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Solving Linear Systems of Equations by Using the Concept of Grover’s Search Algorithm: an IBM Quantum Experience

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Abstract

Quantum algorithm, as compared to classical algorithm, plays a notable role in solving linear systems of equations with an exponential speedup. Here, we demonstrate a method for solving a particular system of equations by using the concept of well-known Grover’s quantum search algorithm. The algorithm finds the solution by rotating the initial state vector in the Hilbert space to get the target solution state. It mainly involves finding particular matrices that solve the set of equations and constructing corresponding quantum circuits using the basic quantum gates. We explicitly illustrate the whole process by taking 48 different set of equations and solving them by using the concept of Grover’s algorithm. We propose new quantum circuits for each set of equations and design those on the IBM quantum simulator. We run the quantum circuit for one set of equations and obtain the desired results, and hence verify the working of the algorithm.

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Acknowledgements

B.K.B. is financially supported by IISER-K Institute fellowship. R.M. acknowledges all her teachers for their continuous support and guidance and her family for their love and moral support. This work was done when R.M. was a student at Central University of Karnataka and visited IISER-K. R.M. acknowledges the hospitality provided by IISER Kolkata during the project work. We are extremely grateful to IBM team and IBM Quantum Experience project.

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Authors and Affiliations

  1. Department of Physics, Central University of Karnataka, Karnataka, 585367, India

    Rituparna Maji

  2. Bikash’s Quantum (OPC) Pvt. Ltd., Balindi, Mohanpur, 741246, West Bengal, India

    Bikash K. Behera

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

    Bikash K. Behera & Prasanta K. Panigrahi

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  1. Rituparna Maji
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  3. Prasanta K. Panigrahi
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Correspondence to Bikash K. Behera.

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Maji, R., Behera, B.K. & Panigrahi, P.K. Solving Linear Systems of Equations by Using the Concept of Grover’s Search Algorithm: an IBM Quantum Experience. Int J Theor Phys 60, 1980–1988 (2021). https://doi.org/10.1007/s10773-021-04817-w

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  • DOI: https://doi.org/10.1007/s10773-021-04817-w

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