Gauge Fixed Nonlinear Regression for Two-Qubit Processors

We show that nonlinear regression produces accurate state characterizations of in-house modeled two-qubit processors with well known gates. This regression-based tomography scheme characterizes a processor's starting state and qubit measuring apparatus, modeled by “state preparation and measurement” (SPAM) parameters. We demonstrate our regression on synthesized data; we simulate a processor's impure two-qubit states, native gate sequences, and simultaneous measurements (not subject to cross-talk) of two one-qubit states. Solutions to this SPAM problem have a gauge issue whereby many characterizations produce the same state measurement frequencies. Our regression however produces unique solutions because we implement a gauge fixing procedure which uses expectations for the purity of the processor's starting state. The regression enforces physicality as it looks for system characterizations and thus we do not require any additional method to pullback nonphysical solutions. When we have reliable expectations for the state purity, our unique SPAM characterizations are more accurate than those which are not gauge-fixed with these expectations.