A routine for uniquely specifying state preparation and readout

Most state preparation and measurement (SPAM) characterizations of common SPAM tomography procedures cannot distinguish processors with pure states and nonprojective readout from those with mixed states and projective readout. The problem is that there is a mathematical gauge symmetry in the likelihood of the outcomes of quantum computations. The symmetry comes from coupling the system’s state density and positive-operator-value-measure (POVM), which models state measurement. Our presentation is of asymptotic state POVM (ASP) gauge-fixing, a method for choosing a unique solution from the family of characterizations of common SPAM tomography.

Our method, ASP gauge-fixing, uses idling qubits and a noise model for them to break the symmetry inherent to most SPAM characterizations. That is, the gauge symmetry is no longer present when we add measurement data of idling qubits and we can thus calculate a preferred solution. The procedure first uses the noise to identify a unique POVM and then the POVM to identify the system’s unique initial state density. We expect that procedures like ASP gauge-fixing are applicable for breaking the gauge symmetry of related tomography procedures, like gate set tomography.