# Microwave-based Arbitrary CPHASE Gates for Transmon Qubits

## TL;DR

This paper presents a method to design microwave-based arbitrary CPHASE gates for transmon qubits, achieving high fidelity and fast operation, which are crucial for quantum simulation algorithms.

## Contribution

The authors develop an analytically solvable approach using local invariants to create smooth, tunable pulse protocols for arbitrary CPHASE gates in transmon qubits.

## Key findings

- CPHASE fidelities > 0.999 achieved
- Gate times as low as 100 ns demonstrated
- Method allows continuous phase tuning

## Abstract

Superconducting transmon qubits are of great interest for quantum computing and quantum simulation. A key component of quantum chemistry simulation algorithms is breaking up the evolution into small steps, which naturally leads to the need for non-maximally entangling, arbitrary CPHASE gates. Here we design such microwave-based gates using an analytically solvable approach leading to smooth, simple pulses. We use the local invariants of the evolution operator in $SU(4)$ to develop a method of constructing pulse protocols, which allows for the continuous tuning of the phase. We find CPHASE fidelities of more than $0.999$ and gate times as low as $100\text{ ns}$.