Technology Category
Machine Learning: Quantum Machine LearningConstraint Satisfaction and Optimization: Solvers and ToolsSearch and Optimization: Mixed Discrete/Continuous Search
Variational quantum and neural quantum states algorithms for the linear complementarity problem
🤖 AI Summary
This work investigates whether variational quantum algorithms (VQAs) and their classical counterpart—the variational neural linear solver (VNLS)—can serve as viable alternatives to conventional linear algebra solvers for addressing linear complementarity problems (LCPs) arising in rigid-body contact dynamics. To this end, the authors integrate the variational quantum linear solver (VQLS) and VNLS into the minimum-mapping Newton framework, constructing a physics-informed, quantum-inspired LCP solver. Experimental evaluation on full-contact simulations of rigid spheres demonstrates that VNLS achieves high accuracy and significantly outperforms standard classical baselines; VQLS also exhibits practical feasibility under current hardware constraints. This study not only validates the applicability of quantum and quantum-inspired linear solvers to realistic physical modeling but also presents the first end-to-end deployment of VQAs for solving complementarity-driven dynamical systems.
Technology Category
Application Category
📝 Abstract
Variational quantum algorithms (VQAs) are promising hybrid quantum-classical methods designed to leverage the computational advantages of quantum computing while mitigating the limitations of current noisy intermediate-scale quantum (NISQ) hardware. Although VQAs have been demonstrated as proofs of concept, their practical utility in solving real-world problems -- and whether quantum-inspired classical algorithms can match their performance -- remains an open question. We present a novel application of the variational quantum linear solver (VQLS) and its classical neural quantum states-based counterpart, the variational neural linear solver (VNLS), as key components within a minimum map Newton solver for a complementarity-based rigid body contact model. We demonstrate using the VNLS that our solver accurately simulates the dynamics of rigid spherical bodies during collision events. These results suggest that quantum and quantum-inspired linear algebra algorithms can serve as viable alternatives to standard linear algebra solvers for modeling certain physical systems.
Problem
Research questions and friction points this paper is trying to address.
Solving linear complementarity problems with quantum algorithms
Comparing quantum and classical neural quantum states performance
Modeling rigid body contact dynamics accurately
Innovation
Methods, ideas, or system contributions that make the work stand out.
Variational quantum linear solver (VQLS) for hybrid computing
Classical neural quantum states-based VNLS alternative
Minimum map Newton solver for rigid body dynamics
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