Measurement Reduction in Variational Quantum Algorithms*

Variational quantum algorithms are promising applications of noisy intermediate-scale quantum (NISQ) computers. These algorithms consist of a number of separate prepare-and-measure experiments that estimate terms in the Hamiltonian. The number of separate measurements required can become overwhelmingly large for problems at the scale of NISQ hardware that may soon be available. We approach this problem from the perspective of contextuality, and use unitary partitioning to define VQE procedures in which additional unitary operations are appended to the ansatz preparation circuit to reduce the number of terms one needs to measure. This approach may be tuned to hardware specifications in order to use all coherent resources available after ansatz preparation. We investigate this technique for a variety of Hamiltonian classes, in particular the electronic structure Hamiltonian from quantum chemistry. There, we prove that term reduction always scales at least linearly with respect to the number of orbitals, and we supplement this result with numerical studies.