# Variational quantum and neural quantum states algorithms for the linear complementarity problem

arXiv: https://arxiv.org/abs/2504.08141 · HTML: https://mlsanity.com/paper/2504.08141/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 26 references that are in the map.
- First posted on arXiv 10 Apr 2025.

## Builds on (most cited first, 6 of 6)

- [Predicting Many Properties of a Quantum System from Very Few Measurements](https://mlsanity.com/paper/2002.08953/) (2020)
- [Deep autoregressive models for the efficient variational simulation of many-body quantum systems](https://mlsanity.com/paper/1902.04057/) (2019)
- [Overcoming barriers to scalability in variational quantum Monte Carlo](https://mlsanity.com/paper/2106.13308/) (2021)
- [NNQS-Transformer: an Efficient and Scalable Neural Network Quantum States Approach for Ab initio Quantum Chemistry](https://mlsanity.com/paper/2306.16705/) (2023)
- [Toward Neural Network Simulation of Variational Quantum Algorithms](https://mlsanity.com/paper/2211.02929/) (2022)
- [An Active Learning Framework for Constructing High-fidelity Mobility Maps](https://mlsanity.com/paper/2003.03517/) (2020)

## Abstract (arXiv)

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.