Two-qubit gate using conditional driving for highly detuned Kerr-nonlinear parametric oscillators

Abstract

A Kerr-nonlinear parametric oscillator (KPO) is one of the promising devices to realize qubits for universal quantum computing. The KPO can stabilize two coherent states with opposite phases, yielding a quantum superposition called a Schrödinger cat state. Universal quantum computing with KPOs requires three kinds of quantum gates: Rz, Rx, and Rzz gates. We theoretically propose a two-qubit gate Rzz for highly detuned KPOs. In the proposed scheme, we add another twophoton drive for the first KPO. This leads to the Rzz gate based on the driving of the second KPO depending on the first-KPO state, which we call "conditional driving." First, we perform simulations using a conventional KPO Hamiltonian derived from a superconducting-circuit model under some approximations and evaluate the gate fidelity. Next, we also perform numerical simulations of the two-qubit gate using the superconducting-circuit model without the approximations. The simulation results indicate that two-qubit gates can be implemented with high fidelity (> 99.9%) for rotation angles required for universality.I.

Two-photon driven Kerr quantum oscillator with multiple spectral degeneracies

“…One approach uses an engineered two-photon dissipation, whose only two steady states are the cat states [12,[22][23][24][25]. The other approach is to use a Hamiltonian confinement, combining a squeezing drive with Kerr non-linearity [26][27][28][29][30][31][32][33]. The cat states are the degenerate ground states of this Kerr Hamiltonian, protected by an energy gap proportional to the Kerr non-linearity.…”