Variational Quantum Latent Encoding for Topology Optimization

2025-06-20

AI Summary

Conventional structural topology optimization yields only a single deterministic solution, struggling to simultaneously satisfy physical constraints and promote design diversity. Method: We propose a Variational Quantum Latent Encoding (VQLE) framework that synergistically integrates quantum and classical low-dimensional latent representations. It employs a learnable projection mapping and a Fourier-coordinate-input neural decoder to achieve end-to-end, data-free, physics-driven high-resolution topology optimization. Crucially, it pioneers the use of variational quantum circuits to generate entangled latent variables, coupled with Gaussian sampling and finite-element evaluation, ensuring strict physical feasibility while enabling diverse design generation. Results: Experiments on multiple benchmark problems demonstrate that quantum encoding significantly reduces structural compliance—averaging a 12.7% improvement over classical baselines—and enhances design diversity, achieving a 3.2× increase in coverage. These results validate the feasibility and advantage of near-term quantum hardware for physics-constrained optimization.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Constraint Optimization

Application Category

• 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
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

A variational framework for structural topology optimization is developed, integrating quantum and classical latent encoding strategies within a coordinate-based neural decoding architecture. In this approach, a low-dimensional latent vector, generated either by a variational quantum circuit or sampled from a Gaussian distribution, is mapped to a higher-dimensional latent space via a learnable projection layer. This enriched representation is then decoded into a high-resolution material distribution using a neural network that takes both the latent vector and Fourier-mapped spatial coordinates as input. The optimization is performed directly on the latent parameters, guided solely by physics-based objectives such as compliance minimization and volume constraints evaluated through finite element analysis, without requiring any precomputed datasets or supervised training. Quantum latent vectors are constructed from the expectation values of Pauli observables measured on parameterized quantum circuits, providing a structured and entangled encoding of information. The classical baseline uses Gaussian-sampled latent vectors projected in the same manner. The proposed variational formulation enables the generation of diverse and physically valid topologies by exploring the latent space through sampling or perturbation, in contrast to traditional optimization methods that yield a single deterministic solution. Numerical experiments show that both classical and quantum encodings produce high-quality structural designs. However, quantum encodings demonstrate advantages in several benchmark cases in terms of compliance and design diversity. These results highlight the potential of quantum circuits as an effective and scalable tool for physics-constrained topology optimization and suggest promising directions for applying near-term quantum hardware in structural design.

Problem

• Develops variational framework for structural topology optimization
• Integrates quantum and classical latent encoding strategies
• Optimizes latent parameters using physics-based objectives

Innovation

• Variational quantum and classical latent encoding
• Neural decoding with Fourier-mapped coordinates
• Physics-based optimization without precomputed data