One of the main challenges in the variational quantum eigensolver (VQE) framework is construction of the unitary transformation. The dimensionality of the space for unitary rotations of N qubits is 4- 1, which makes the choice of a polynomial subset of generators an exponentially difficult process. Moreover, due to non-commutativity of generators, the order in which they are used strongly affects results. Choosing the optimal order in a particular subset of generators requires testing the factorial number of combinations. We propose an approach based on the Lie algebra-Lie group connection and corresponding closure relations that systematically eliminates the order problem.
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