Effective Hamiltonian models of the cross-resonance gate

TL;DR

This paper develops effective Hamiltonian models for the cross-resonance gate, providing analytic and numerical solutions that match experimental data, including effects of higher energy levels and classical cross-talk.

Contribution

It introduces comprehensive Hamiltonian models for the cross-resonance gate, incorporating higher levels and cross-talk, with solutions validated against experimental results.

Findings

Analytic expressions for the ideal two-qubit case.

Numerical solutions including higher levels agree with perturbative results.

Models accurately predict experimental outcomes when classical cross-talk is included.

Abstract

Effective Hamiltonian methods are utilized to model the two-qubit cross-resonance gate for both the ideal two-qubit case and when higher levels are included. Analytic expressions are obtained in the qubit case and the higher-level model is solved both perturbatively and numerically with the solutions agreeing well in the weak drive limit. The methods are applied to parameters from recent experiments and accounting for classical cross-talk effects results in good agreement between theory and experimental results.