Fernando G.S.L. Brandão

Preserving phase coherence and linearity in cat qubits with exponential bit-flip suppression

  1. Harald Putterman,
  2. Kyungjoo Noh,
  3. Rishi N. Patel,
  4. Gregory A. Peairs,
  5. Gregory S. MacCabe,
  6. Menyoung Lee,
  7. Shahriar Aghaeimeibodi,
  8. Connor T. Hann,
  9. Ignace Jarrige,
  10. Guillaume Marcaud,
  11. Yuan He,
  12. Hesam Moradinejad,
  13. John Clai Owens,
  14. Thomas Scaffidi,
  15. Patricio Arrangoiz-Arriola,
  16. Joe Iverson,
  17. Harry Levine,
  18. Fernando G.S.L. Brandão,
  19. Matthew H. Matheny,
  20. and Oskar Painter
Cat qubits, a type of bosonic qubit encoded in a harmonic oscillator, can exhibit an exponential noise bias against bit-flip errors with increasing mean photon number. Here, we focus
on cat qubits stabilized by two-photon dissipation, where pairs of photons are added and removed from a harmonic oscillator by an auxiliary, lossy buffer mode. This process requires a large loss rate and strong nonlinearities of the buffer mode that must not degrade the coherence and linearity of the oscillator. In this work, we show how to overcome this challenge by coloring the loss environment of the buffer mode with a multi-pole filter and optimizing the circuit to take into account additional inductances in the buffer mode. Using these techniques, we achieve near-ideal enhancement of cat-qubit bit-flip times with increasing photon number, reaching over 0.1 seconds with a mean photon number of only 4. Concurrently, our cat qubit remains highly phase coherent, with phase-flip times corresponding to an effective lifetime of T1,eff≃70 μs, comparable with the bare oscillator lifetime. We achieve this performance even in the presence of an ancilla transmon, used for reading out the cat qubit states, by engineering a tunable oscillator-ancilla dispersive coupling. Furthermore, the low nonlinearity of the harmonic oscillator mode allows us to perform pulsed cat-qubit stabilization, an important control primitive, where the stabilization can remain off for a significant fraction (e.g., two thirds) of a 3 μs cycle without degrading bit-flip times. These advances are important for the realization of scalable error-correction with cat qubits, where large noise bias and low phase-flip error rate enable the use of hardware-efficient outer error-correcting codes.
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