# Optimized cross-resonance gate for coupled transmon systems

## TL;DR

This paper explores optimal control techniques to significantly speed up the cross-resonance entangling gate in superconducting qubits, approaching the quantum speed limit and outperforming current experimental implementations.

## Contribution

It demonstrates that using a frequency-based ansatz in optimal control can nearly double the speed of the cross-resonance gate, approaching the quantum speed limit.

## Key findings

- Optimal control pulses can reduce gate duration to under 30ns.
- A frequency-based ansatz achieves over twice the speed of traditional methods.
- Theoretical quantum speed limit estimated at 15ns for typical parameters.

## Abstract

The cross-resonant gate is an entangling gate for fixed frequency superconducting qubits introduced for untunable qubits. While being simple and extensible, it suffers from long duration and limited fidelity. Using two different optimal control algorithms, we probe the quantum speed limit for a CNOT gate in this system. We show that the ability to approach this limit depends strongly on the ansatz used to describe the optimal control pulse. A piecewise constant ansatz with a single carrier leads to an experimentally feasible pulse shape, shorter than the one currently used in experiments, but that remains relatively far from the speed limit. On the other hand, an ansatz based on the two dominant frequencies involved in the optimal control problem allows to generate an optimal solution more than twice as fast, in under $30$ns. This comes close to the theoretical quantum speed limit, which we estimate at $15$ns for typical circuit-QED parameters, which is more than an order of magnitude faster than current experimental microwave-driven realizations, and more than twice as fast as tunable direct-coupling experimental realizations.