SPAM Error Correction: Transition Matrix versus Quasiprobabilities

State preparation and measurement (SPAM) errors limit the performance
of noisy intermediate-scale quantum computers and their potential for
practical application. Two techniques have been used to partially
mitigate these SPAM errors. Both approaches build approximate models
of the errors via tomography and then attempt to invert it. The first
technique is to measure the transition matrix between all initial and
final classical states, and to use this information to classically
correct subsequently measured data. The second technique recently proposed
by Temme, Bravyi, and Gambetta decomposes an ideal circuit into a
quasiprobabilistic mixture of noisy measured ones. While neither approach
is scalable, it would be useful to know their effectiveness when applied
to real SPAM errors. Here apply both methods to online IBM qubits, and
find very similar predictions for one- and two-qubit corrected Pauli
expectation values, with some indication that the simpler transition
matrix method performs slightly better than the quasiprobability
representation, at least for the SPAM errors encountered in superconducting
qubits.