Building a fault-tolerant quantum computer using concatenated cat codes

TL;DR

This paper proposes a detailed architecture for a fault-tolerant quantum computer using concatenated cat codes, analyzing hardware, error correction, and resource requirements to enable practical quantum computation.

Contribution

It introduces a comprehensive hardware design, error analysis, and new protocols for fault-tolerant Toffoli gate implementation and magic state distillation.

Findings

Realistic error thresholds for hardware components.

Feasibility of running complex quantum algorithms with ~1,000 qubits.

Potential to simulate complex physical models beyond classical capabilities.

Abstract

We present a comprehensive architectural analysis for a proposed fault-tolerant quantum computer based on cat codes concatenated with outer quantum error-correcting codes. For the physical hardware, we propose a system of acoustic resonators coupled to superconducting circuits with a two-dimensional layout. Using estimated physical parameters for the hardware, we perform a detailed error analysis of measurements and gates, including CNOT and Toffoli gates. Having built a realistic noise model, we numerically simulate quantum error correction when the outer code is either a repetition code or a thin rectangular surface code. Our 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, we devise a new magic-state distillation protocol for Toffoli states. Combining these results together, we obtain realistic full-resource estimates of the physical error rates and overheads needed to run useful fault-tolerant quantum algorithms. We find that with around 1,000 superconducting circuit components, one could construct a fault-tolerant quantum computer that can run circuits which are currently intractable for classical computers. Hardware with 18,000 superconducting circuit components, in turn, could simulate the Hubbard model in a regime beyond the reach of classical computing.