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<p>Quantum image processing is a rapidly growing subdiscipline in quantum computation. An important question in the field is how to effectively encode and preserve data from images without losing information. A quantum image representation adapted to three-dimensional images is proposed based on the novel enhanced quantum representation for quantum image and the Fourier transform representation. The representation store the coordinate and color information of each point in the 2-qubit and the <i>l</i>-qubit, respectively. It allows for more precise encoding of image position information and reduces data loss, as it can store non-integer points. In light of this premise, applying the quantum multiplication based on quaternion multiplication, the rotation of a 3D image is carried out. Moreover, the translation of a 3D image is investigated. By taking advantage of the parallelism of quantum computing, the entire image transformation (rotation and translation) can be achieved at once by executing simple quantum gates.</p>

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Quantum representation and geometric transformation of 3D images

  • 期刊论文

  • 发表日期：

    2025年7月14日

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  • Shi-Ping He,
  • Jin-Chuan Yang,
  • Ming-Qiang Bai,
  • Wen-Bo Du,
  • Peng-Heng Jiang,
  • Jia-Wei Liu,
  • Jia-Xin Cheng

摘要

Quantum image processing is a rapidly growing subdiscipline in quantum computation. An important question in the field is how to effectively encode and preserve data from images without losing information. A quantum image representation adapted to three-dimensional images is proposed based on the novel enhanced quantum representation for quantum image and the Fourier transform representation. The representation store the coordinate and color information of each point in the 2-qubit and the l-qubit, respectively. It allows for more precise encoding of image position information and reduces data loss, as it can store non-integer points. In light of this premise, applying the quantum multiplication based on quaternion multiplication, the rotation of a 3D image is carried out. Moreover, the translation of a 3D image is investigated. By taking advantage of the parallelism of quantum computing, the entire image transformation (rotation and translation) can be achieved at once by executing simple quantum gates.