  Exactly solvable Hamiltonians are useful in the study of quantum many-body
systems using quantum computers. In the variational quantum eigensolver, a
decomposition of the target Hamiltonian into exactly solvable fragments can be
used for evaluation of the energies via repeated quantum measurements. In this
work, we apply more general classes of exactly solvable qubit Hamiltonians than
previously considered to address the Hamiltonian measurement problem. The most
general exactly solvable Hamiltonians are defined by the condition that, within
each simultaneous eigenspace of a set of Pauli symmetries, the Hamiltonian acts
effectively as an element of a direct sum of so(N) Lie algebras, and can
therefore be measured using a combination of unitaries in the associated Lie
group, Clifford unitaries, and mid-circuit measurements. Application of such
Hamiltonians to decomposing molecular electronic Hamiltonians via graph
partitioning techniques shows a reduction in the total number of measurements
required to estimate the expectation value compared with previously used
exactly solvable qubit Hamiltonians.
