A multi-channel quantum image representation model with qubit sequences for quantum-inspired image and image retrieval

Nawres A. Alwan; Suzan J. Obaiys; Nadia M. G. Al-Saidi; Nurul Fazmidar Binti Mohd Noor; Yeliz Karaca; Nawres A. Alwan; Suzan J. Obaiys; Nadia M. G. Al-Saidi; Nurul Fazmidar Binti Mohd Noor; Yeliz Karaca

doi:10.3934/math.2025499

AIMS Mathematics

2025, Volume 10, Issue 5: 10994-11035. doi: 10.3934/math.2025499

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A multi-channel quantum image representation model with qubit sequences for quantum-inspired image and image retrieval

1.
Department of Computer System & Technology, Faculty of Computer Science and Information Technology, Universiti Malaya, Kuala Lumpur, 50603, Malaysia
2.
Department of Applied Sciences, University of Technology, Baghdad, 10066, Iraq
3.
University of Massachusetts Chan Medical School (UMASS), 55 Lake Avenue North, Worcester, MA 01655, USA

Received: 20 January 2025 Revised: 27 March 2025 Accepted: 28 March 2025 Published: 14 May 2025
MSC : 81Q35, 68Q12, 81P94, 94A60

Quantum image processing (QIP) has become one of the most significant fields in quantum computing (QC); it merges quantum mechanics with image processing to improve classical image-processing speed, which involves various operations to advance quantum image representation (QIR). Accordingly, we introduce two new QIRs: The first is based on the wavelength and bit plane, called the quantum image representation bit plane (QIRBP), and the second is based on the wavelength and adjacency pixels, which is called the quantum image representation wavelength correlation (QIRWC). The QIRBP model uses $ b+2n+6 $ quantum bit (qubits) to store a digital color image of size $ {2}^{n}\times {2}^{n} $. In contrast, the QIRWC needs $ 2b+4n+8 $ qubits to store a digital color image of size $ {2}^{n}\times {2}^{n} $ and to entangle the wavelength between two neighboring pixels. While the QIRWC approach is more complex, it is also more efficient on the basis of the transformation data. The complexity arises from the level of information being transmitted. In this work, two new representation methods (QIRBP and QIRWC) are proposed to overcome existing QIR weaknesses by enhancing storage efficiency, enabling compact high-resolution representation, improving data transformation through wavelength correlation and pixel adjacency, reducing noise, achieving greater versatility, and advancing scalable QIR. To prove the efficiency of the proposed methods, they were analyzed and compared with other efficient quantum image representations, outlining their similar and different aspects.
- quantum image representation,
- quantum computing,
- quantum image processing,
- quantum mechanics,
- quantum image retrieval,
- quantum-inspired image
Citation: Nawres A. Alwan, Suzan J. Obaiys, Nadia M. G. Al-Saidi, Nurul Fazmidar Binti Mohd Noor, Yeliz Karaca. A multi-channel quantum image representation model with qubit sequences for quantum-inspired image and image retrieval[J]. AIMS Mathematics, 2025, 10(5): 10994-11035. doi: 10.3934/math.2025499

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Abstract

Quantum image processing (QIP) has become one of the most significant fields in quantum computing (QC); it merges quantum mechanics with image processing to improve classical image-processing speed, which involves various operations to advance quantum image representation (QIR). Accordingly, we introduce two new QIRs: The first is based on the wavelength and bit plane, called the quantum image representation bit plane (QIRBP), and the second is based on the wavelength and adjacency pixels, which is called the quantum image representation wavelength correlation (QIRWC). The QIRBP model uses $ b+2n+6 $ quantum bit (qubits) to store a digital color image of size $ {2}^{n}\times {2}^{n} $. In contrast, the QIRWC needs $ 2b+4n+8 $ qubits to store a digital color image of size $ {2}^{n}\times {2}^{n} $ and to entangle the wavelength between two neighboring pixels. While the QIRWC approach is more complex, it is also more efficient on the basis of the transformation data. The complexity arises from the level of information being transmitted. In this work, two new representation methods (QIRBP and QIRWC) are proposed to overcome existing QIR weaknesses by enhancing storage efficiency, enabling compact high-resolution representation, improving data transformation through wavelength correlation and pixel adjacency, reducing noise, achieving greater versatility, and advancing scalable QIR. To prove the efficiency of the proposed methods, they were analyzed and compared with other efficient quantum image representations, outlining their similar and different aspects.

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