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Benchmarking Adaptive Variational Quantum Eigensolvers

by Daniel Chaves Claudino, Jerimiah B Wright, Alexander J Mccaskey, Travis S Humble
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Frontiers in Chemistry
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By design, the variational quantum eigensolver (VQE) recovers the lowest-energy eigenvalue of a given Hamiltonian by preparing quantum states guided by the variational principle. In practice, the prepared quantum state is indirectly assessed by the value of the associated energy. Novel adaptive derivative-assembled pseudo-trotter (ADAPT) ansatz approaches and recent formal advances now establish a clear connection between the theory of quantum chemistry and the quantum state ansatz used to solve the electronic structure problem. Here we benchmark the accuracy of VQE and ADAPT-VQE to calculate the electronic ground states and potential energy curves for a few selected diatomic molecules, namely H2, NaH, and KH. Using numerical simulation, we find both methods provide good estimates of the energy and ground state, but only ADAPT-VQE proves to be robust to particularities in optimization methods. The results also identify small errors in the prepared state fidelity which show an increasing trend with molecular size.