Building efficient VQE ansatze with complete pools of operators.

In this talk we discuss the novel adapt-VQE algorithm [1] and show how to build an efficient ansatz for it. We found that a set of 2n-2 unitaries is sufficient to transform any real state to any other, and the generators of these unitaries we thus call a complete pool. We give a proof for the minimality of such pools, discuss their algebraic properties and present a technique to efficiently find all of them. We also discuss the performance of these pools in the presence of symmetries in the Hamiltonian, that exhibits nontrivial features.

[1] Ho Lun Tang, V. O. Shkolnikov, George S. Barron, Harper R. Grimsley, Nicholas J. Mayhall, Edwin Barnes, Sophia E. Economou
qubit-ADAPT-VQE: An adaptive algorithm for constructing hardware-efficient ansatze on a quantum processor, arXiv:1911.10205v2