Tailoring surface codes: Improvements in quantum error correction with biased noise

Tuckett, David K.

doi:10.25910/x8xw-9077

Cited by 9 publications

(7 citation statements)

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“…For larger bias, α = 5, we find good correspondence with the results using the MPS decoder as implemented in Ref. [66,76], with a threshold near p ≈ 30 %, as shown in Fig. 3(a).…”

Section: A Test Casessupporting

confidence: 80%

“…Here we also see that using only the most likely chains in The solid curves show the results for the EWD decoder. The dashed curves are obtained using the MPS decoder as implemented in [76]. The vertical blue line indicates the threshold at 30.5 %.…”

Section: B a Specific Syndrome Example 1 Integer Weightsmentioning

confidence: 99%

“…The software for running the EWD and MCMC decoders is available on the repository [80], while the implementation of the MPS decoder used in this work is available from Ref. [76].…”

Section: Acknowledgmentsmentioning

confidence: 99%

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Error-rate-agnostic decoding of topological stabilizer codes

Hammar,

Orekhov,

Hybelius

et al. 2021

Preprint

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Efficient high-performance decoding of topological stabilizer codes has the potential to crucially improve the balance between logical failure rates and the number and individual error rates of the constituent qubits. High-threshold maximum-likelihood decoders require an explicit error model for Pauli errors to decode a specific syndrome, whereas lower-threshold heuristic approaches such as minimum weight matching are "error agnostic". Here we consider an intermediate approach, formulating a decoder that depends on the bias, i.e., the relative probability of phase-flip to bit-flip errors, but is agnostic to error rate. Our decoder is based on counting the number and effective weight of the most likely error chains in each equivalence class of a given syndrome. We use Metropolisbased Monte Carlo sampling to explore the space of error chains and find unique chains, which can be run efficiently by exploiting the error-rate invariance and without the need for "thermalization" between chains in different equivalence classes. Applied to the surface code and the XZZX code, the decoder matches maximum-likelihood decoders for moderate code sizes or low error rates. We anticipate that, because of the compressed information content per syndrome, it can be taken full advantage of in combination with machine-learning methods to extrapolate Monte Carlo-generated data.

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“…For larger bias, α = 5, we find good correspondence with the results using the MPS decoder as implemented in Ref. [66,76], with a threshold near p ≈ 30 %, as shown in Fig. 3(a).…”

Section: A Test Casessupporting

confidence: 80%

Section: B a Specific Syndrome Example 1 Integer Weightsmentioning

confidence: 99%

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Error-rate-agnostic decoding of topological stabilizer codes

Hammar,

Orekhov,

Hybelius

et al. 2021

Preprint

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show abstract

“…For the XZZX code, we use the matrix-product-state (MPS) decoder as implemented in Ref. [63]. As shown in [62], the two methods give almost identical results for the XZZX code for moderate code distances.…”

Section: Methodsmentioning

confidence: 99%

The XYZ$^2$ hexagonal stabilizer code

Srivastava,

Kockum,

Granath

2021

Preprint

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We consider a topological stabilizer code on a honeycomb grid, the "XYZ 2 " code. The code is inspired by the Kitaev honeycomb model and is a simple realization of a "matching code" discussed by Wootton [1], with a specific implementation of the boundary. It utilizes weight-six (XY ZXY Z) plaquette stabilizers and weight-two (XX) link stabilizers on a planar hexagonal grid composed of 2d 2 qubits for code distance d, with weight-three stabilizers at the boundary, stabilizing one logical qubit. We study the properties of the code using maximum-likelihood decoding, assuming perfect stabilizer measurements. For pure X, Y , or Z noise, we can solve for the logical failure rate analytically, giving a threshold of 50 %. In contrast to the rotated surface code and the XZZX code, which have code distance d 2 only for pure Y noise, here the code distance is 2d 2 for both pure Z and pure Y noise. Thresholds for noise with finite Z bias are similar to the XZZX code, but with markedly lower sub-threshold logical failure rates. The code possesses distinctive syndrome properties with unidirectional pairs of plaquette defects along the three directions of the triangular lattice for isolated errors, which may be useful for efficient matching-based or other approximate decoding.

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“…AD thanks Eric Huang for sharing his plotting routines. The tensor network decoder for the random CDSCs was implemented via an appropriate adaptation of qecsim [33] (a Python3 package for simulating quantum error correction using stabilizer codes) and simulations were run on the NIST Raritan cluster. The simulation code and data are available on request.…”

Section: (B)mentioning

confidence: 99%

Clifford-deformed Surface Codes

Dua¹,

Kubica²,

Jiang³

et al. 2022

Preprint

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Various realizations of Kitaev's surface code perform surprisingly well for biased Pauli noise. Attracted by these potential gains, we study the performance of Clifford-deformed surface codes (CDSCs) obtained from the surface code by the application of single-qubit Clifford operators. We first analyze CDSCs on the 3 × 3 square lattice and find that depending on the noise bias, their logical error rates can differ by orders of magnitude. To explain the observed behavior, we introduce the effective distance d , which reduces to the standard distance for unbiased noise. To study CDSC performance in the thermodynamic limit, we focus on random CDSCs. Using the statistical mechanical mapping for quantum codes, we uncover a phase diagram that describes random CDSCs with 50% threshold at infinite bias. In the high-threshold region, we further demonstrate that typical code realizations at finite bias outperform the thresholds and subthreshold logical error rates of the best known translationally invariant codes.

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Tailoring surface codes: Improvements in quantum error correction with biased noise

Cited by 9 publications

References 0 publications

Error-rate-agnostic decoding of topological stabilizer codes

Error-rate-agnostic decoding of topological stabilizer codes

The XYZ$^2$ hexagonal stabilizer code

Clifford-deformed Surface Codes

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