Many-body approach to projective solution of generalized operators: Formulation and application to quantum computing

In this paper, we propose a novel many-body approach for determining the amplitudes of generalized operators in a projection-based formalism. To implicitly account for the effects of higher-order excitations, we begin with the well-established double-exponential coupled-cluster (CC) ansatz, parametrized by both one- and two-body excitation operators, complemented by a set of vacuum-annihilating two-body generalized operators with effective excitation rank of one. A systematic formalism is developed that effectively bypasses the constraints due to the vacuum-annihilation property of the generalized operators toward a set of closed-form residual equations for their optimization. Such a strategy requires the removal of the underlying redundancy in high-rank excited determinants, generated due to the presence of the generalized operators in the ansatz, by projecting them onto an internally contracted lower-dimensional manifold. This many-body formalism is integrated with the near-term projective quantum eigensolver (PQE) framework that leverages the conventional CC-like residual minimization to iteratively decouple the excited manifold from the reference. With the application of several molecular systems within PQE architecture, we demonstrate that the developed methodology enables us to achieve similar accuracy to the disentangled unitary coupled cluster with singles, doubles, and triples ansatz while utilizing an order of magnitude fewer quantum resources. Furthermore, when simulated under stochastic Gaussian noise or depolarizing hardware noise, our method shows significantly improved noise resilience compared to the other members of PQE family and the state-of-the-art variational quantum eigensolver.