Image retrieval systems rely heavily on computing similarity between high-dimensional feature vectors, an operation that grows computationally expensive as databases scale. Recent advances in quantum computing offer promising alternatives through quantum inner product algorithms. This chapter presents a comprehensive experimental comparison of two approaches: the Swap Test-based Quantum Inner Product (ST-QIP) and the Amplitude Estimation-based Quantum Inner Product (AE-QIP). Through systematic evaluation across feature dimensions ranging from 4 to 32, the chapter analyzes performance characteristics, resource requirements, and practical trade-offs. The experiments reveal that ST-QIP achieves superior accuracy, with an average error of 0.350 compared to AE-QIP's 1.045, while AE-QIP demonstrates a 5.45× speed advantage. The theoretical complexity scaling of O(1/ε^2) for ST-QIP and O(1/ε) for AE-QIP is empirically validated, achieving up to 1000× sample complexity reduction. These findings offer practical guidelines for algorithm selection based on application requirements.
Image retrieval systems rely heavily on computing similarity between high-dimensional feature vectors, an operation that grows computationally expensive as databases scale. Recent advances in quantum computing offer promising alternatives through quantum inner product algorithms. This chapter presents a comprehensive experimental comparison of two approaches: the Swap Test-based Quantum Inner Product (ST-QIP) and the Amplitude Estimation-based Quantum Inner Product (AE-QIP). Through systematic evaluation across feature dimensions ranging from 4 to 32, the chapter analyzes performance characteristics, resource requirements, and practical trade-offs. The experiments reveal that ST-QIP achieves superior accuracy, with an average error of 0.350 compared to AE-QIP's 1.045, while AE-QIP demonstrates a 5.45× speed advantage. The theoretical complexity scaling of O(1/ε^2) for ST-QIP and O(1/ε) for AE-QIP is empirically validated, achieving up to 1000× sample complexity reduction. These findings offer practical guidelines for algorithm selection based on application requirements.
The measurement of image similarity represents a fundamental task within the domain of image processing, enabling the application of sophisticated computational techniques to ascertain the degree of similarity between two images. To enhance the performance of these similarity measurement algorithms, the academic community has investigated a range of quantum algorithms. Notably, the swap test-based quantum inner product algorithm (ST-QIP) has emerged as a pivotal method for computing image similarity. However, the inherent destructive nature of the swap test necessitates multiple quantum state evolutions and measurements, which leads to consumption of quantum resources and prolonged computational time, ultimately constraining its practical applicability. To address these limitations, this study introduces an advanced quantum inner product algorithm based on amplitude estimation (AE-QIP) designed to compute image similarity. This innovative approach circumvents the repetitive measurement processes associated with the swap test, thereby optimizing the utilization of quantum resources and substantially enhancing the algorithm's performance. We conducted experiments using a quantum simulator to implement the AE-QIP algorithm and evaluate its effectiveness in the image retrieval tasks. It is found that the AE-QIP algorithm achieves comparable precision to the ST-QIP algorithm while exhibiting significant reductions in qubit consumption and average processing time. Additionally, our findings suggest that increasing the number of ancillary qubits can further enhance the accuracy of the AE-QIP algorithm. Overall, within the acceptable error thresholds, the AE-QIP algorithm exhibits enhanced efficiency relative to the ST-QIP algorithm. However, significant further research is needed to address the challenges involved in optimizing the performance of quantum retrieval systems as a whole.
The exponential growth of high-dimensional data in domains such as computer vision, genomics, and natural language processing has made similarity search a foundational yet challenging operation, primarily due to the "curse of dimensionality" that forces classical systems into computationally prohibitive exhaustive searches. This comprehensive report examines the transformative potential of integrating quantum computing to circumvent these classical bottlenecks. Quantum similarity search utilizes superposition and entanglement to evaluate exponential state spaces, promising quadratic speedups over classical algorithms. The analysis details the transition from classical indexing innovations like memory vectors to modalities of quantum data encoding, notably Amplitude Encoding and the Quantum Pixel Mamun, SM (2026) ……………………………………1 Quantum Similarity Search: Bridging Classical and Quantum Paradigms in High-Dimensional Data Retrieval Representation (QPIXL). It critically assesses vanguard quantum algorithms, particularly the Amplitude Estimation-based Quantum Inner Product (AE-QIP)—which provides a deterministic quadratic speedup over the prohibitive SWAP test—and Quantum Unsupervised Similarity Learning (QUSL), which uses evolutionary algorithms to optimize quantum circuits for complex tasks like image retrieval. Also available on Academia.edu: https://www.academia.edu/attachments/132047821/download_file?s=portfolio
Quantum Image Representation (QIR) has become a key component of Quantum Image Processing (QIP), enabling the encoding and manipulation of visual data within quantum computing environments.Its integration with Quantum Artificial Intelligence (QAI) and Quantum Machine Learning (QML) has attracted significant research interest due to the potential advantages of quantum parallelism and compact data representation.This survey reviews major QIR techniques, analyzes their encoding strategies and computational characteristics, and examines their opportunities, challenges, and future relevance in quantum AI and machine learning applications.A systematic review of 70 peer-reviewed journal and conference publications published between 1992 and 2025 was conducted.The selected studies were evaluated based on encoding mechanisms, qubit requirements, circuit complexity, retrieval capability, scalability, and suitability for quantum image processing and learning tasks.The review covers prominent QIR models, including FRQI, NEQR, MCQI, QPIE, GQIR, QRMW, and tensor-network-based representations.Comparative analysis reveals important trade-offs between qubit efficiency, encoding complexity, retrieval accuracy, and scalability.Amplitude-based approaches provide compact image encoding but suffer from probabilistic retrieval, whereas basis-state representations offer deterministic recovery at the expense of increased circuit complexity.QIR demonstrates significant potential in image classification, feature extraction, image compression, and hybrid quantum-classical learning frameworks.QIR provides a promising foundation for next-generation quantum-enhanced visual intelligence systems.However, practical implementation remains constrained by state preparation overhead, noise, decoherence, limited qubit availability, and the lack of standardized evaluation frameworks.Future research should focus on scalable encoding methods, fault-tolerant quantum architectures, benchmarking standards, and deeper integration with advanced QML models to accelerate the development of practical quantum image analytics.
Quantum machine learning promises computational advantages for certain tasks, yet rigorous empirical evaluation of quantum clustering algorithms against classical baselines remains limited. This paper presents a comprehensive implementation and comparative analysis of two quantum K-means clustering algorithms—SWAP Test-based and Quantum Fidelity-based—against classical K-means on benchmark datasets. Both quantum approaches employ amplitude encoding to map classical data into quantum state amplitudes and use quantum-native distance metrics derived from inner products in Hilbert space. All three methods are evaluated on the ENB2012 energy efficiency dataset (768 samples, 8 features) and a synthetically expanded high-dimensional dataset (4,998 samples, 16 features), measuring silhouette score, inertia, and wall-clock execution time across cluster counts k ∈ {2, . . . , 7}. The experiments, conducted on Qiskit’s AerSimulator and Statevector backends, show that classical K-means achieves substantially higher silhouette scores (0.391 vs. 0.031 on the original dataset) and orders-of-magnitude faster execution. A rigorous analysis attributes these results to three factors: (i) the information loss inherent in amplitude encoding normalization, (ii) the geometric mismatch between Euclidean and Hilbert-space distance metrics, and (iii) the absence of quantum parallelism in classical simulation. The implications for quantum advantage in unsupervised learning are discussed and concrete requirements for near-term quantum hardware to achieve competitive clustering performance are outlined.
Retrieval-Augmented Generation (RAG) systems rely on high-dimensional vector similarity search to retrieve relevant documents for large language models. However, classical nearest-neighbor methods face scalability limits dueto the "curse of dimensionality" and the computational cost of comparing massive vector sets.The authors propose a hybrid quantum-classical pipeline that leverages quantum computing for similarity evaluation.Experimental results on synthetic data demonstrate that the swap-test similarity estimates closely match classical dot products, and that clustering dramatically reduces search overhead.The present studies show the feasibility of quantum-enhanced retrieval: the quantum similarity scores approximate classical results within statistical error.We discuss accuracy, runtime trade-offs, and the challenges of state preparation in the Noisy Intermediate-Scale Quantum (NISQ) era.
For the essential operation, namely inner product (IP) as widely adopted in classic computing e.g. matrix multi-plication, its quantum counterpart: quantum inner product (QIP), has also been recently theoretically explored with a verifiable lower complexity on quantum computers. How-ever, it remains unclear for the embodiment of the quantum circuits (QC) for QIP, let alone a (thorough) evaluation of the QIP circuits, especially in a practical context in the NISQ era by applying QIP to ML via hybrid quantum-classic pipelines. In this paper, we carefully design the QIP circuits from scratch, whose complexity is in accordance with the theoretical complexity. To make the simulation tractable on classic computers, especially when it is integrated in the gradient-based hybrid ML pipelines, we further devise a highly-efficient simulation scheme by directly simulates the output state. Experiments show that the scheme acceler-ates the simulation for more than 68k times compared with the previous circuit simulator. This allows our empirical evaluation on typical machine learning tasks, ranging from supervised and self-supervised learning via neural nets, to K-Means clustering. The results show that the calculation error brought by typical quantum mechanisms would incur in general little influence on the final numerical results given sufficient qubits. However, certain tasks e.g. ranking in K-Means could be more sensitive to quantum noise.