Quantum computing sets the foundation for new ways of designing algorithms, thanks to the peculiar properties inherited by quantum mechanics. The exploration of this new paradigm faces new challenges concerning which field quantum speedup can be achieved. Toward finding solutions, looking for the design of quantum subroutines that are more efficient than their classical counterpart poses solid pillars to new powerful quantum algorithms. Herewith, we delve into a grounding subroutine, the computation of the variance, whose usefulness spaces across different fields of application, particularly the artificial intelligence (AI) one. Indeed, the finding of the quantum counterpart of these building blocks impacts vertically those algorithms that leverage this metric. In this work, we propose QVAR, a quantum subroutine, to compute the variance that exhibits a logarithmic complexity both in the circuit depth and width, excluding the state preparation cost. With the vision of showing the use of QVAR as a subroutine for new quantum algorithms, we tackle two tasks from the AI domain: feature selection and outlier detection. In particular, we showcase two AI hybrid quantum algorithms that leverage QVAR: the hybrid quantum feature selection (HQFS) algorithm and the quantum outlier detection algorithm (QODA). In this manuscript, we describe the implementation of QVAR, HQFS, and QODA, providing their correctness and complexities and showing the effectiveness of these hybrid quantum algorithms with respect to their classical counterpart.
Quantum computing sets the foundation for new ways of designing algorithms, thanks to the peculiar properties inherited by quantum mechanics. The exploration of this new paradigm faces new challenges concerning which field quantum speedup can be achieved. Toward finding solutions, looking for the design of quantum subroutines that are more efficient than their classical counterpart poses solid pillars to new powerful quantum algorithms. Herewith, we delve into a grounding subroutine, the computation of the variance, whose usefulness spaces across different fields of application, particularly the artificial intelligence (AI) one. Indeed, the finding of the quantum counterpart of these building blocks impacts vertically those algorithms that leverage this metric. In this work, we propose QVAR, a quantum subroutine, to compute the variance that exhibits a logarithmic complexity both in the circuit depth and width, excluding the state preparation cost. With the vision of showing the use of QVAR as a subroutine for new quantum algorithms, we tackle two tasks from the AI domain: feature selection and outlier detection. In particular, we showcase two AI hybrid quantum algorithms that leverage QVAR: the hybrid quantum feature selection (HQFS) algorithm and the quantum outlier detection algorithm (QODA). In this manuscript, we describe the implementation of QVAR, HQFS, and QODA, providing their correctness and complexities and showing the effectiveness of these hybrid quantum algorithms with respect to their classical counterpart.
The promise of quantum computation to achieve a speedup over classical computation led to a surge of interest in exploring new quantum algorithms for data analysis problems.Feature Selection, a technique that selects the most relevant features from a dataset, is a critical step in data analysis.With several Quantum Feature Selection techniques proposed in the literature, this study exhibits the potential of quantum algorithms to enhance Feature Selection and other tasks that leverage the variance.This study proposes a novel quantum algorithm for estimating the variance over a set of real data.Importantly, after state preparation, the algorithm's complexity exhibits logarithmic characteristics in both its width and depth.The quantum algorithm applies to the Feature Selection problem by designing a Hybrid Quantum Feature Selection (HQFS) algorithm.This work showcases an implementation of HQFS and assesses it on two synthetic datasets and a real dataset.* This study was carried out within the National Centre on HPC, Big Data and Quantum Computing -SPOKE 10 (Quantum Computing) and received funding from the European Union Next-GenerationEU -National Recovery and Resilience Plan (NRRP) -MISSION 4, COMPONENT 2 -CUP N. I53C22000690001.This manuscript reflects only the authors' views and opinions, neither the European Union nor the European Commission can be considered responsible for them.
Quantum computing exploits superposition, entanglement, and interference to address problems beyond classical reach, yet current devices are limited by noise and scale. Hybrid quantum–classical approaches therefore play a key role in achieving near-term utility by integrating quantum subroutines into classical workflows. Within this setting, Quantum Artificial Intelligence (QAI) offers new opportunities for machine learning. This thesis focuses on unsupervised Quantum Machine Learning, motivated by the abundance of unlabeled data and the importance of tasks such as clustering, dimensionality reduction, and anomaly detection. We study how to design hardware-efficient quantum subroutines, identify unsupervised paradigms well suited to hybrid computation, and assess potential advantages over classical methods. The contributions include a critical review of existing QAI approaches, the development of shallow-depth quantum subroutines for core operations, and the proposal of hybrid algorithms evaluated on synthetic and real datasets. The results highlight when quantum components provide practical value and clarify trade-offs between performance and complexity under current hardware constraints.
Quantum AI is a new way to think about the future of Artificial Intelligence through the merging of two technologies: quantum computing and advanced machine learning. Quantum AI has the potential to provide solutions to computationally difficult problems that traditional systems cannot solve. Quantum AI's continued success will rely on advancements in hybrid quantum-classical solutions, as well as the expansion of quantum hardware; hence, research remains necessary to conduct systematic benchmarks as well as performance analysis in order to determine both how well quantum AI algorithms perform practically, and where their limitations lie. In this chapter, detailed examinations of benchmarks that have been developed specifically for quantum AI are presented alongside evaluative metrics across various key areas of performance including algorithmic efficiency, scalability, noise immunity, and resource use for various types of quantum architectures. The chapter integrates dialogue between theory and practice to demonstrate ways in which performance metrics (i.e., quantum circuit depth, fidelity, convergence behaviour and computational complexity) can effectively compare Quantum AI algorithms to classical algorithms. Particular attention is given to hybrid variational algorithms, quantum-enhanced optimization algorithms, and quantum machine learning. Using benchmark datasets, simulation frameworks and new evaluation methods, there are several challenges in terms of reproducibility, hardware variability and algorithm/hardware co-design that emerge through analysis of the above metrics as well. Aside from focusing on a more broad view of how Performance Evaluation relates to developing more effective Quantum AI Solutions. In addition to viewing Benchmarking as a technical exercise solely, this chapter provides a more holistic view in relation to a human perspective of the situation. This paper outlines how performance evaluation practices can be used as a considerable and well-designed means of bridging the gap between the promise of Quantum Technology at an abstract level, and the ability of Quantum Technology to produce tangible outcomes in the real world by adopting a more comprehensive Governance-oriented approach to Benchmarking Quantum AI Systems. The purpose of this chapter is to assist the growing community of researchers, practitioners, and Strategic Technology Professionals by providing them with a clear and structured framework for Evaluation of Quantum AI Algorithms. There is a significant focus of the chapter on establishing important reference points that organizations can use to determine when an intelligent system has successfully achieved a true and validated quantum advantage. The ultimate goal is to assist in guiding the responsible development and implementation of Quantum AI to enable the Potential Benefits of Quantum AI to be realized, in ways that are meaningful and impactful.
Hybrid quantum-classical algorithms represent the dominant computational paradigm for near-term quantum advantage: classical co-processors handle data pre-processing, parameter optimisation, and post-processing, while quantum processors execute short-depth circuits that exploit superposition and entanglement for tasks classically hard to simulate. Despite growing interest, a systematic framework for designing, benchmarking, and selecting hybrid architectures across diverse computational task categories has been absent. This paper proposes the Hybrid Quantum-Classical Algorithm Design (HQCAD) framework, covering four hybrid paradigms: Variational Quantum-Classical Loops (VQCL) for optimisation and ground-state estimation; Quantum-Enhanced Machine Learning (QEML) combining quantum feature maps with classical classifiers; Quantum-Classical Divide-and-Conquer (QCDC) for graph and combinatorial problems; and Quantum-Accelerated Monte Carlo (QAMC) for sampling-based inference. HQCAD is benchmarked on six tasks -- molecular ground-state energy, binary classification, graph partitioning, financial Monte Carlo, protein fold scoring, and logistics routing -- on IBM Quantum Eagle (127-qubit) and IonQ Aria (25-qubit). VQCL achieves chemical accuracy (error < 1.6 mHa) for H2O ground-state energy. QEML achieves test AUC = 0.924 vs. classical SVM 0.884 on a quantum-advantage dataset. QAMC delivers 8.4x variance reduction for financial option pricing vs. classical Monte Carlo at equal shot budget. HQCAD provides a task-adaptive hybrid algorithm selection methodology validated across six computational domains.
Quantum Artificial Intelligence (Quantum AI) embodies the integration of quantum computational paradigms with artificial intelligence frameworks to address the computational intractability and scalability constraints inherent in classical AI systems. By leveraging quantum mechanical properties such as superposition, entanglement, and quantum interference, Quantum AI enables enhanced representation learning, accelerated optimization, and improved probabilistic inference in high-dimensional problem spaces. In parallel, deep-tech innovations—including advanced deep learning architectures, neuromorphic computing, and edge-based intelligent processing—are redefining the architectural foundations of next- generation intelligent systems through energy-efficient, adaptive, and real-time computation. This paper presents a technically rigorous and comprehensive review of Quantum AI and deep-tech innovations, focusing on algorithmic formulations, architectural models, and system-level integration strategies. Core methodologies such as quantum machine learning algorithms, parameterized quantum circuits, variational quantum algorithms, and hybrid quantum–classical optimization frameworks are critically analysed with respect to computational complexity, repressibility, and feasibility on noisy intermediate-scale quantum (NISQ) hardware. Additionally, the role of neuromorphic computing in enabling spiking neural architectures and event-driven processing is examined as a complementary paradigm to quantum-enhanced learning models, particularly for low-power and latency-critical applications. The paper further investigates application- driven deployments of Quantum AI across domains including medical diagnostics, cryptographic security, autonomous decision-making, and smart cyber-physical systems, highlighting performance trade-offs and implementation constraints. Key challenges such as quantum noise, decoherence, data encoding bottlenecks, limited qubit connectivity, and ethical governance are systematically discussed. Finally, future research directions are identified, emphasizing fault-tolerant quantum learning architectures, scalable hybrid integration with deep-tech systems, and co-design methodologies for realizing practical next-generation intelligence platforms.
Quantum-AI hybrid algorithms represent the most practical near-term pathway for leveraging quantum computing's probabilistic power alongside classical AI's scalability and optimization strengths. In the noisy intermediate-scale quantum (NISQ) era, these hybrids—primarily variational quantum algorithms (VQAs) such as the Variational Quantum Eigensolver (VQE) and Quantum Approximate Optimization Algorithm (QAOA)—delegate hard subproblems (e.g., high-dimensional sampling, optimization under quantum constraints, or feature extraction in entangled spaces) to quantum processors while classical optimizers or neural networks handle parameter tuning, error mitigation, and large-scale data processing (Ferguson et al., 2026; Acampora, 2026). This exploration builds on the 2025 NSF AI+MPS community paper by integrating accelerated timelines: mass deployment of utility-scale quantum computing by August 2027 and AGI substantially before 2030. Hybrid approaches become critical enablers for MPS grand challenges in Mamun, SM (2026)…………………………………………1 Quantum-AI Hybrid Algorithms: Bridging Classical Intelligence, Quantum Acceleration, and Scientific Discovery in the MPS Domains (Vol-I) chemistry (molecular ground states), materials (inverse design), physics (many-body simulation), and astronomy (anomaly detection under uncertainty). Also available on Academia.edu: https://www.academia.edu/attachments/132469868/download_file?s=portfolio