Imposing Constraints on Quantum Machine Learning Models - College of Engineering - Purdue University

Project Description

Using parameterized quantum circuits (PQCs) as machine learning (ML) models has been identified as one area where quantum computing could potentially exhibit an edge over classical computing. Similar to a deep neural network (DNN), a PQC or quantum neural network (QNN) can be trained to learn a mapping between features and target data by tuning externally controlled parameters using a classical computer. Recent results demonstrate that QNNs can serve as universal approximators using fewer trainable parameters compared to DNNs, while depending on the quantum observable, they may be computationally more efficient during inference. To improve upon generalization and ensure safety, this project focuses on imposing constraints and other desirable properties to QNNs. We have recently put forth a comprehensive framework for solving large-scale optimization problems with constraints using PQCs. We have also shown the speedups possible with quantum computing in reinforcement learning. The focus of this project is to extend those results to the machine learning setting, where some of the PQC parameters are used to encode data. The goal is to endow QML models with safety, stability, or other desirable properties.

Start Date

November 1, 2025

Postdoc Qualifications

A Ph.D. in Electrical/Computer/Industrial Engineering, Computer Science, or (Applied) Math, expertise in quantum computing and optimization, a strong analytical background, and the ability to work both independently and collaboratively. 

Co-advisors

Vassilis Kekatos, kekatos@purdue.edu, Associate Professor, Elmore Family School of Electrical and Computer Engineering, https://engineering.purdue.edu/~kekatos/.

Vaneet Aggarwal, vaneet@purdue.edu, Professor, Edwardson School of Industrial Engineering, ECE(c), and CS(c), https://engineering.purdue.edu/CLANLabs.

Bibliography

1. T. V. Le, M. M. Wilde, and V. Kekatos, "Solving Optimal Power Flow using a Variational Quantum Approach," Quantum, (submitted September 2025). [https://arxiv.org/abs/2509.00341]
2. T. V. Le and V. Kekatos, "Solving Constrained Optimization Problems via the Variational Quantum Eigensolver with Constraints," Physical Review A, Vol. 110, No. 2, pp. 1-19, Aug. 2024.
3. Dhrumil Patel, Patrick J. Coles, and Mark M. Wilde. “Variational Quantum Algorithms for Semidefinite Programming”. Quantum, 8, p. 1374 (2024).
4. Z. Yu, Q. Chen, Y. Jiao, Y. Li, X. Lu, X. Wang, and J. Yang, “Non-asymptotic approximation error bounds of parameterized quantum circuits,” Advances in Neural Information Processing Systems, vol. 37, pp. 99 089–99 127, Sep 2024.
5. Yang Xu and Vaneet Aggarwal, "Accelerating Quantum Reinforcement Learning with a Quantum Natural Policy Gradient Based Approach," in Proc. ICML, Jul 2025.