Driving superconducting qubits into chaos

  1. Jorge Chávez-Carlos,
  2. Rodrigo G. Cortiñas,
  3. Miguel A. Prado Reynoso,
  4. Ignacio García-Mata,
  5. Victor S. Batista,
  6. Francisco Pérez-Bernal,
  7. Diego A. Wisniacki,
  8. and Lea F. Santos
Kerr parametric oscillators are potential building blocks for fault-tolerant quantum computers. They can stabilize Kerr-cat qubits, which offer advantages towards the encoding and manipulation
of error-protected quantum information. Kerr-cat qubits have been recently realized with the SNAIL transmon superconducting circuit by combining nonlinearities and a squeezing drive. These superconducting qubits can lead to fast gate times due to their access to large anharmonicities. However, we show that when the nonlinearities are large and the drive strong, chaos sets in and melts the qubit away. We provide an equation for the border between regularity and chaos and determine the regime of validity of the Kerr-cat qubit, beyond which it disintegrates. This is done through the quantum analysis of the quasienergies and Floquet states of the driven system, and is complemented with classical tools that include Poincaré sections and Lyapunov exponents. By identifying the danger zone for parametric quantum computation, we uncover another application for driven superconducting circuits, that of devices to investigate quantum chaos.

The squeezed Kerr oscillator: spectral kissing and phase-flip robustness

  1. Nicholas E. Frattini,
  2. Rodrigo G. Cortiñas,
  3. Jayameenakshi Venkatraman,
  4. Xu Xiao,
  5. Qile Su,
  6. Chan U Lei,
  7. Benjamin J. Chapman,
  8. Vidul R. Joshi,
  9. S. M. Girvin,
  10. Robert J. Schoelkopf,
  11. Shruti Puri,
  12. and Michel H. Devoret
By applying a microwave drive to a specially designed Josephson circuit, we have realized an elementary quantum optics model, the squeezed Kerr oscillator. This model displays, as the
squeezing amplitude is increased, a cross-over from a single ground state regime to a doubly-degenerate ground state regime. In the latter case, the ground state manifold is spanned by Schrödinger-cat states, i.e. quantum superpositions of coherent states with opposite phases. For the first time, having resolved up to the tenth excited state in a spectroscopic experiment, we confirm that the proposed emergent static effective Hamiltonian correctly describes the system, despite its driven character. We also find that the lifetime of the coherent state components of the cat states increases in steps as a function of the squeezing amplitude. We interpret the staircase pattern as resulting from pairwise level kissing in the excited state spectrum. Considering the Kerr-cat qubit encoded in this ground state manifold, we achieve for the first time quantum nondemolition readout fidelities greater than 99%, and enhancement of the phase-flip lifetime by more than two orders of magnitude, while retaining universal quantum control. Our experiment illustrates the crucial role of parametric drive Hamiltonian engineering for hardware-efficient quantum computation.