Abstract
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.
Highlights
Q UANTUM computation has the advantage of having a lower complexity than classical computation in many algorithms [1]–[6]
Once we describe the system in graph theory, we can use a search algorithm in the same manner as graph coloring problem (GCP)
This paper proposes a quantum search algorithm (QSA) that considers the sum of rewards of each solution, such that it can be used in GCPs with rewards
Summary
Q UANTUM computation has the advantage of having a lower complexity than classical computation in many algorithms [1]–[6]. Grover’s quantum search algorithm (QSA) solves a data-searching problem with quadratic speed-up [5]. After Grover had suggested the QSA, many improved quantum search algorithms have been proposed. Boyer-Brassard-Høyer-Tapp presented a tight bound of QSA and a method that solve the problem having unknown number of solutions [7]. Dürr-Høyer proposed a quantum minimum search algorithm [8]. Dürr-Høyer algorithm can find a minimum value through higher complexity rather than QSA. Hogg presented a heuristic algorithm for quantum method [9]. The quantum heuristic algorithm can solve a satisfiability problem with lower complexity than QSA. Fabrikant and Hogg presented the quantum heuristic algorithm for a graph coloring problem (GCP) [10]. QSA can be applied to a resource assignment problem such as the GCP [11]
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call