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The Pauli strings appearing in the decomposition of an operator can be can begrouped into commuting families, reducing the number of quantum circuits neededto measure the expectation value of the operator. We detail an algorithm tocompletely partition the full set of Pauli strings acting on any number ofqubits into the minimal number of sets of commuting families, and we providepython code to perform the partitioning. The partitioning method scaleslinearly with the size of the set of Pauli strings and it naturally provides afast method of diagonalizing the commuting families with quantum gates. Weprovide a package that integrates the partitioning into Qiskit, and use this tobenchmark the algorithm with dense Hamiltonians, such as those that arise inmatrix quantum mechanics models, on IBM hardware. We demonstrate computationalspeedups close to the theoretical limit of $(3/2)^m$ relative to qubit-wisecommuting groupings, for $m=2,\dotsc,6$ qubits.

Fast Partitioning of Pauli Strings into Commuting Families for Optimal Expectation Value Measurements of Dense Operators