  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 $4^N-1$, which makes the
choice of a polynomial subset of generators 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.
