IQI Weekly Seminar
Abstract: Hamiltonians govern the equations of motion in quantum mechanics. While they are often seen as being given, it is in practice far from obvious from basic principles what their precise parameters actually are. However, the precise knowledge of these parameters is crucial in analog quantum simulation, which relies on the accurate implementation of a targeted Hamiltonian. Both to certify and to engineer an analog quantum simulator, characterizing a Hamiltonian from experimental data is therefore a task of paramount importance. In this work, we develop a methodology to robustly and accurately identify Hamiltonians of non-interacting bosons from dynamical data. Already in this simple setting, achieving the required levels of precision requires maximally exploiting the model structure, making the identification robust to incoherent errors during the evolution. Importantly, in addition to precise estimates of the Hamiltonian parameters, we obtain tomographic information about state preparation and measurement phase errors, crucial for the experimental applicability of Hamiltonian identification in dynamical quantum-quench experiments. We use our method to precisely identify the hopping parameters of bosonic excitations in a `Sycamore' superconducting-qubit analog quantum simulator. For five and six coupled qubits, we identify the Hamiltonian parameters with sub-MHz precision compared to their targeted values. Our approach introduces not only a mindset but also a practical diagnostic toolkit for understanding, calibrating, and improving analog quantum processors.