  To obtain estimates of electronic energies, the Variational Quantum
Eigensolver (VQE) technique performs separate measurements for multiple parts
of the system Hamiltonian. Current quantum hardware is restricted to projective
single-qubit measurements, and thus, only parts of the Hamiltonian which form
mutually qubit-wise commuting groups can be measured simultaneously. The number
of such groups in the electronic structure Hamiltonians grows as $N^4$, where
$N$ is the number of qubits, and thus puts serious restrictions on the size of
the systems that can be studied. Using a partitioning of the system Hamiltonian
as a linear combination of unitary operators we found a circuit formulation of
the VQE algorithm that allows one to measure a group of fully anti-commuting
terms of the Hamiltonian in a single series of single-qubit measurements.
Numerical comparison of the unitary partitioning to previously used grouping of
Hamiltonian terms based on their qubit-wise commutativity shows an $N$-fold
reduction in the number of measurable groups.
