VQE is accelerated by performing receiving a qubit Hamiltonian representing a linear combination of a plurality of Pauli strings. Selecting, among the plurality of Pauli strings, one or more Pauli strings that have less influence than a threshold on an eigenvalue of the qubit Hamiltonian. Grouping, based on joint measurability, the unselected Pauli strings among the plurality of Pauli strings into a plurality of groups of jointly measurable Pauli strings Determining that one or more of the selected one or more Pauli strings is jointly measurable with Pauli strings in one of the plurality of groups And adding one or more of the selected one or more Pauli strings to the one of the plurality of groups.