Stabilized Cat in Driven Nonlinear Cavity: A Fault-Tolerant Error Syndrome Detector

  1. Shruti Puri,
  2. Alexander Grimm,
  3. Philippe Campagne-Ibarcq,
  4. Alec Eickbusch,
  5. Kyungjoo Noh,
  6. Gabrielle Roberts,
  7. Liang Jiang,
  8. Mazyar Mirrahimi,
  9. Michel H. Devoret,
  10. and Steven M. Girvin
low-weight operations with an ancilla to extract information about errors without causing backaction on the encoded system. Essentially, ancilla errors must not propagate to the encoded
system and induce errors beyond those which can be corrected. The current schemes for achieving this fault-tolerance to ancilla errors come at the cost of increased overhead requirements. An efficient way to extract error syndromes in a fault-tolerant manner is by using a single ancilla with strongly biased noise channel. Typically, however, required elementary operations can become challenging when the noise is extremely biased. We propose to overcome this shortcoming by using a bosonic-cat ancilla in a parametrically driven nonlinear cavity. Such a cat-qubit experiences only bit-flip noise and is stabilized against phase-flips. To highlight the flexibility of this approach, we illustrate the syndrome extraction process in a variety of codes such as qubit-based toric codes, bosonic cat- and Gottesman-Kitaev-Preskill (GKP) codes. Our results open a path for realizing hardware-efficient, fault-tolerant error syndrome extraction.

Stabilizer quantum error correction toolbox for superconducting qubits

  1. Simon E. Nigg,
  2. and Steven M. Girvin
We present a general protocol for stabilizer measurements and pumping in a system of N superconducting qubits. We assume always-on, equal dispersive couplings to a single mode of a
high-Q microwave resonator in the ultra-strong dispersive limit where the dispersive shifts largely exceed the spectral linewidth. In this limit, we show how to map the two eigenvalues of an arbitrary weight M < N Pauli operator, onto two quasi-orthogonal coherent states of the cavity. Together with a fast cavity readout, this enables the efficient measurement of stabilizer operators.