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Machine-Learning-Assisted Parameterization of Quantum Walk Algorithms

Parham Ghayour

Published Dec 23, 2025• 0 citations
Publisher

Abstract

Abstract Quantum walk algorithms constitute a central primitive in quantum computation, yet their practical performance often depends sensitively on the choice of execution parameters such as walk depth and initial state. Analytical parameter choices are typically conservative and instance-agnostic, which can lead to suboptimal behavior on specific problem instances. In this work, we propose a general framework for machine-learning-assisted parameterization of quantum walk algorithms, in which classical learning is used to adapt algorithmic parameters without modifying the underlying quantum decision logic. The machine learning component op erates exclusively as a classical control layer, preserving correctness guarantees while improving average-case performance. We demonstrate the framework through an application to the s–t connectivity problem, a canonical benchmark in graph algorithms and complexity theory. Classical simulations of discrete-time quantum walks on randomly generated sparse graphs show that ML-assisted pa rameter selection substantially improves success probability compared to fixed-parameter base lines, yielding multiplicative gains in average performance. These improvements are achieved despite only coarse prediction accuracy, highlighting the robustness of the approach. The results suggest a principled role for machine learning as an adaptive optimization layer in quantum algorithms, offering a practical path toward hybrid quantum–classical methods that enhance performance while maintaining theoretical soundness

DOI
10.21203/rs.3.rs-8391412/v1

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Abstract Quantum walk algorithms constitute a central primitive in quantum computation, yet their practical performance often depends sensitively on the choice of execution parameters such as walk depth and initial state. Analytical parameter choices are typically conservative and instance-agnostic, which can lead to suboptimal behavior on specific problem instances. In this work, we propose a general framework for machine-learning-assisted parameterization of quantum walk algorithms, in which classical learning is used to adapt algorithmic parameters without modifying the underlying quantum decision logic. The machine learning component op erates exclusively as a classical control layer, preserving correctness guarantees while improving average-case performance. We demonstrate the framework through an application to the s–t connectivity problem, a canonical benchmark in graph algorithms and complexity theory. Classical simulations of discrete-time quantum walks on randomly generated sparse graphs show that ML-assisted pa rameter selection substantially improves success probability compared to fixed-parameter base lines, yielding multiplicative gains in average performance. These improvements are achieved despite only coarse prediction accuracy, highlighting the robustness of the approach. The results suggest a principled role for machine learning as an adaptive optimization layer in quantum algorithms, offering a practical path toward hybrid quantum–classical methods that enhance performance while maintaining theoretical soundness
Quantum computing has emerged as one of the most influential paradigms capable of transforming computational processes that struggle under classical limitations. In recent years, hybrid quantum–classical algorithms have gained significant attention for their ability to leverage the strengths of both architectures, especially within the Noisy Intermediate-Scale Quantum (NISQ) era. This research paper explores a quantum-enhanced optimization framework designed to improve machine learning model performance through parameterized quantum circuits (PQCs). The goal of this study is to provide a practical, scalable approach that can be integrated into existing machine learning workflows without requiring fully developed fault-tolerant quantum hardware. The proposed framework uses classical preprocessing to encode data into quantum states, followed by quantum transformations that explore richer feature spaces due to quantum superposition and entanglement. A classical optimizer then updates the quantum circuit parameters based on measurement results, forming an end-to-end feedback loop. This hybrid model aims to demonstrate improved optimization efficiency, reduction in loss-function plateaus, and better generalization for specific ML tasks involving small to medium-sized datasets. This paper provides a comprehensive investigation of methodology, literature background, and experimental reasoning with statistical analysis, along with conceptual diagrams illustrating system architecture and circuit layouts. The outcomes further strengthen the viability of hybrid quantum–classical computation as a promising direction for advanced machine learning systems.
Abstract This research presents a comprehensive hybrid quantum classical machine learning framework designed to overcome the computational limitations of classical algorithms when processing high dimensional data. The study integrates parameterized quantum circuits within classical neural network architectures and demonstrates their application across optimization tasks and supervised learning problems. The framework was evaluated on combinatorial optimization benchmarks including Max Cut and Job Shop Scheduling problems alongside classification tasks using quantum annealing based feature selection. Results demonstrate that hybrid quantum classical models achieve faster convergence rates and improved accuracy in high dimensional spaces compared to classical counterparts with the quantum algorithm for Max Cut optimization outperforming complete solution searches on larger problem instances. The findings provide machine learning practitioners and quantum computing researchers with validated hybrid architectures for near term quantum device deployment.
Quantum Machine Learning (QML) has emerged as a promising field with the potential to revolutionize various machine learning tasks. This paper explores the application of quantum algorithms to enhance the optimization process for machine learning models. Specifically, we propose a novel quantum-enhanced parameter adjustment algorithm, termed "Adaptive Quantum Parameter Adjustment" (AQPA), designed to dynamically adjust model parameters based on the learning process. The core of AQPA leverages quantum entanglement and quantum algorithms to achieve a higher degree of optimization efficiency compared to traditional methods. We present a detailed mathematical framework for the algorithm, including the quantum state representations and the adjustment process. The paper discusses the potential benefits of this approach, including improved accuracy, faster convergence, and the ability to handle complex loss functions. We provide a preliminary analysis of the algorithm's performance on several benchmark datasets, demonstrating its effectiveness. The aim is to contribute to the advancement of QML and offer a practical solution for optimizing machine learning models.
Adaptive quantum computing control is important for the stability and efficiency of quantum systems, especially in the presence of dynamic environmental noise and hardware fluctuations. We present a unified strategy for machine learning (ML) techniques to improve adaptive quantum control in two main directions: optimization speed and out-of-sample error. Here, we propose a hybrid learning method combining reinforcement learning (RL), deep neural networks (DNNs), and quantum-inspired models to actively and adaptively update quantum gate parameters and error mitigation strategies on the fly. Embedding of quantum noise models directly into the learning allows the system to predict and correct for decoherence, gate errors and measurement inaccuracy before they affect computational fidelity. Using extensive simulations as well as experimental validation on noisy intermediate-scale quantum (NISQ) processors, our improved ML model achieves a substantially higher fidelity and robustness compared to standard model-free and static control approaches. We introduce a novel feedback-loop mechanism based on online learning algorithms enabling the system to adjust for changing noise profiles and hardware drift without retraining. The optimization part uses metaheuristic methods to quickly converge to control parameters that perform well, and the error prevention mechanism features anomaly detection and prediction correction layers to minimize the effects of cumulative decoherence. The results demonstrate that our adaptive control framework can be used to not only speed up the convergence in training quantum algorithms, but also sustain the performance of gates against error at a variety of error rates with the reduction of the real-time impact of the error up to 35 %. This work highlights the promise of machine learningaugmented quantum control for improving reliability and scalability in quantum computing and serves as a stepping stone for future incorporation with fault-tolerant designs.
Quantum Machine Learning (QML) is a rapidly evolving field that leverages the unique properties of quantum systems to solve complex computational problems. Traditional machine learning algorithms often struggle with scaling to larger datasets and complex models, limiting their applicability in diverse domains. This paper introduces a novel adaptive parameter adjustment algorithm for quantum machine learning, aiming to address these limitations by dynamically adjusting model parameters during training. The core mechanism involves a feedback loop that continuously optimizes parameters based on observed performance, leading to improved model accuracy and generalization capabilities. The proposed algorithm offers a significant advancement over existing techniques by providing a more flexible and responsive approach to parameter tuning. This research explores the potential of this adaptive approach to enhance the performance of various quantum machine learning models.
Quantum Machine Learning (QML) utilizes the principles of quantum computations to improve the performance of learning by the use of parameterized quantum circuits and variational algorithms. But despite the qubit number, circuit depth, and patterns of entanglement, creating the optimal quantum circuit architectures for particular machine learning applications remains an important problem. Fixed circuits, or classical Neural Architecture Search (NAS), are not enough to transfer knowledge to other tasks and/or to search the quantum search space efficiently. In this context, this paper presents an Adaptive Quantum Circuit Architecture Search (AQ CAS) framework that dynamically generates and optimizes quantum circuit architectures using a hybrid search algorithm that integrates reinforcement learning, evolutionary operators, and evaluation without gradient. AQ CAS involves a task-specific feedback mechanism to eliminate those candidates that perform poorly and concentrate the search on those candidates with good performance. The framework is evaluated on benchmark data sets such as Iris, synthetic classical ML tasks, and hybrid quantum-classical tasks, and compared to fixed circuits, existing quantum NAS methods, and classical machine learning models. Experimental results indicate that AQ CAS can achieve higher accuracy for the task, using fewer qubits, fewer layers, and less training time, which further shows the need for adaptivity and task specialization. These results inform us about efficient hybrid classical-quantum pipelines, and give a glimpse of the directions that adaptive architecture search might take in enabling scalable and practical QML deployment.