  Today's quantum computers are comprised of tens of qubits interacting with
each other and the environment in increasingly complex networks. In order 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 article, 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 to other qubits, resonators, two-level
state defects, or other 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 roughly estimate resonant
interactions from a state of zero knowledge. It produces a square-root
reduction in the number of measurements. The online algorithm subsequently
refines the estimate of the parameters to comparable accuracy as 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 one order of
magnitude. We believe the method investigated 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.
