Clifford-deformed Surface Codes

Dua, Arpit; Kubica, Aleksander; Jiang, Liang; Flammia, Steven T.; Gullans, Michael

doi:10.48550/arxiv.2201.07802

Cited by 7 publications

(6 citation statements)

References 31 publications

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“…While the XZZX and subsystem surface codes both offer improved performance compared to the CSS surface code near threshold for biased circuit-level noise [9,10], a more detailed analysis will be required to assess whether this also translates into a reduced qubit overhead for a noise regime of practical interest below threshold. The CSS, XY and XZZX surface codes all fall within the broader family Clifford-deformed surface codes [45], which provide even more flexibility for tailoring the surface code to the noise bias, and further work is required to investigate these codes in a fault-tolerant setting. Finally, for architectures with improved qubit connectivity, it is possible that bias-tailored quantum LDPC codes will offer a further reduction in qubit overhead [25].…”

Section: Discussionmentioning

confidence: 99%

Fragile boundaries of tailored surface codes and improved decoding of circuit-level noise

Higgott¹,

Bohdanowicz²,

Kubica³

et al. 2022

Preprint

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Biased noise is common in physical qubits, and tailoring a quantum code to the bias by locally modifying stabilizers or changing boundary conditions has been shown to greatly increase error correction thresholds. In this work, we explore the challenges of using a specific tailored code, the XY surface code, for fault-tolerant quantum computation. We introduce an efficient and fault-tolerant decoder, belief-matching, which we show has good performance for biased circuit-level noise. Using this decoder, we find that for moderately biased noise, the XY surface code has a higher threshold and lower overhead than the square CSS surface code, however it performs worse when below threshold than the rectangular CSS surface code. We identify a contributor to the reduced performance that we call fragile boundary errors. These are string-like errors that can occur along spatial or temporal boundaries in planar architectures or during logical state preparation and measurement. While we make partial progress towards mitigating these errors by deforming the boundaries of the XY surface code, our work suggests that fragility could remain a significant obstacle, even for other tailored codes. We expect belief-matching will have other uses, and find that it increases the threshold of the surface code to 0.940(3)% in the presence of circuit-level depolarising noise, compared to 0.817(5)% for a minimum-weight perfect matching decoder.

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Section: Discussionmentioning

confidence: 99%

Fragile boundaries of tailored surface codes and improved decoding of circuit-level noise

Higgott¹,

Bohdanowicz²,

Kubica³

et al. 2022

Preprint

Self Cite

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“…In Ref. [22], it is shown that random Clifford deformations of the CSS surface codes can lead to better codes. It is worth investigating whether a similar transformation can boost the performance of our XZZX codes.…”

Section: Discussionmentioning

confidence: 99%

“…To estimate the performance of different error-correcting codes under the asymmetric channel, we define the effective distance d of a stabilizer code as the minimum modified weight of logical operators, with the noise-modified weight of a Pauli σ given by wt (σ) ≡ log p σ /N , where N is a normalization factor; see Ref. [22] for an alternative but related definition of the effective code distance. To normalize the effective weight of the most probable Pauli error to 1, we choose N = log p m .…”

Section: Effective Code Distance For Asymmetric Pauli Noisementioning

confidence: 99%

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Tailored XZZX codes for biased noise

Xu¹,

Nam²,

Seif³

et al. 2022

Preprint

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Quantum error correction (QEC) for generic errors is challenging due to the demanding threshold and resource requirements. Interestingly, when physical noise is biased, we can tailor our QEC schemes to the noise to improve performance. Here we study a family of codes having XZZX-type stabilizer generators, including a set of cyclic codes generalized from the five-qubit code and a set of topological codes that we call generalized toric codes (GTCs). We show that these XZZX codes are highly qubit efficient if tailored to biased noise. To characterize the code performance, we use the notion of effective distance, which generalizes code distance to the case of biased noise and constitutes a proxy for the logical failure rate. We find that the XZZX codes can achieve a favorable resource scaling by this metric under biased noise. We also show that the XZZX codes have remarkably high thresholds that reach what is achievable by random codes, and furthermore they can be efficiently decoded using matching decoders. Finally, by adding only one flag qubit, the XZZX codes can realize fault-tolerant QEC while preserving their large effective distance. In combination, our results show that tailored XZZX codes give a resource-efficient scheme for fault-tolerant QEC against biased noise.

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“…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? -28].…”

Section: Introductionmentioning

confidence: 99%

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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Clifford-deformed Surface Codes

Cited by 7 publications

References 31 publications

Fragile boundaries of tailored surface codes and improved decoding of circuit-level noise

Fragile boundaries of tailored surface codes and improved decoding of circuit-level noise

Tailored XZZX codes for biased noise

Tailored cluster states with high threshold under biased noise

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