ETRI Journal

Electronics and Telecommunications Research Institute (한국전자통신연구원)
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Quantum-based exact pattern matching algorithms for biological sequences

  • Soni, Kapil Kumar (Department of Computer Science and Engineering, Maulana Azad National Institute of Technology) ;
  • Rasool, Akhtar (Department of Computer Science and Engineering, Maulana Azad National Institute of Technology)
  • Received : 2020.01.21
  • Accepted : 2020.09.23
  • Published : 2021.06.01
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Abstract

In computational biology, desired patterns are searched in large text databases, and an exact match is preferable. Classical benchmark algorithms obtain competent solutions for pattern matching in O (N) time, whereas quantum algorithm design is based on Grover's method, which completes the search in $O(\sqrt{N})$ time. This paper briefly explains existing quantum algorithms and defines their processing limitations. Our initial work overcomes existing algorithmic constraints by proposing the quantum-based combined exact (QBCE) algorithm for the pattern-matching problem to process exact patterns. Next, quantum random access memory (QRAM) processing is discussed, and based on it, we propose the QRAM processing-based exact (QPBE) pattern-matching algorithm. We show that to find all t occurrences of a pattern, the best case time complexities of the QBCE and QPBE algorithms are $O(\sqrt{t})$ and $O(\sqrt{N})$, and the exceptional worst case is bounded by O (t) and O (N). Thus, the proposed quantum algorithms achieve computational speedup. Our work is proved mathematically and validated with simulation, and complexity analysis demonstrates that our quantum algorithms are better than existing pattern-matching methods.

Keywords

Acknowledgement

We are grateful to Ashwini Kumar Malviya for his rigorous efforts to help us simulate our algorithms and consistent support overall.

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