Convergence properties of fixed-point search with general but equal phase shifts for any iterations

Performance of Equal Phase-Shift Search for One Iteration

Grover presented the phase-shift search by replacing the selective inversions by selective phase shifts of $π/3$. In this paper, we investigate the phase-shift search with general equal phase shifts. We show that for small uncertainties, the failure probability of the Phase-$π/3$ search is smaller than the general phase-shift search and for large uncertainties, the success probability of the large phase-shift search is larger than the Phase-$π/3$ search. Therefore, the large phase-shift search is suitable for large-size of databases.

Fixed-point Quantum Search for Different Phase Shifts

Grover recently presented the fixed-point search algorithm. In this letter, we study the fixed-point search algorithm obtained by replacing equal phase shifts of $π/3$ by different phase shifts.

Optimization of the damped quantum search

The damped quantum search proposed in [A. Mizel, Phys. Rev. Lett., 102 150501 (2009)] was analyzed by calculating the highest possible probability of finding the target state in each iteration. A new damping parameter that depends on the number of iterations was obtained, this was compared to the critical damping parameter for different values of target to database size ratio. The result shows that the range of the new damping parameter as a function of the target to database size ratio increases as the number of iterations is increased. Furthermore, application of the new damping parameter pe…

洛伦兹锥的最大指数

Maximal exponent of the Lorentz cones

本研究证明n维洛伦兹锥的最大指数等于n，并由此推导出量子比特信道下量子Wielandt不等式的最优指数为3，为相关锥理论与量子信息研究提供了关键结论。