Earl T. Campbell

Reducing the error rate of a superconducting logical qubit using analog readout information

  1. Hany Ali,
  2. Jorge Marques,
  3. Ophelia Crawford,
  4. Joonas Majaniemi,
  5. Marc Serra-Peralta,
  6. David Byfield,
  7. Boris Varbanov,
  8. Barbara M. Terhal,
  9. Leonardo DiCarlo,
  10. and Earl T. Campbell
Quantum error correction enables the preservation of logical qubits with a lower logical error rate than the physical error rate, with performance depending on the decoding method.
Traditional error decoding approaches, relying on the binarization (`hardening‘) of readout data, often ignore valuable information embedded in the analog (`soft‘) readout signal. We present experimental results showcasing the advantages of incorporating soft information into the decoding process of a distance-three (d=3) bit-flip surface code with transmons. To this end, we use the 3×3 data-qubit array to encode each of the 16 computational states that make up the logical state $\ket{0_{\mathrm{L}}}$, and protect them against bit-flip errors by performing repeated Z-basis stabilizer measurements. To infer the logical fidelity for the $\ket{0_{\mathrm{L}}}$ state, we average across the 16 computational states and employ two decoding strategies: minimum weight perfect matching and a recurrent neural network. Our results show a reduction of up to 6.8% in the extracted logical error rate with the use of soft information. Decoding with soft information is widely applicable, independent of the physical qubit platform, and could reduce the readout duration, further minimizing logical error rates.
arxiv pdf

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.
arxiv pdf