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Quantum Block-Matching Algorithm using Dissimilarity Measure

M. Martínez-Felipe, J. Montiel-Pérez, V. Onofre, A. Maldonado-Romo, Ricky Young

TL;DR

This paper formulates a quantum block-matching algorithm that uses a dissimilarity measure based on the Euclidean distance $D$ to locate similar image blocks within a search region. It explores two quantum routes: a QFT-based Draper adder and a quantum Swap Test with amplitude-encoded blocks, combined with a hierarchical search to reduce vector size. Classical preprocessing reduces images to $64 \times 64$ and introduces noise realism, while quantum encoding uses amplitudes with $n = \log_{2}(M) + 1$ qubits; experiments include ideal simulations and hardware runs on IonQ, OQC, and IBM Q devices, showing Swap Test can closely approximate the classical distance $CED$ at practical fidelities, whereas the QFT route remains resource-intensive for near-term devices. The work demonstrates near-term feasibility of quantum BM, compares two quantum routes, analyzes noise impacts, and outlines steps toward scaling to full video sequences and integrating error mitigation.

Abstract

Finding groups of similar image blocks within an ample search area is often necessary in different applications, such as video compression, image clustering, vector quantization, and nonlocal noise reduction. A block-matching algorithm that uses a dissimilarity measure can be applied in such scenarios. In this work, a measure that utilizes the quantum Fourier transform or the Swap test based on the Euclidean distance is proposed. Experiments on small cases with ideal and noisy simulations are implemented. In the case of the Swap test, the IBM and IonQ quantum devices have been used, demonstrating potential for future near-term applications.

Quantum Block-Matching Algorithm using Dissimilarity Measure

TL;DR

This paper formulates a quantum block-matching algorithm that uses a dissimilarity measure based on the Euclidean distance to locate similar image blocks within a search region. It explores two quantum routes: a QFT-based Draper adder and a quantum Swap Test with amplitude-encoded blocks, combined with a hierarchical search to reduce vector size. Classical preprocessing reduces images to and introduces noise realism, while quantum encoding uses amplitudes with qubits; experiments include ideal simulations and hardware runs on IonQ, OQC, and IBM Q devices, showing Swap Test can closely approximate the classical distance at practical fidelities, whereas the QFT route remains resource-intensive for near-term devices. The work demonstrates near-term feasibility of quantum BM, compares two quantum routes, analyzes noise impacts, and outlines steps toward scaling to full video sequences and integrating error mitigation.

Abstract

Finding groups of similar image blocks within an ample search area is often necessary in different applications, such as video compression, image clustering, vector quantization, and nonlocal noise reduction. A block-matching algorithm that uses a dissimilarity measure can be applied in such scenarios. In this work, a measure that utilizes the quantum Fourier transform or the Swap test based on the Euclidean distance is proposed. Experiments on small cases with ideal and noisy simulations are implemented. In the case of the Swap test, the IBM and IonQ quantum devices have been used, demonstrating potential for future near-term applications.
Paper Structure (14 sections, 4 equations, 10 figures, 2 tables)

This paper contains 14 sections, 4 equations, 10 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Block-matching algorithms
  3. QFT approach
  4. Swap Test
  5. Methodology
  6. Classical approach
  7. Quantum approach
  8. QFT approach
  9. Quantum Swap Test approach
  10. Quantum noise models
  11. Results
  12. Results for QFT approach
  13. Results for Swap Tets approach
  14. Conclusions

Figures (10)

  • Figure 1: A representation of block-matching algorithms.
  • Figure 2: Quantum circuit swap test to compute the quantum Euclidean distance.
  • Figure 3: Diagram of the proposal methodology for a quantum block-matching algorithm using dissimilarity measure.
  • Figure 4: (a) The original image. (b) The original image with Gaussian noise $\mu=0$ and $\sigma = 20$ and 4-bit grayscale.
  • Figure 5: Quantum Circuit for the QFT approach.
  • ...and 5 more figures