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.
@article{osti_2423785,
author = {Xu, Qian and Zheng, Guo and Wang, Yu-Xin and Zoller, Peter and Clerk, Aashish A. and Jiang, Liang},
title = {Autonomous quantum error correction and fault-tolerant quantum computation with squeezed cat qubits},
annote = {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.},
doi = {10.1038/s41534-023-00746-0},
url = {https://www.osti.gov/biblio/2423785},
journal = {npj Quantum Information},
issn = {ISSN 2056-6387},
number = {1},
volume = {9},
place = {United States},
publisher = {Nature Partner Journals},
year = {2023},
month = {08}}
Knill, Emanuel; Laflamme, Raymond; Zurek, Wojciech H.
Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, Vol. 454, Issue 1969https://doi.org/10.1098/rspa.1998.0166