Using non-standard and non-uniform 2-qubit basis gates

Near-term quantum computers are primarily limited by errors in 2-qubit (2Q) gates. A physical machine typically provides a set of basis gates that include primitive 2Q and 1Q gates that can be implemented in a given technology. 2Q entangling gates, coupled with some 1Q gates, allow for universal quantum computation. In superconducting technologies, the current state of the art is to implement the same 2Q gate between every pair of qubits (typically an XX- or XY-type gate). This strict hardware uniformity requirement for 2Q gates in a large quantum computer has made scaling up a time and resource-intensive endeavor in the lab.We argue for a radical idea – allow the 2Q basis gate(s) to differ between every pair of qubits, selecting the best entangling gates that can be calibrated between given pairs of qubits. We develop a theoretical framework for identifying good 2Q basis gates on "nonstandard" Cartan trajectories that deviate from "standard" trajectories like XX and XY. We then discuss the calibration and compilation with nonstandard 2Q gates, and introduce practical methods. We hope our work will enable the use of a much broader variety of novel 2Q gates for quantum computing.