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 to develop a method of constructing pulse protocols, which allows for the continuous tuning of the phase. We find CPHASE fidelities of more than and gate times as low as .