Two-qubit gate using conditional driving for highly detuned Kerr nonlinear parametric oscillators
Hiroomi Chono, Taro Kanao, Hayato Goto
Abstract
A Kerr nonlinear parametric oscillator (KPO) is one of the promising devices used to realize qubits for universal quantum computing. The KPO can stabilize two coherent states with opposite phases, yielding a quantum superposition called a Schr\"odinger cat state. Universal quantum computing with KPOs requires three kinds of quantum gates: ${R}_{z},{R}_{x}$, and ${R}_{zz}$ gates. We theoretically propose a two-qubit gate ${R}_{zz}$ for highly detuned KPOs. In the proposed scheme, we add a parametric drive for the first KPO. This leads to the ${R}_{zz}$ 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 the conditional-driving gates can be implemented with high fidelity ($>99.9%$) for rotation angles required for universality.