# Operation and intrinsic error budget of a two-qubit cross-resonance gate

## TL;DR

This paper provides a comprehensive analysis of the operation and intrinsic error sources of the two-qubit cross-resonance gate in superconducting qubits, offering methods to optimize gate duration and fidelity.

## Contribution

It introduces a semi-analytical approach for accurate gate duration estimation and decomposes the intrinsic error budget, highlighting dominant error mechanisms at different drive amplitudes.

## Key findings

- Semi-analytical method accurately predicts CNOT-equivalent gate duration.
- Intrinsic fidelity can be less than 10^{-3} with simple pulse shapes.
- Error sources vary with drive amplitude, from rotation imperfections to leakage.

## Abstract

We analyze analytically, semi-analytically, and numerically the operation of Cross-Resonance (CR) gate for superconducting qubits (transmons). We find that a relatively simple semi-analytical method gives accurate results for the CNOT-equivalent gate duration and compensating single-qubit rotations. It also allows us to minimize the CNOT gate duration over the amplitude of the applied microwave drive and find dependence on the detuning between the qubits. However, full numerical simulations are needed to calculate intrinsic fidelity of the CR gate. We decompose numerical infidelity into contributions from various physical mechanisms, thus finding the intrinsic error budget. In particular, at small drive amplitudes the CR gate fidelity is limited by imperfections of the target-qubit rotations, while at large amplitudes it is limited by leakage. The gate duration and fidelity are analyzed numerically as functions of the detuning between qubits, their coupling, drive frequency, relative duration of pulse ramps, and microwave crosstalk. The effect of the echo sequence is also analyzed numerically. Our results show that the CR gate can provide intrinsic infidelity of less than $10^{-3}$ when a simple pulse shape is used.