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arXiv:2504.13041

QI-MPC: A Hybrid Quantum-Inspired Model Predictive Control for Learning Optimal Policies

Muhammad Al-Zafar Khan, Jamal Nazzal Al-Karaki

Published Apr 17, 2025• 0 citations
arXivHTMLPDF

Abstract

In this paper, we present Quantum-Inspired Model Predictive Control (QIMPC), an approach that uses Variational Quantum Circuits (VQCs) to learn control polices in MPC problems. The viability of the approach is tested in five experiments: A target-tracking control strategy, energy-efficient building climate control, autonomous vehicular dynamics, the simple pendulum, and the compound pendulum. Three safety guarantees were established for the approach, and the experiments gave the motivation for two important theoretical results that, in essence, identify systems for which the approach works best.

DOI
10.48550/arxiv.2504.13041

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In this paper, we present Quantum-Inspired Model Predictive Control (QIMPC), an approach that uses Variational Quantum Circuits (VQCs) to learn control polices in MPC problems. The viability of the approach is tested in five experiments: A target-tracking control strategy, energy-efficient building climate control, autonomous vehicular dynamics, the simple pendulum, and the compound pendulum. Three safety guarantees were established for the approach, and the experiments gave the motivation for two important theoretical results that, in essence, identify systems for which the approach works best.
We introduce a new hybrid quantum-classical algorithm inspired by an advanced control strategy known as model predictive control (MPC). This algorithm unifies the optimization-based design of variational quantum algorithms (VQAs) with the feedback-based design of feedback-based quantum algorithms (FQAs). Variational circuit parameters are optimized using a layer-wise receding horizon strategy, where observable measurements after every layer initialize a classically simulated dynamic model used to predict quantum state evolution and optimize over future parameterized gates. This hybrid algorithm can be used for applications such as ground state preparation and approximate combinatorial optimization, and presents an ideal use case for the integration of quantum computers with high-performance computing, where the latter resource can be used to increase the scale and efficiency of the predictions critical to MPC. We show through mathematical proof and numerical evidence that the MPC-based algorithm can be guaranteed to at least match the performance of FQAs. Through simulations on Max-Cut problems and a two-dimensional transverse-field Ising model, we demonstrate that relaxed implementations of the MPC-based algorithm can also provide improved performance in practice compared to an FQA.
This paper presents a novel Lyapunov-Based Quantum Reinforcement Learning (LQRL) framework that integrates quantum policy optimization with Lyapunov stability analysis for continuous-time vehicle control. The proposed approach combines the representational power of variational quantum circuits (VQCs) with a stability-aware policy gradient mechanism to ensure asymptotic convergence and safe decision-making under dynamic environments. The vehicle longitudinal control problem was formulated as a continuous-state reinforcement learning task, where the quantum policy network generates control actions subject to Lyapunov stability constraints. Simulation experiments were conducted in a closed-loop adaptive cruise control scenario using a quantum-inspired policy trained under stability feedback. The results demonstrate that the LQRL framework successfully embeds Lyapunov stability verification into quantum policy learning, enabling interpretable and stability-aware control performance. Although transient overshoot and Lyapunov divergence were observed under aggressive acceleration, the system maintained bounded state evolution, validating the feasibility of integrating safety guarantees within quantum reinforcement learning architectures. The proposed framework provides a foundational step toward provably safe quantum control in autonomous systems and hybrid quantum-classical optimization domains.
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Reinforcement learning (RL) is considered a powerful technology with the potential to revolutionize quantum control. However, the application effectiveness of traditional RL is often limited by some insurmountable experimental conditions. Thus, developing new RL algorithms that can efficiently manipulate the quantum system dynamics is a crucial task. Prior research has shown that incorporating quantum mechanical properties into RL can improve learning performance. In this article, we consider the quantum control problem where only the target state can be accurately identified and introduce a quantum-inspired RL (QiRL) method. In particular, we propose a quantum-inspired exploration strategy to replace a commonly used$\epsilon $-greedy strategy, as well as a quantum-inspired reward scheme to incentivize the learning agent. Numerical results on three quantum system control problems, i.e., one-qubit closed quantum system, two-level open quantum system, and many-qubit closed quantum system, verify the effectiveness of QiRL. Comparison results show that the proposed QiRL outperforms existing RL algorithms (deep Q-network and proximal policy optimization) in terms of stability and efficiency for solving quantum control problems.
This research presents an ensemble Reinforcement Learning (RL) approach that combines Deep Q-Network (DQN) and Proximal Policy Optimization (PPO) algorithms to tackle quantum control problems. This research aims to use the complementary strengths of DQN and PPO algorithms to develop robust and adaptive control policies for noisy and uncertain quantum systems. We comprehensively analyse the proposed ensemble learning, including algorithmic details, implementation specifics, and experimental results. Through extensive experimentation and evaluation, we demonstrate the effectiveness of the ensemble approach in learning control strategies for manipulating quantum systems towards a random target state. The results highlight the potential of ensemble RL techniques in addressing the challenges of quantum control tasks, such as system noise and dynamics. By integrating multiple RL agents within an ensemble framework, We aim to advance current developments in quantum control and create a new path for the development of adaptive control systems for quantum systems. The performance of the ensemble model is assessed against Gradient Ascent Pulse Engineering (GRAPE) and robust Model Predictive Control (MPC) to demonstrate its efficiency in highly challenging and noisy environments.
The potential for greater algorithmic efficiency for some problems on quantum computers compared to classical computers is appealing in many fields including, for example, the process systems engineering field. While quantum algorithms have been studied for a variety of applications related to optimization, molecular modeling, and machine learning, there remain many applications in process systems engineering, including process control, where it is not clear how quantum computing algorithms would be beneficial. One idea for attempting to understand when a quantum algorithm might provide benefits for control is to start with algorithms that would be expected to benefit “similar” problems (e.g., optimization problems) and to see if controllers can be implemented within those algorithmic frameworks. Therefore, in this work, we study the use of a quantum computing algorithm related to Grover’s algorithm, which is an amplitude amplification strategy that can search an unordered list with improved efficiency compared to a classical algorithm for the task. It has been extended to perform a search for optimal paths over a graph. Given its potential utility for search and optimization, this is an example of an algorithm where we might wonder if it could be adjusted or used to provide speed-ups for large control problems if the controller could function within this algorithmic framework. This work provides the first steps toward attempting to address this question by investigating how optimization-based control problems would fit into this framework. A process described by ẋ=x+u is considered as a test case. The modified Grover’s algorithm requires the optimization problem to be mapped into quantum gates. We discuss ideas for attempting to represent an optimization-based controller known as model predictive control (MPC) in the modified Grover’s algorithm framework. We test how various parameters of the control and quantum algorithm designs, including fundamental parameters in MPC such as the number of sampling periods and length of the sampling periods, impact the success of using the quantum algorithm for the MPC. We provide analyses regarding why the results are what they are to give perspective on how quantum computing algorithms work and intersect with engineering problems.