  Variational Bayes (VB) inference algorithm is used widely to estimate both
the parameters and the unobserved hidden variables in generative statistical
models. The algorithm -- inspired by variational methods used in computational
physics -- is iterative and can get easily stuck in local minima, even when
classical techniques, such as deterministic annealing (DA), are used. We study
a variational Bayes (VB) inference algorithm based on a non-traditional quantum
annealing approach -- referred to as quantum annealing variational Bayes (QAVB)
inference -- and show that there is indeed a quantum advantage to QAVB over its
classical counterparts. In particular, we show that such better performance is
rooted in key concepts from quantum mechanics: (i) the ground state of the
Hamiltonian of a quantum system -- defined from the given variational Bayes
(VB) problem -- corresponds to an optimal solution for the minimization problem
of the variational free energy at very low temperatures; (ii) such a ground
state can be achieved by a technique paralleling the quantum annealing process;
and (iii) starting from this ground state, the optimal solution to the VB
problem can be achieved by increasing the heat bath temperature to unity, and
thereby avoiding local minima introduced by spontaneous symmetry breaking
observed in classical physics based VB algorithms. We also show that the update
equations of QAVB can be potentially implemented using $\lceil \log K \rceil$
qubits and $\mathcal{O} (K)$ operations per step. Thus, QAVB can match the time
complexity of existing VB algorithms, while delivering higher performance.
