codes—a greater than 2 dimensional (2D) error correction code based on the double semion model—are used to suppress errors during quantum teleportation, using a NN to build a decoder based on semion codes and to simulate the quantum information error suppression process and the suppression effect. The proposed convolutional neural network (CNN) decoder is suitable for small distance topological semion codes. The aim is to optimize the NN for better decoder performance while deriving the relationship between decoder performance and slope and pseudothreshold during training and calculate the thresholds for different noise areas when the code distances are the same, P t h r e s h o l d = 0.082 for A r e a < 0.007 d B and P t h r e s h o l d = 0.096 for A r e a < 0.01 d B . This paper demonstrates the ability of CNNs to suppress errors in quantum transmission information and the great potential of NNs in the field of quantum computing.

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“…When the physical error rate of the logical qubit is better than that of the physical qubit, it is called the pseudo-threshold. We encode the physical qubits with different code distances into logical qubits and obtain the decoding threshold by suppressing the logical error rates [6]. We need to infinitely approach the pseudo-threshold to the decoding threshold to achieve the best fault-tolerant effect.…”

Section: Introductionmentioning

confidence: 99%

Quantum Information Protection Scheme Based on Reinforcement Learning for Periodic Surface Codes

Xue

¹

,

Wang

²

,

Tian

³

et al. 2022

Quantum Engineering

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Quantum information transfer is an information processing technology with high speed and high entanglement with the help of quantum mechanics principles. To solve the problem of quantum information getting easily lost during transmission, we choose topological quantum error correction codes as the best candidate codes to improve the fidelity of quantum information. The stability of topological error correction codes brings great convenience to error correction. The quantum error correction codes represented by surface codes have produced very good effects in the error correction mechanism. In order to solve the problem of strong spatial correlation and optimal decoding of surface codes, we introduced a reinforcement learning decoder that can effectively characterize the spatial correlation of error correction codes. At the same time, we use a double-layer convolutional neural network model in the confrontation network to find a better error correction chain, and the generation network can approach the best correction model, to ensure that the discriminant network corrects more nontrivial errors. To improve the efficiency of error correction, we introduced a double-Q algorithm and ResNet network to increase the error correction success rate and training speed of the surface code. Compared with the previous MWPM 0.005 decoder threshold, the success rate has slightly improved, which can reach up to 0.0068 decoder threshold. By using the residual neural network architecture, we saved one-third of the training time and increased the training accuracy to about 96.6%. Using a better training model, we have successfully increased the decoder threshold from 0.0068 to 0.0085, and the depolarized noise model being used does not require a priori basic noise, so that the error correction efficiency of the entire model has slightly improved. Finally, the fidelity of the quantum information has successfully improved from 0.2423 to 0.7423 by using the error correction protection schemes.

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Determination of the semion code threshold using neural decoders

Cited by 15 publications

References 49 publications

Non-Pauli topological stabilizer codes from twisted quantum doubles

Non-Pauli topological stabilizer codes from twisted quantum doubles

Quantum Teleportation Error Suppression Algorithm Based on Convolutional Neural Networks and Quantum Topological Semion Codes

Quantum Information Protection Scheme Based on Reinforcement Learning for Periodic Surface Codes

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