Simulating Many-Body Systems with a Projective Quantum Eigensolver

We present a new hybrid quantum-classical algorithm for optimizing unitary coupled-cluster (UCC) wave functions deemed the projective quantum eigensolver (PQE), amenable to near-term noisy quantum hardware. Contrary to variational quantum algorithms, PQE optimizes a trial state using residuals (projections of the Schrodinger equation) rather than energy gradients. We show that the residuals may be evaluated by simply measuring two energy expectation values per element. We also introduce a selected variant of PQE (SPQE) that uses an adaptive ansatz built from arbitrary-order particle-hole operators, offering an alternative to gradient-based selection procedures. PQE and SPQE are tested on a set of molecular systems covering both the weak and strong correlation regimes, including hydrogen clusters with four to ten atoms and the BeH2 molecule. When employing a fixed ansatz, we find that PQE can converge disentangled (factorized) UCC wave functions to essentially identical energies as variational optimization while requiring fewer computational resources. A comparison of SPQE and adaptive variational quan tum algorithms shows that for ansatze containing the same number of parameters the two methods yield results of comparable accuracy. Finally, we show that for a target energy accuracy, SPQE provides a parameterization of similar size or more concise than the one obtained via selected configuration interaction and the density matrix renormalization group on one- to three-dimensional strongly correlated H10 systems in terms of number of variational parameters.