Encoding a Qubit into a Cavity Mode in Circuit-QED using Phase Estimation

  1. B. M. Terhal,
  2. and D. Weigand
Gottesman, Kitaev and Preskill have formulated a way of encoding a qubit into an oscillator such that the encoded qubit is protected against small shifts in phase space. We propose
and analyze the approximate creation of these encoded states with ancilla qubits. The preparation of the code states uses the idea of phase estimation where the phase of the stabilizer checks is approximately determined. We propose a physical implementation of this protocol using the dispersive coupling between a transmon ancilla qubit and a cavity mode in circuit-QED. We provide an estimate that in a current experimental set-up one can prepare a good code state from a squeezed vacuum state using 8 rounds of adapative phase estimation, lasting in total less than 5 {\mu} sec., with 80 % (heralded) chance of success.