Improving operator averaging in hybrid algorithms with approximate N-representability constraints

The two most well known hybrid classical/quantum algorithms require calculating expected values of Pauli operators by repeated state preparation and measurement. Accelerating the operator averaging step correlates directly with accelerating the total algorithm runtime. We propose the use of approximate N-representability constraints as a set of conditions for reconstructing marginals generated with noise from measurement. These techniques take the form of projections onto the set of N-representable two-electron reduced density matrices (2-RDMs) enforcing non-negativity of the marginal, particle number conservation, and the appropriate magnetization of the targeted Fermionic state prepared on the quantum resource. We present the performance of the N-representability inspired 2-RDM reconstruction procedures on marginals mimicking real measured data. For small systems, the projection techniques give a significant reduction in the number of samples required for operator averaging to a given precision.