Sure success partial search

Sure-Success Quantum Algorithms on Weight Decision Problem

Conditions on sure-success decidability of weights of Boolean functions are presented for a given number of generalized Grover iterations. It is shown that the decidability problem reduces to a system of algebraic equations of a single variable. For problems that require a large number of iterations, it is observed that the iteration number of sure-success quantum algorithms scale as the square root of the iteration number of the corresponding classical probabilistic algorithms. It is also demonstrated that for a few iterations, quantum algorithms can be more efficient than this.

Formulation of a Family of Sure-Success Quantum Search Algorithms

In this work, we consider a family of sure-success quantum algorithms, which is grouped into even and odd members for solving a generalized Grover search problem. We prove the matching conditions for both groups and give the corresponding formulae for evaluating the iterations or oracle calls required in the search computation. We also present how to adjust the phase angles in the generalized Grover operator to ensure the sure-success if minimal oracle calls are demanded in the search.

A family of sure-success quantum algorithms for solving a generalized Grover search problem

This work considers a generalization of Grover's search problem, viz., to find any one element in a set of acceptable choices which constitute a fraction f of the total number of choices in an unsorted data base. An infinite family of sure-success quantum algorithms are introduced here to solve this problem, each member for a different range of f. The nth member of this family involves n queries of the data base, and so the lowest few members of this family should be very convenient algorithms within their ranges of validity. The even member {A}_{2n} of the family covers ever larger range of f…

一种具有确定成功概率的优化量子最小值搜索算法及其基于 Cirq 的实验模拟

An optimized quantum minimum searching algorithm with sure-success probability and its experiment simulation with Cirq

针对量子最小值搜索问题，提出一种结合 Grover-Long 精确搜索、动态迭代策略与 oracle 电路优化的确定成功概率算法，并通过 Cirq 模拟验证其可行性。