Quantum Advantage in Variational Bayes Inference

TL;DR

This paper introduces a quantum annealing-based variational Bayes inference method that leverages quantum mechanics principles to avoid local minima and achieve better performance than classical algorithms.

Contribution

The paper proposes QAVB, a quantum annealing approach to variational Bayes inference, demonstrating quantum advantage and potential implementation with logarithmic qubits.

Findings

QAVB outperforms classical VB algorithms in avoiding local minima.

Ground state of the quantum Hamiltonian corresponds to optimal VB solution.

QAVB can be implemented efficiently with logarithmic qubits.

Abstract

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.