Resonant coupling parameter estimation with superconducting qubits

Today's quantum computers are composed of tens of qubits interacting with each other and the environment in increasingly complex networks. To achieve the best possible performance when operating such systems, it is necessary to have accurate knowledge of all parameters in the quantum computer Hamiltonian. In this paper, we demonstrate theoretically and experimentally a method to efficiently learn the parameters of resonant interactions for quantum computers consisting of frequency-tunable superconducting qubits. Such interactions include, for example, those with other qubits, resonators, two-level systems, or other wanted or unwanted modes. Our method is based on a significantly improved swap spectroscopy calibration and consists of an offline data collection algorithm, followed by an online Bayesian learning algorithm. The purpose of the offline algorithm is to detect and coarsely estimate resonant interactions from a state of zero knowledge. It produces a quadratic speedup in the scaling of the number of measurements. The online algorithm subsequently refines the estimate of the parameters to accuracy comparable with that of traditional swap spectroscopy calibration but in constant time. We perform an experiment implementing our technique with a superconducting qubit. By combining both algorithms, we observe a reduction of the calibration time by 1 order of magnitude. Our method will improve present medium-scale superconducting quantum computers and will also scale up to larger systems. Finally, the two algorithms presented here can be readily adopted by communities working on different physical implementations of quantum computing architectures.