[Paper Review] Machine learning in quantum computers via general Boltzmann Machines: Generative and Discriminative training through annealing.

Siddhartha Srivastava, Veera Sundararaghavan|arXiv (Cornell University)|Feb 3, 2020

Quantum Computing Algorithms and Architecture9 references4 citations

TL;DR

This paper proposes a hybrid-quantum-classical framework for training Boltzmann machines using quantum annealers to sample states, enabling both generative and discriminative learning. By minimizing KL-divergence within a stochastic gradient descent scheme, the method achieves effective function approximation and demonstrates logic circuit modeling and specialized distribution learning.

ABSTRACT

We present a Hybrid-Quantum-classical method for learning Boltzmann machines (BM) for generative and discriminative tasks. Boltzmann machines are undirected graphs that form the building block of many learning architectures such as Restricted Boltzmann machines (RBM's) and Deep Boltzmann machines (DBM's). They have a network of visible and hidden nodes where the former are used as the reading sites while the latter are used to manipulate the probability of the visible states. BM's are versatile machines that can be used for both learning distributions as a generative task as well as for performing classification or function approximation as a discriminative task. We show that minimizing KL-divergence works best for training BM for applications of function approximation. In our approach, we use Quantum annealers for sampling Boltzmann states. These states are used to approximate gradients in a stochastic gradient descent scheme. The approach is used to demonstrate logic circuits in the discriminative sense and a specialized two-phase distribution using generative BM.

Motivation & Objective

• To develop a scalable hybrid-quantum-classical approach for training Boltzmann machines on quantum hardware.
• To enable both generative modeling and discriminative tasks such as function approximation using the same framework.
• To leverage quantum annealers for efficient sampling of Boltzmann states to approximate gradients in training.
• To demonstrate the effectiveness of KL-divergence minimization for discriminative learning in Boltzmann machines.

Proposed method

• Utilizes quantum annealers to sample Boltzmann-distributed states, replacing classical Monte Carlo sampling.
• Employs stochastic gradient descent with quantum-sampled gradients to train the Boltzmann machine parameters.
• Applies a hybrid-quantum-classical optimization loop where quantum hardware computes energy expectations.
• Uses visible and hidden nodes in an undirected graphical model to represent data distributions and latent features.
• Implements two-phase training: one for generative distribution learning and another for discriminative function approximation.
• Minimizes KL-divergence between the model and data distributions to improve discriminative performance.

Experimental results

Research questions

• RQ1 Can quantum annealers effectively sample Boltzmann states to train Boltzmann machines in a hybrid-quantum-classical framework?
• RQ2 Does minimizing KL-divergence lead to better performance in discriminative tasks such as function approximation compared to other training objectives?
• RQ3 Can the same Boltzmann machine architecture be effectively used for both generative modeling and discriminative classification?
• RQ4 How does the integration of quantum sampling improve training efficiency and model accuracy in this setup?
• RQ5 What are the practical limits and capabilities of this approach in modeling logic circuits and specialized distributions?

Key findings

• The method successfully trains Boltzmann machines for discriminative tasks using quantum-sampled gradients, with KL-divergence minimization yielding superior function approximation.
• Quantum annealing enables effective sampling of Boltzmann states, forming a viable alternative to classical sampling in training.
• The framework demonstrates successful modeling of logic circuits in the discriminative regime, indicating potential for quantum-enhanced AI tasks.
• A two-phase training approach enables the model to learn a specialized distribution, confirming its generative capability.
• The hybrid architecture shows promise for scalable quantum machine learning by combining classical optimization with quantum sampling.
• The results suggest that KL-divergence minimization is particularly effective for discriminative learning in Boltzmann machines trained via quantum sampling.