Training-efficient density quantum machine learning

2024-05-30

arXiv.org

AI Summary

Quantum machine learning urgently requires models that simultaneously achieve high expressivity and hardware-efficient trainability. To address this, we propose the Density Quantum Neural Network (DQNN), introducing a unified modeling paradigm based on density matrices. Our method leverages the Hastings–Campbell mixing lemma to construct shallow yet high-performance quantum circuits; employs commuting-generator parameterization to enable efficient analytical gradient computation; and integrates linear combinations of unitaries (LCU), mixture-of-experts architectures, Hamiltonian-weight conservation, and equivariance constraints. This framework unifies post-variational optimization and measurement-basis learning. Experiments demonstrate that DQNN significantly improves training efficiency and generalization across diverse tasks—including equivariant and Hamming-weight-conserving models—while effectively mitigating overfitting and substantially reducing circuit depth.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Natural Language Processing: Learning & Optimization for NLP

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Security and Privacy: Security and privacy of machine learning and AI applications
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

Quantum machine learning (QML) requires powerful, flexible and efficiently trainable models to be successful in solving challenging problems. We introduce density quantum neural networks, a model family that prepares mixtures of trainable unitaries, with a distributional constraint over coefficients. This framework balances expressivity and efficient trainability, especially on quantum hardware. For expressivity, the Hastings-Campbell Mixing lemma converts benefits from linear combination of unitaries into density models with similar performance guarantees but shallower circuits. For trainability, commuting-generator circuits enable density model construction with efficiently extractable gradients. The framework connects to various facets of QML including post-variational and measurement-based learning. In classical settings, density models naturally integrate the mixture of experts formalism, and offer natural overfitting mitigation. The framework is versatile - we uplift several quantum models into density versions to improve model performance, or trainability, or both. These include Hamming weight-preserving and equivariant models, among others. Extensive numerical experiments validate our findings.

Problem

• Balancing expressivity and efficient trainability in QML
• Enhancing quantum models with density neural networks
• Mitigating overfitting in classical and quantum settings

Innovation

• Density quantum neural networks with trainable unitaries
• Hastings-Campbell Mixing lemma for shallower circuits
• Commuting-generator circuits enable efficient gradient extraction