Abstract Grover's algorithm solves the unstructured search problem. Grover's algorithm can find the target state with certainty only if searching one out of four. Designing the deterministic search algorithm can avoid any repetition of the algorithm, especially when Grover's algorithm is a subroutine in other algorithms. Grover's algorithm can be deterministic if the phase of the oracle or the diffusion operator is delicately designed. The precision of the phases could be a problem. A near‐deterministic quantum search algorithm without the phase design is proposed. The algorithm has the same oracle and diffusion operators as Grover's algorithm. One additional component is the rescaled diffusion operator. It acts partially on the database. The success probability of Grover's algorithm is improved by the partial diffusion operator in two different ways. The possible cost is one or two more queries to the oracle. The deterministic search algorithm is also designed when searching one out of eight, sixteen, and thirty‐two.Abstract Grover's algorithm solves the unstructured search problem. Grover's algorithm can find the target state with certainty only if searching one out of four. Designing the deterministic search algorithm can avoid any repetition of the algorithm, especially when Grover's algorithm is a subroutine in other algorithms. Grover's algorithm can be deterministic if the phase of the oracle or the diffusion operator is delicately designed. The precision of the phases could be a problem. A near‐deterministic quantum search algorithm without the phase design is proposed. The algorithm has the same oracle and diffusion operators as Grover's algorithm. One additional component is the rescaled diffusion operator. It acts partially on the database. The success probability of Grover's algorithm is improved by the partial diffusion operator in two different ways. The possible cost is one or two more queries to the oracle. The deterministic search algorithm is also designed when searching one out of eight, sixteen, and thirty‐two.

arXiv:2407.10748Advanced Quantum TechnologiesJan 3, 20253 citations

Grover’s Search Algorithm

Mika Hirvensalo

Springer eBooksJan 1, 20010 citations

Grover’s Search Algorithm

Taylor & Francis eBooksMar 11, 20081 citation

Phase Matching in Quantum Searching and the Improved Grover Algorithm

Yang Sun

We briefly introduced some of our recent work related to the phase matching condition in quantum searching algorithms and the improved Grover algorithm. When one replaces the two phase inversions in the Grover algorithm with arbitrary phase rotations, the modified algorithm usually fails in searching the marked state unless a phase matching condition is satisfied between the two phases. The Grover algorithm is not 100% in success rate, an improved Grover algorithm with zero-failure rate is given by replacing the phase inversions with angles that depends on the size of the database. Other aspects of the Grover algorithm such as the SO(3) picture of quantum searching, the dominant gate imperfections in the Grover algorithm are also mentioned.We briefly introduced some of our recent work related to the phase matching condition in quantum searching algorithms and the improved Grover algorithm. When one replaces the two phase inversions in the Grover algorithm with arbitrary phase rotations, the modified algorithm usually fails in searching the marked state unless a phase matching condition is satisfied between the two phases. The Grover algorithm is not 100% in success rate, an improved Grover algorithm with zero-failure rate is given by replacing the phase inversions with angles that depends on the size of the database. Other aspects of the Grover algorithm such as the SO(3) picture of quantum searching, the dominant gate imperfections in the Grover algorithm are also mentioned.

Yuanzihe wuli pinglunJan 1, 20047 citations

Grover’s Algorithm

Belal Ehsan Baaquie, L. C. Kwek

Springer eBooksJan 1, 20232 citations

Depth-First Grover Search Algorithm on Hybrid Quantum-Classical Computer

Haoxiang Guo

We demonstrated the detailed construction of the hybrid quantum-classical computer. Based on this architecture, the useful concept of amplitude interception is illustrated. It is then embedded into a combination of Depth-First Search and Grover's algorithm to generate a novel approach, the Depth-First Grover Search(DFGS), to handle multi-solution searching problems on unstructured databases with an unknown number of solutions. Our new algorithm attains an average complexity of $\mathcal{O}(m\sqrt{N})$ which performs as efficient as a normal Grover Search, and a $\mathcal{O}(\sqrt{p}N)$ complexity with a manually determined constant $p$ for the case with all elements are solutions, where a normal Grover Search will degenerate to $\mathcal{O}(N\sqrt{N})$ . The DFGS algorithm is more robust and stable in comparison.We demonstrated the detailed construction of the hybrid quantum-classical computer. Based on this architecture, the useful concept of amplitude interception is illustrated. It is then embedded into a combination of Depth-First Search and Grover's algorithm to generate a novel approach, the Depth-First Grover Search(DFGS), to handle multi-solution searching problems on unstructured databases with an unknown number of solutions. Our new algorithm attains an average complexity of $\mathcal{O}(m\sqrt{N})$ which performs as efficient as a normal Grover Search, and a $\mathcal{O}(\sqrt{p}N)$ complexity with a manually determined constant $p$ for the case with all elements are solutions, where a normal Grover Search will degenerate to $\mathcal{O}(N\sqrt{N})$. The DFGS algorithm is more robust and stable in comparison.

arXiv:2210.04664Oct 10, 20220 citations

\mathcal{O}(m\sqrt{N})

which performs as efficient as a normal Grover Search, and a

\mathcal{O}(\sqrt{p}N)

complexity with a manually determined constant

p

for the case with all elements are solutions, where a normal Grover Search will degenerate to

\mathcal{O}(N\sqrt{N})

. The DFGS algorithm is more robust and stable in comparison.