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Proceedings in information and communications technology

Solving the Exact Pattern Matching Problem Constrained to Single Occurrence of Pattern P in String S Using Grover’s Quantum Search Algorithm

Brian Kenneth A. de Jesus, Jeffrey A. Aborot, Henry N. Adorna

Published Jan 1, 2013• 10 citations
Publisher
DOI
10.1007/978-4-431-54436-4_10

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The pattern matching problem is imperative in diversified field of computer science, and it finds occurrences of the pattern string(s) of any arbitrary length “M” in the large text string of length “N”. Since past decades the solutions to a problem have been suggesting through efficient algorithms. Classical benchmark algorithms such as Knuth Morris Pratt and Boyer Moore locates such solution in O(N) time, equivalent quantum algorithms can utilize quantum computations which are inherently parallel and obtains computational speedup by providing the solution in O(√N) time. The quantum pattern matching algorithm uses Grover's search logic that finds an element existence in the large unstructured text data of “N” items in O(√N) time, instead classically it takes O(N) time. The article comprises of introductory pattern matching tactics, quantum basics, Grover's search method, quantum based pattern matching algorithms, their illustration followed by complexity analysis, and finally concludes with the possible algorithmic variations and relevant applications.
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 time, whereas quantum algorithm design is based on Grover's method, which completes the search in 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 occurrences of a pattern, the best case time complexities of the QBCE and QPBE algorithms are , and the exceptional worst case is bounded by . 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.
This article presents efficient quantum solutions for exact multiple pattern matching to process the biological sequences. The classical solution takes Ο ( mN ) time for matching m patterns over N sized text database. The quantum search mechanism is a core for pattern matching, as this reduces time complexity and achieves computational speedup. Few quantum methods are available for multiple pattern matching, which executes search oracle for each pattern in successive iterations. Such solutions are likely acceptable because of classical equivalent quantum designs. However, these methods are constrained with the inclusion of multiplicative factor m in their complexities. An optimal quantum design is to execute multiple search oracle in parallel on the quantum processing unit with a single-core that completely removes the multiplicative factor m , however, this method is impractical to design. We have no effective quantum solutions to process multiple patterns at present. Therefore, we propose quantum algorithms using quantum processing unit with C quantum cores working on shared quantum memory. This quantum parallel design would be effective for searching all t exact occurrences of each pattern. To our knowledge, no attempts have been made to design multiple pattern matching algorithms on quantum multicore processor. Thus, some quantum remarkable exact single pattern matching algorithms are enhanced here with their equivalent versions, namely enhanced quantum memory processing based exact algorithm and enhanced quantum-based combined exact algorithm for multiple pattern matching. Our quantum solutions find all t exact occurrences of each pattern inside the biological sequence in O((m/C)N)O((m/C)\sqrt{N})O((m/C)N​) and O((m/C)t)O((m/C)\sqrt{t})O((m/C)t​) time complexities. This article shows the hybrid simulation of quantum algorithms to validate quantum solutions. Our theoretical–experimental results justify the significant improvements that these algorithms outperform over the existing classical solutions and are proven effective in quantum counterparts.