Building a fault-tolerant quantum computer using concatenated cat codes

  1. Christopher Chamberland,
  2. Kyungjoo Noh,
  3. Patricio Arrangoiz-Arriola,
  4. Earl T. Campbell,
  5. Connor T. Hann,
  6. Joseph Iverson,
  7. Harald Putterman,
  8. Thomas C. Bohdanowicz,
  9. Steven T. Flammia,
  10. Andrew Keller,
  11. Gil Refael,
  12. John Preskill,
  13. Liang Jiang,
  14. Amir H. Safavi-Naeini,
  15. Oskar Painter,
  16. and Fernando G.S.L. Brandão
We present 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, we propose a system of acoustic resonators coupled to superconducting circuits with a two-dimensional layout. Using estimated near-term physical parameters for electro-acoustic systems, 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 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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