Benchmarking adaptive variational quantum eigensolvers

• URL: http://arxiv.org/abs/2011.01279v1
• Date: Mon, 2 Nov 2020 19:52:04 GMT
• Title: Benchmarking adaptive variational quantum eigensolvers
• Authors: Daniel Claudino, Jerimiah Wright, Alexander J. McCaskey, Travis S. Humble
• Abstract summary: We benchmark the accuracy of VQE and ADAPT-VQE to calculate the electronic ground states and potential energy curves. We find both methods provide good estimates of the energy and ground state. gradient-based optimization is more economical and delivers superior performance than analogous simulations carried out with gradient-frees.
• Score: 63.277656713454284
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: By design, the variational quantum eigensolver (VQE) strives to recover 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 H$_2$, 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. Another relevant finding is that gradient-based optimization is overall more economical and delivers superior performance than analogous simulations carried out with gradient-free optimizers. The results also identify small errors in the prepared state fidelity which show an increasing trend with molecular size.

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