Experimental Evaluation of Active Learning of a Two Qubit Cross-Resonance Hamiltonian

An important step in calibration and control is Hamiltonian learning, which involves learning the parameters given a Hamiltonian model and description of noise sources through queries to the quantum system. Standard techniques require $O(\epsilon^{-2})$ queries to achieve learning error $\epsilon$ due to the standard quantum limit. To minimize the number of queries required and improve the scaling with $\epsilon$, we propose a Hamiltonian active learner based on Fisher information (“HAL-FI”). Each input query specifies the initial state, measurement operator and interaction time, and the resulting output is a single shot binary valued measurement. Seeded with data from an initial set of queries, HAL-FI optimizes subsequent queries. Performance of HAL-FI is evaluated on a two-qubit cross-resonance gate on a 20-qubit IBM Quantum device, using Qiskit Pulse to model readout noise, imperfect pulse-shaping and decoherence. HAL-FI realizes a 27% reduction in resource requirements over an uniformly random approach, with an order of magnitude reduction over quantum process tomography. Moreover, by spacing out queries non-uniformly in time, HAL-FI can achieve learning error which scales inversely with the number of queries, meeting the Heisenberg bound.