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

TL;DR

This paper proposes a high-fidelity two-qubit $R_{zz}$ gate for Kerr-nonlinear parametric oscillators using conditional driving, advancing the implementation of universal quantum gates in superconducting circuits.

Contribution

It introduces a novel conditional driving scheme for highly detuned KPOs to realize a two-qubit $R_{zz}$ gate with high fidelity, supported by comprehensive simulations.

Findings

Achieved >99.9% gate fidelity in simulations.

Demonstrated feasibility of the $R_{zz}$ gate with high accuracy.

Validated the scheme using both approximate and exact models.

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 Schr\"{o}dinger 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 another two-photon 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 two-qubit gates can be implemented with high fidelity ($>99.9\%$) for rotation angles required for universality.