A team at Amazon has presented a comprehensive architectural analysis for a fault-tolerant quantum computer based on cat codes concatenated with outer quantum error-correcting codes.
For the physical hardware, they have proposed a system of acoustic resonators coupled to superconducting circuits with a two-dimensional layout. Using estimated near-term physical parameters for electro-acoustic systems, they have performed a detailed error analysis of measurements and gates, including CNOT and Toffoli gates.
Having built a realistic noise model, they numerically have simulated quantum error correction when the outer code is either a repetition code or a thin rectangular surface code.
The next step toward universal fault-tolerant quantum computation is a protocol for fault-tolerant Toffoli magic state preparation that significantly improves upon the fidelity of physical Toffoli gates at very low qubit cost. To achieve even lower overheads, they have devised a new magic-state distillation protocol for Toffoli states.
Combining these results together, they have obtained realistic full-resource estimates of the physical error rates and overheads needed to run useful fault-tolerant quantum algorithms.
They found that with around 1,000 superconducting circuit components, one could construct a fault-tolerant quantum computer that can run circuits which are intractable for classical supercomputers.
Hardware with 32,000 superconducting circuit components, in turn, could simulate the Hubbard model in a regime beyond the reach of classical computing.
Jeff Barr at Amazon has posted further information on this blog.