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

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 circuit 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 II, we apply the dissipatively stabilized squeezed cat for concatenated QEC and fault-tolerant quantum computing. With a set of carefully-designed bias-preserving operations, the stabilized SC leads to substantially better logical performance when concatenating with an outer discrete-variable code compared to the cat. The surface-SC scheme has a more than one-order-of-magnitude increase in the threshold noise ratio between the loss rate and the engineered dissipation rate. Under a practical noise ratio of 10^-3, the repetition-SC scheme can reach a 10^-15 logical error rate even with a small mean photon number of 4, which already suffices for useful quantum algorithms.