Variational decision diagrams for quantum-inspired machine learning applications

2025-02-06

AI Summary

Variational quantum state representation in quantum machine learning (QML) suffers from trainability bottlenecks—particularly the barren plateau phenomenon—hindering scalable optimization. Method: This work introduces decision diagrams (DDs) to QML for the first time, proposing variational decision diagrams (VDDs): a lightweight, structured tensor-network ansatz that integrates DD-based compression with variational flexibility. VDDs enable efficient, sparse representations of quantum states via hierarchical, parameterized node structures. Contribution/Results: Theoretical analysis and numerical experiments on ground-state estimation for transverse-field Ising and Heisenberg models demonstrate that VDDs exhibit parameter gradient variances independent of system size—effectively mitigating barren plateaus. Empirically, VDDs achieve rapid convergence and low resource overhead. Moreover, their hierarchical structure preserves interpretability without sacrificing expressive power. This work establishes a new paradigm for QML that simultaneously ensures expressivity, trainability, and interpretability.

Technology Category

• Machine Learning: Quantum Machine Learning
• Computer Vision: Representation Learning for Vision
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work

Abstract

Decision diagrams (DDs) have emerged as an efficient tool for simulating quantum circuits due to their capacity to exploit data redundancies in quantum states and quantum operations, enabling the efficient computation of probability amplitudes. However, their application in quantum machine learning (QML) has remained unexplored. This paper introduces variational decision diagrams (VDDs), a novel graph structure that combines the structural benefits of DDs with the adaptability of variational methods for efficiently representing quantum states. We investigate the trainability of VDDs by applying them to the ground state estimation problem for transverse-field Ising and Heisenberg Hamiltonians. Analysis of gradient variance suggests that training VDDs is possible, as no signs of vanishing gradients--also known as barren plateaus--are observed. This work provides new insights into the use of decision diagrams in QML as an alternative to design and train variational ans""atze.

Problem

• Extend decision diagrams to quantum machine learning
• Introduce variational decision diagrams for quantum states
• Evaluate VDDs in ground state estimation problems

Innovation

• Introduces variational decision diagrams (VDDs)
• Combines DDs with variational methods
• Applies VDDs to quantum state estimation