Fig. 1: Outline of the experiment and identification algorithm.
From: Robustly learning the Hamiltonian dynamics of a superconducting quantum processor
a The time evolution under a target Hamiltonian h0 is implemented on an part of the Google Sycamore chip (gray) using the pulse sequence depicted in the middle. b The expected value of canonical coordinates xm and pm for each qubit m over time is estimated from measurements using different ψn as input states. c The data shown in (b) for each time t0 can be interpreted as a (complex-valued) matrix with entries indexed by measured and initial excited qubit, m and n. The identification algorithm proceeds in two steps: 1. From the matrix time-series, the Hamiltonian eigenfrequencies are extracted using our newly introduced algorithm coined tensorESPRIT, introduced in the Supplemental Material, or an adapted version of the ESPRIT algorithm. The blue line indicates the denoised, high-resolution signal as “seen” by the algorithm. 2. After removing the initial ramp using the data at some fixed time, the Hamiltonian eigenspaces are reconstructed using a non-convex optimization algorithm over the orthogonal group. We obtain a diagonal orthogonal estimate of the final ramp. From the extracted frequencies and reconstructed eigenspaces, we can calculate the identified Hamiltonian \(\hat{h}\) that describes the measured time evolution and a tomographic estimate of the initial ramp.
