Model Based Tomography: Learning System Hamiltonians Through Gate Errors

We propose and demonstrate a QCVV technique that we call Model Based Tomography (MBT). The standard techniques used to construct the process matrices for a gate set, such as Gate Set Tomography (GST), exhibits a exponential growth in the number of fit parameters, a growth behavior that makes studying large systems unpractical. This is before taking into account the amount of fiducial states and measurements and germs required to fully probe the process matrix, requirements which lead to costly experiments. Instead, we propose to learn the operators present in the Hamiltonian. By populating our Hamiltonian with well reasoned operators, we can optimize their weights, of which there are polynomially many. This gives a more manageable scaling behavior. Using the same gate sets that one would for GST, not only can we recover the process matrices (as done in GST), we can also identify the root cause of noise channels, including non-Markovian and correlated errors, as they appear explicitly in the simulations. While the cost per iteration can be high, particularly for large systems, we expect that the benefits of MBT will make it a valuable tool for characterizing quantum devices.