  The cost of measuring quantum expectation values of an operator can be
reduced by grouping the Pauli string ($SU(2)$ tensor product) decomposition of
the operator into maximally commuting sets. We detail an algorithm, presented
in [1], to partition the full set of $m$-qubit Pauli strings into the minimal
number of commuting families, and benchmark the performance with dense
Hamiltonians on IBM hardware. Here we also compare how our method scales
compared to graph-theoretic techniques for the generally commuting case.
