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

Bosonic codes encode information into infinite dimensional Hilbert space and provide a hardware-efficient approach to fault tolerant quantum computing. Moreover, autonomous quantum error correction (AutoQEC) emerges as a promising method to extract entropy from the while avoiding measurement overheads. Therefore, it is desirable to design a bosonic code that can both correct excitation loss errors, the dominant error source, and be autonomously stabilized with a low order of nonlinearity. In part I, we propose an AutoQEC scheme using a two-component squeezed cat (SC) code. Through reservoir engineering, we show that a structured dissipation can stabilize the code space while autonomously correcting loss errors. The stabilized SC also exhibits an even stronger noise bias than the conventional cat code. 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.