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We develop analytical gradients of ground- and excited-state energies withrespect to system parameters including the nuclear coordinates for the hybridquantum/classical multistate contracted variational quantum eigensolver(MC-VQE) applied to fermionic systems. We show how the resulting responsecontributions to the gradient can be evaluated with a quantum effort similar tothat of obtaining the VQE energy and independent of the total number ofderivative parameters (e.g. number of nuclear coordinates) by adopting aLagrangian formalism for the evaluation of the total derivative. We alsodemonstrate that large-step-size finite-difference treatment of directionalderivatives in concert with the parameter shift rule can significantly mitigatethe complexity of dealing with the quantum parameter Hessian when solving thequantum response equations. This enables the computation of analyticalderivative properties of systems with hundreds of atoms, while solving anactive space of their most strongly correlated orbitals on a quantum computer.We numerically demonstrate the exactness the analytical gradients and discussthe magnitude of the quantum response contributions.

Analytical Ground- and Excited-State Gradients for Molecular Electronic Structure Theory from Hybrid Quantum/Classical Methods