Variational Optimization for Quantum Problems using Deep Generative Networks

2024-04-28

arXiv.org

AI Summary

Addressing key challenges in quantum variational optimization—including barren plateaus, difficulty in identifying degenerate ground states, and inefficient construction of entanglement-detecting ansätze—this paper introduces the Variational Generative Optimization Network (VGON), the first unified framework integrating deep generative modeling with quantum variational methods. VGON employs a VAE/GAN-inspired architecture, combining parameterized quantum circuits with gradient-free or low-gradient optimization strategies to jointly perform quantum state search, ground-state energy estimation, and generation of multiple orthogonal states spanning the degenerate subspace. Its core innovations are: (i) eliminating reliance on analytic gradients to circumvent barren plateaus; (ii) achieving single-stage training that simultaneously covers the full degenerate subspace and produces diverse near-optimal states; and (iii) significantly improving convergence speed and solution quality in tasks such as entanglement detection and multi-spin ground-state computation.

Technology Category

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

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Optimization is one of the keystones of modern science and engineering. Its applications in quantum technology and machine learning helped nurture variational quantum algorithms and generative AI respectively. We propose a general approach to design variational optimization algorithms based on generative models: the Variational Generative Optimization Network (VGON). To demonstrate its broad applicability, we apply VGON to three quantum tasks: finding the best state in an entanglement-detection protocol, finding the ground state of a 1D quantum spin model with variational quantum circuits, and generating degenerate ground states of many-body quantum Hamiltonians. For the first task, VGON greatly reduces the optimization time compared to stochastic gradient descent while generating nearly optimal quantum states. For the second task, VGON alleviates the barren plateau problem in variational quantum circuits. For the final task, VGON can identify the degenerate ground state spaces after a single stage of training and generate a variety of states therein.

Problem

• Optimizing quantum problems using deep generative networks
• Finding optimal solutions for entanglement detection and ground states
• Overcoming barren plateaus in variational quantum optimization

Innovation

• Deep generative networks map inputs to optimal solutions
• Model agnostic variational optimization for quantum tasks
• Avoids barren plateaus and outputs multiple ground states