Nonlinear Regression Versus Maximum Likelihood Estimation for State Preparation and Measurement Tomography

Developers use state preparation and measurement (SPAM) tomography to model quantum processors. Although SPAM tomography almost ubiquitously employs maximum likelihood estimation (MLE), it is computationally expensive and its performance against other optimization methods like linear or nonlinear regression, is absent from the literature. To address this gap, we compare nonlinear regression tomography (NLRT) and MLE for SPAM tomography.

We present how well NLRT and MLE characterize the SPAM of synthesized systems, and compare their respective data processing metrics, based on data from our in-house two-qubit processor simulation software. Our software simulates ion trap and superconducting systems initialized to a mixed state with noisy qubits, gate errors, and nonprojective, destructive measurements. The processors have varied degrees of initial state mixing, qubit decoherence, qubit relaxation, gate errors, readout bias, and readout discrimination. Our conclusions are of how accurate NLRT is compared to MLE while reducing computation expense. This work is relevant to similar system characterization methods like state, process, measurement, and gate set tomography.