Design and Analysis of Pattern Matching Algorithms Based on QuRAM Processing

Abstract

The pattern matching problem remains in survival since past decades and becomes more sophisticated due to exponential increase in size of text databases. An effective deterministic classical algorithm is always expected to be at least $${\\rm O}\\left( N \\right)$$\n time. Quantum computations are enough capable of performing exponential operations in single step of execution, so the quantum algorithms are effective. In general, the quantum pattern matching solution is possible in $${\\rm O}\\left( {\\sqrt N } \\right)$$\n time as its design is based on Grover’s quantum search algorithm. To our knowledge, quantum algorithms for single pattern matching are available with limitations, and no algorithm has designed for multiple pattern matching. The main objective is to design quantum algorithm for both single and multiple patterns on a processing architecture of quantum random access memory $$\\left( {QuRAM} \\right)$$\n . This gives a significant advantage to process large text databases in an efficient manner. Our complexity analysis justifies that the quantum algorithmic solutions achieve computational speedup over classical methods. We summarize the emergence of quantum-based pattern matching algorithms to process biological applications. The simulation is additionally done to validate and analyze the performance of proposed quantum algorithms. Lastly, we justify that our algorithms outperform the classical and quantum solutions and they are competent for implementing over quantum computer.