Quantum search by measurement with prior information

Abstract

We show that a quantum algorithm, quantum search by measurement, can be performed even more efficiently when a priori information about a target is provided. In a searching problem, it is known that circuit-based quantum algorithms, Grover’s algorithm can achieve a quadratic speedup compared to classical algorithms. Furthermore, it has been shown that quantum search by adiabatic evolution or measurement can also yield similar results. If priori information about a target is available, it has been shown that Grover’s algorithm and quantum search by adiabatic evolution can reduce the running time based on the prior probabilities. In this thesis, we show that quantum search by measurement can also reduce the running time based on the prior probabilities and the reduced running time is the same with the one in the quantum search by adiabatic evolution with prior probabilities. On the other hand, in the quantum search by measurement, we show that by modifying the measurement, we can reduce the running time of the algorithm and the proposed method in the original paper can be explained by the extreme case of the modified method. From results, we suggest that we can adapt the proposed modification into the other problems that can be solved by measurement method.