Advantages of versatile neural-network decoding for topological codes

Maskara, Nishad; Kubica, Aleksander; Jochym-O’Connor, Tomas

doi:10.1103/physreva.99.052351

Cited by 64 publications

(55 citation statements)

References 82 publications

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“…Thus, one should not expect the inferior error-correction performance of the color code. Indeed, this was confirmed with color code decoders matching the performance of the toric code decoders [29][30][31] assuming perfect syndrome measurement circuits.…”

Section: Introductionmentioning

confidence: 77%

Triangular color codes on trivalent graphs with flag qubits

Chamberland¹,

Kubica

Yoder³

et al. 2020

New J. Phys.

Self Cite

102

107

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The color code is a topological quantum error-correcting code supporting a variety of valuable faulttolerant logical gates. Its two-dimensional version, the triangular color code, may soon be realized with currently available superconducting hardware despite constrained qubit connectivity. To guide this experimental effort, we study the storage threshold of the triangular color code against circuitlevel depolarizing noise. First, we adapt the Restriction Decoder to the setting of the triangular color code and to phenomenological noise. Then, we propose a fault-tolerant implementation of the stabilizer measurement circuits, which incorporates flag qubits. We show how information from flag qubits can be used in an efficient and scalable way with the Restriction Decoder to maintain the effective distance of the code. We numerically estimate the threshold of the triangular color code to be 0.2%, which is competitive with the thresholds of other topological quantum codes. We also prove that 1-flag stabilizer measurement circuits are sufficient to preserve the full code distance, which may be used to find simpler syndrome extraction circuits of the color code. OPEN ACCESS RECEIVED

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Section: Introductionmentioning

confidence: 77%

Triangular color codes on trivalent graphs with flag qubits

Chamberland¹,

Kubica

Yoder³

et al. 2020

New J. Phys.

Self Cite

102

107

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“…Independently of our investigation, three recent works have shown how a neural network can be applied to color code decoding. References [42] and [44] only consider single rounds of error correction, and cannot be extended to a multi-round experiment or circuit-level noise. References [43] uses the Steane and Knill error correction schemes when considering color codes, which are also fault-tolerant against circuit-level noise, but have larger physical qubit requirements than flag error correction.…”

Section: Resultsmentioning

confidence: 99%

“…This job can be split into a computationally easy task of determining a unitary that maps     ( ) s t L (a so called 'pure error' [47]), and a computationally difficult task of determining a logical operation within  L to undo any unwanted logical errors. The former task (known as 'excitation removal' [44]) can be performed by a 'simple decoder' [38]. The latter task is reduced, within the stabilizer formalism, to determining at most two parity bits per logical qubit, which is equivalent to determining the logical parity of the qubit upon measurement at time t [39].…”

Section: Description Of the Problem 21 Color Codementioning

confidence: 99%

“…No a priori knowledge of the error model is required. Machine learning approaches have been previously shown to be successful for the families of surface and toric codes [37][38][39][40][41], and applications to color codes are now being investigated [42][43][44]. We adapt the recurrent neural network of [39] to decode color codes with distances up to 7, fully incorporating the information from flag qubits.…”

Section: Introductionmentioning

confidence: 99%

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Neural network decoder for topological color codes with circuit level noise

et al. 2019

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A quantum computer needs the assistance of a classical algorithm to detect and identify errors that affect encoded quantum information. At this interface of classical and quantum computing the technique of machine learning has appeared as a way to tailor such an algorithm to the specific error processes of an experiment-without the need for a priori knowledge of the error model. Here, we apply this technique to topological color codes. We demonstrate that a recurrent neural network with long short-term memory cells can be trained to reduce the error rate ò L of the encoded logical qubit to values much below the error rate ò phys of the physical qubits-fitting the expected power law scaling   µ + ( ) d L phys 1 2 , with d the code distance. The neural network incorporates the information from 'flag qubits' to avoid reduction in the effective code distance caused by the circuit. As a test, we apply the neural network decoder to a density-matrix based simulation of a superconducting quantum computer, demonstrating that the logical qubit has a longer life-time than the constituting physical qubits with near-term experimental parameters.

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“…Torlai and Melko were the first to propose a decoder for surface codes based on neural networks [6]. Since then, many other researchers have applied neural networks to study a variety of problems in the context of decoding [6][7][8][9][10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Neural Decoder for Topological Codes using Pseudo-Inverse of Parity Check Matrix

Chinni¹,

Kulkami

MPai

et al. 2019

2019 IEEE Information Theory Workshop (ITW)

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Recent developments in the field of deep learning have motivated many researchers to apply these methods to problems in quantum information. Torlai and Melko first proposed a decoder for surface codes based on neural networks. Since then, many other researchers have applied neural networks to study a variety of problems in the context of decoding. An important development in this regard was due to Varsamopoulos et al. who proposed a two-step decoder using neural networks. Subsequent work of Maskara et al. used the same concept for decoding for various noise models. We propose a similar two-step neural decoder using inverse parity-check matrix for topological color codes. We show that it outperforms the state-of-the-art performance of non-neural decoders for independent Pauli errors noise model on a 2D hexagonal color code. Our final decoder is independent of the noise model and achieves a threshold of 10%. Our result is comparable to the recent work on neural decoder for quantum error correction by Maskara et al.. It appears that our decoder has significant advantages with respect to training cost and complexity of the network for higher lengths when compared to that of Maskara et al.. Our proposed method can also be extended to arbitrary dimension and other stabilizer codes.

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Advantages of versatile neural-network decoding for topological codes

Cited by 64 publications

References 82 publications

Triangular color codes on trivalent graphs with flag qubits

Triangular color codes on trivalent graphs with flag qubits

Neural network decoder for topological color codes with circuit level noise

Neural Decoder for Topological Codes using Pseudo-Inverse of Parity Check Matrix

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