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Hybrid Phase-Based Representation of Quantum Images

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Abstract

We propose a novel and hybrid quantum-classical algorithm that requires only \(O(\log {HW})\) qubits and reduces the multi-qubit gate costs required to represent an image of dimension \((H \times W)\). In this algorithm, no qubit is needed to store the color information of the image. We represent the location information of an image with a superposition of mutually orthogonal vectors of an arbitrary basis and store the pixel information in the phases of the corresponding basis vectors without any extra qubit cost. We further present a classical algorithm to encode the phases and show that the inclusion of the classical algorithm significantly reduces the number of multi-qubit quantum gates required for image representation. Finally, we implement our algorithm on the classical simulator provided by IBM quantum as a proof of concept.

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Data sharing not applicable to this article as no datasets were generated or analysed during the current study.

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Acknowledgements

The authors acknowledge IBM Quantum for providing access to their quantum simulators.

Author information

Authors and Affiliations

  1. Department of Physics, Indian Institute of Technology Madras, Chennai, 600036, Tamil Nadu, India

    Arijit Mandal

  2. Departement de physique and Institut Quantique, Université de Sherbrooke, Sherbrooke, J1K 2R1, Québec, Canada

    Shreya Banerjee

  3. Department of Physical Sciences, Indian Institute of Science Education and Research Kolkata, Mohanpur, 741246, West Bengal, India

    Arijit Mandal, Shreya Banerjee & Prasanta K. Panigrahi

Authors
  1. Arijit Mandal
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  2. Shreya Banerjee
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  3. Prasanta K. Panigrahi
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Contributions

A.M. proposed and developed the hybrid algorithm and wrote the initial manuscript. S.B. modified the algorithm and manuscript. P.K.P supervised the work. All the authors reviewed the manuscript.

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Correspondence to Arijit Mandal.

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Mandal, A., Banerjee, S. & Panigrahi, P.K. Hybrid Phase-Based Representation of Quantum Images. Int J Theor Phys 62, 115 (2023). https://doi.org/10.1007/s10773-023-05354-4

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