This paper presents a quantum search algorithm (QSA) for weighted solutions. In a QSA, the final quantum state has an equal probability of solutions. However, solutions should have different probabilities in specific problems, such as dynamic spectrum management (DSM). We propose a method to make differences with probability in accordance with rewards for each solution, and present an application to DSM. The proposed algorithm has some error terms for the final quantum state, and we provide the error terms in accordance with the number of iterations. In addition, we present the simulation results of the proposed algorithm compared with a classical exact algorithm and QSA. The proposed algorithm has a lower complexity and relative difference than the classical exact algorithm. Furthermore, the proposed algorithm has a higher performance than the QSA in specific cases.
Abstract While Grover’s search algorithm is asymptotically optimal, it does not always result in a real solution. If the search fails, the algorithm must be ran again from the beginning, conditionally doubling the effective number of oracle calls. Previous research attempted to fix this issue by modifying the oracle or alternating between numerically optimized reflectors. In this paper, we present an optimal initial state and reflector that produce an exact search with Grover’s algorithm at the cost of at most one additional oracle call beyond the optimum, a cost which can be nullified if we know a non-solution. We do this without modifying the oracle, without changing the diffuser at each step and even without any numerical optimization procedure required.
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) and 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.