Quantum advantage in variational Bayes inference.

Area of Science:

• Computational Physics
• Quantum Computing
• Statistical Inference

Background:

• Variational Bayes (VB) is widely used for parameter and hidden variable estimation in generative models.
• Classical VB algorithms, including those using deterministic annealing (DA), can get trapped in local minima.
• Traditional VB methods are inspired by variational methods in computational physics.

Purpose of the Study:

• To investigate a novel quantum annealing variational Bayes (QAVB) inference algorithm.
• To demonstrate a quantum advantage of QAVB over classical VB inference techniques.
• To explore the theoretical underpinnings of QAVB's performance improvements.

Main Methods:

• Developed a QAVB inference algorithm utilizing quantum annealing principles.
• Defined a quantum system Hamiltonian based on input data.
• Analyzed the ground state of the Hamiltonian and its relation to variational free energy minimization.

Main Results:

• The ground state of the quantum system Hamiltonian corresponds to the optimal solution for variational free energy minimization at low temperatures.
• Quantum annealing enables reaching this ground state, which, upon controlled temperature increase, yields the optimal VB solution, avoiding local minima.
• QAVB update equations are potentially implementable with logarithmic qubits and polynomial operations, matching classical VB time complexity.

Conclusions:

• QAVB demonstrates a quantum advantage, outperforming classical VB algorithms by avoiding local minima.
• Key quantum mechanics concepts, including ground state energy and quantum annealing, are central to QAVB's effectiveness.
• QAVB offers a computationally efficient and high-performance alternative for statistical inference tasks.