PyMatching: A Python Package for Decoding Quantum Codes with Minimum-Weight Perfect Matching

Higgott, Oscar

doi:10.1145/3505637

Cited by 58 publications

(37 citation statements)

References 31 publications

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“…Additionally, for decoding, we have used the PyMatching library [43], which implements the MWPM algorithm [27] to calculate the data qubits that need correction from a provided error syndrome.…”

Section: Resultsmentioning

confidence: 99%

Surface code design for asymmetric error channels

Azad

Lipińska

Shilpa

et al. 2022

IET Quantum Communication

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Surface codes are quantum error correcting codes typically defined on a 2D array of qubits. A [dx, dz] surface code design is being introduced, where dx(dz) represents the distance of the code for bit (phase) error correction, motivated by the fact that the severity of bit flip and phase flip errors in the physical quantum system is asymmetric. We present pseudo‐threshold and threshold values for the proposed surface code design for asymmetric error channels in the presence of various degrees of asymmetry of PauliX^,trueY^ $\text{Pauli}\,\hat{X},\,\hat{Y}$, andZ^ $\text{and}\,\hat{Z}$ errors in a depolarisation channel. We demonstrate that compared to symmetric surface codes, our asymmetric surface codes can provide almost double the pseudo‐threshold rates while requiring less than half the number of physical qubits in the presence of increasing asymmetry in the error channel. Our results show that for low degree of asymmetry, it is advantageous to increase dx along with dz. However, as the asymmetry of the channel increases, higher pseudo‐threshold is obtained with increasing dz when dx is kept constant at a low value. Additionally, we also show that the advantage in the pseudo‐threshold rates begins to saturate for any possible degree of asymmetry in the error channel as the surface code asymmetry is continued to be increased.

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Section: Resultsmentioning

confidence: 99%

Surface code design for asymmetric error channels

Azad

Lipińska

Shilpa

et al. 2022

IET Quantum Communication

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“…On the other hand, one could also bring ideas from UF decoders into the blossom algorithm to improve the latter's speed. For example, we have recently shown that instead of the syndrome graph, MWPM decoders can be made faster [22] by adopting the decoding graph used by UF decoders, which has also been indepen-dently discovered by Higgott and Gidney [23]. two error patterns, E 1 and E 2 , we define their sum as…”

Section: Discussionmentioning

confidence: 99%

An interpretation of Union-Find Decoder on Weighted Graphs

Wu¹,

Liyanage²,

Lin³

2022

Preprint

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Union-Find (UF) and Minimum-Weight Perfect Matching (MWPM) are popular decoder designs for surface codes. The former has significantly lower time complexity than the latter but is considered somewhat inferior, in terms of decoding accuracy. In this work we present an interpretation of UF decoders that explains why UF and MWPM decoders perform closely in some cases: the UF decoder is an approximate implementation of the blossom algorithm used for MWPM. This interpretation allows a generalization of UF decoders for weighted decoding graphs and explains why UF decoders achieve high accuracy for certain surface codes.

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“…In the current paper we use a slightly modified lookup table decoder that is foolproof and fast. The proposed code is not a Calderbank-Shor-Steane code [8,11], thus we cannot analyze X and Z errors separately and use common minimum-weight perfect matching decoding algorithm [35,36]. However, there are other alternative promising decoding methods, that for example use neural network approach [30,37] or approximate matrix product state simulations [38], but they are usually time and memory consuming.…”

Section: Discussionmentioning

confidence: 99%

Scalable quantum error correction code on a ring topology of qubits

Simakov¹,

Besedin²

2022

Preprint

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Quantum error correction is an important ingredient for scalable quantum computing. Stabilizer codes are one of the most promising and straightforward ways to correct quantum errors, since they do not require excessive complexity of physical qubits, are convenient for logical operations, and improve performance with increasing the involved qubits number. Here, we propose a linear scalable code of the permutative stabilizers for small distances on the ring architecture, which takes into account the topological features of the superconducting platform. We present the way to construct the quantum circuit of the code and provide numerical simulation that demonstrate the exponential logical error rate suppression.

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PyMatching: A Python Package for Decoding Quantum Codes with Minimum-Weight Perfect Matching

Cited by 58 publications

References 31 publications

Surface code design for asymmetric error channels

Surface code design for asymmetric error channels

An interpretation of Union-Find Decoder on Weighted Graphs

Scalable quantum error correction code on a ring topology of qubits

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