Building a Quantum Computer with Cat Codes

Abstract

A comprehensive architectural analysis for a fault-tolerant quantum computer based on cat codes concatenated with outer quantum error-correcting codes is presented. The construction significantly improves upon the fidelity of physical Toffoli gates at very low qubit cost. To achieve even lower overheads,  a new magic-state distillation protocol for Toffoli states is devised.  For the physical hardware, we propose a system of acoustic resonators coupled to superconducting circuits with a two-dimensional layout. We find 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.

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