Tailored XZZX codes for biased noise

Xu, Qian; Nam, Mannucci,; Seif, Alireza; Kubica, Aleksander; Flammia, Steven T.; Jiang, Liang

doi:10.1103/physrevresearch.5.013035

Cited by 10 publications

(1 citation statement)

References 44 publications

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“…Stabillizer codes [6,7] are an important and promising family of QECCs. In recent years, among the stabilizer codes, quantum low density parity-check (QLDPC) codes [8][9][10][11][12][13][14][15][16][17][18][19][20][21], such as planar surface codes [16][17][18], toric codes [19,20] and XZZX surface codes [21], tend to attract more and more attentions [22][23][24] due to the following two reasons. First, their stabilizer generators have low weight, which means that the number of qubits involved by each generator is small.…”

Section: Introductionmentioning

confidence: 99%

Divorce in China : a case study of Shenzhen

Song-guo¹,

易松國.²

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We propose a new method called decoupling representation to represent Pauli operators as vectors over GF (2), based on which we propose partially decoupled belief propagation and fully decoupled belief propagation decoding algorithm for quantum low density parity-check codes. Under the assumption that there is no measurement error, compared with traditional belief propagation algorithm in symplectic representation over GF (2), within the same number of iterations, the decoding accuracy of partially decoupled belief propagation and fully decoupled belief propagation algorithm is significantly improved in pure Y noise channel and depolarizing noise channel, which supports that decoding algorithms of quantum error correcting codes might have better performance in decoupling representation than in symplectic representation. The impressive performance of fully decoupled belief propagation algorithm might promote the realization of quantum error correcting codes in engineering.

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Section: Introductionmentioning

confidence: 99%

Divorce in China : a case study of Shenzhen

Song-guo¹,

易松國.²

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Autonomous quantum error correction and fault-tolerant quantum computation with squeezed cat qubits

Zheng

Wang

et al. 2023

npj Quantum Inf

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We propose an autonomous quantum error correction scheme using squeezed cat (SC) code against excitation loss in continuous-variable systems. Through reservoir engineering, we show that a structured dissipation can stabilize a two-component SC while autonomously correcting the errors. The implementation of such dissipation only requires low-order nonlinear couplings among three bosonic modes or between a bosonic mode and a qutrit. While our proposed scheme is device independent, it is readily implementable with current experimental platforms such as superconducting circuits and trapped-ion systems. Compared to the stabilized cat, the stabilized SC has a much lower dominant error rate and a significantly enhanced noise bias. Furthermore, the bias-preserving operations for the SC have much lower error rates. In combination, the stabilized SC leads to substantially better logical performance when concatenating with an outer discrete-variable code. The surface-SC scheme achieves more than one order of magnitude increase in the threshold ratio between the loss rate κ1 and the engineered dissipation rate κ2. Under a practical noise ratio κ1/κ2 = 10−3, the repetition-SC scheme can reach a 10−15 logical error rate even with a small mean excitation number of 4, which already suffices for practically useful quantum algorithms.

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