The XZZX surface code

Ataides, J. Bonilla; Tuckett, David K.; Bartlett, Stephen D.; Flammia, Steven T.; Brown, Benjamin J.

doi:10.21203/rs.3.rs-90087/v1

Cited by 17 publications

(33 citation statements)

References 6 publications

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“…Intuitively, this makes decoding the XZZX cluster state easier in the presence of biased noise. This effective reduction in dimensionality of the matching graph in the case biased noise has previously been noted [46] as a mechanism for increased thresholds in the tailored [26] and XZZX [28] surface codes.…”

Section: B Building the Bias-preserving Xzzx Cluster Statesupporting

confidence: 61%

“…This method of creating fault-tolerant cluster states can also be used to generate cluster states that realize the tailored [25][26][27] or XZZX [28] surface codes (Fig. 1b).…”

Section: A the Standard Fault-tolerant Cluster Statementioning

confidence: 99%

“…In circuit model quantum computing, there has recently been intense interest in developing error-correcting codes for qubits with biased noise; an example of biased noise is a scenario in which the errors which can cause bit-flips are far less likely than those which cause only phase-flips [25][26][27][28][29][30]. By modifying the stabilizers of the surface code [31] by local Pauli frame change, one can generate the tailored [25][26][27] or XZZX [28] surface codes (see Fig. 1) as well as other Clifford-deformed surface codes [32], all of which have much higher thresholds than the standard surface code in the presence of biased noise [25?…”

Section: Introductionmentioning

confidence: 99%

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Tailored cluster states with high threshold under biased noise

Claes¹,

Bourassa²,

Puri³

2022

Preprint

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Fault-tolerant cluster states form the basis for scalable measurement-based quantum computation. Recently, new stabilizer codes for scalable circuit-based quantum computation have been introduced that have very high thresholds under biased noise where the qubit predominantly suffers from one type of error, e.g. dephasing. However, extending these advances in stabilizer codes to generate high-threshold cluster states for biased noise has been a challenge, as the standard method for foliating stabilizer codes to generate fault-tolerant cluster states does not preserve the noise bias. In this work, we overcome this barrier by introducing a generalization of the cluster state that allows us to foliate stabilizer codes in a bias-preserving way. As an example of our approach, we construct a foliated version of the XZZX code which we call the XZZX cluster state. We demonstrate that under a circuit-level noise model, our XZZX cluster state has a threshold more than double the usual cluster state when dephasing errors are more likely than errors which cause bit flips by a factor of O(100) or more.

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Section: B Building the Bias-preserving Xzzx Cluster Statesupporting

confidence: 61%

“…This method of creating fault-tolerant cluster states can also be used to generate cluster states that realize the tailored [25][26][27] or XZZX [28] surface codes (Fig. 1b).…”

Section: A the Standard Fault-tolerant Cluster Statementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Tailored cluster states with high threshold under biased noise

Claes¹,

Bourassa²,

Puri³

2022

Preprint

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“…Beyond surface codes, it would be interesting to explore these soft decoders with other codes such as color codes [47], other surface code variants [48] and some quantum Low-Density Parity-Check codes [49].…”

Section: Discussionmentioning

confidence: 99%

Improved quantum error correction using soft information

Pattison,

Beverland,

da Silva

et al. 2021

Preprint

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The typical model for measurement noise in quantum error correction is to randomly flip the binary measurement outcome. In experiments, measurements yield much richer information-e.g., continuous current values, discrete photon counts-which is then mapped into binary outcomes by discarding some of this information. In this work, we consider methods to incorporate all of this richer information, typically called soft information, into the decoding of quantum error correction codes, and in particular the surface code. We describe how to modify both the Minimum Weight Perfect Matching and Union-Find decoders to leverage soft information, and demonstrate these soft decoders outperform the standard (hard) decoders that can only access the binary measurement outcomes. Moreover, we observe that the soft decoder achieves a threshold 25% higher than any hard decoder for phenomenological noise with Gaussian soft measurement outcomes. We also introduce a soft measurement error model with amplitude damping, in which measurement time leads to a trade-off between measurement resolution and additional disturbance of the qubits. Under this model we observe that the performance of the surface code is very sensitive to the choice of the measurement time-for a distance-19 surface code, a five-fold increase in measurement time can lead to a thousand-fold increase in logical error rate. Moreover, the measurement time that minimizes the physical error rate is distinct from the one that minimizes the logical performance, pointing to the benefits of jointly optimizing the physical and quantum error correction layers.

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“…The design and selection of an error correction strategy for a particular platform requires accurate prediction of its expected logical performance. For instance, in the presence of biased noise [1][2][3][4][5][6], tailored codes have been shown to outperform traditional codes that are designed to correct unstructured noise. However, bias is only one of the exponentially many parameters that describe the noise on n physical qubits.…”

mentioning

confidence: 99%

Efficient diagnostics for quantum error correction

Iyer¹,

Jain²,

Bartlett³

et al. 2021

Preprint

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Fault-tolerant quantum computing will require accurate estimates of the resource overhead, but standard metrics such as gate fidelity and diamond distance have been shown to be poor predictors of logical performance. We present a scalable experimental approach based on Pauli error reconstruction to predict the performance of concatenated codes. Numerical evidence demonstrates that our method significantly outperforms predictions based on standard error metrics for various error models, even with limited data. We illustrate how this method assists in the selection of error correction schemes.

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The XZZX surface code

Cited by 17 publications

References 6 publications

Tailored cluster states with high threshold under biased noise

Tailored cluster states with high threshold under biased noise

Improved quantum error correction using soft information

Efficient diagnostics for quantum error correction

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