This paper introduces a new approach to improve Grover's search algorithm by utilizing variational learning, with a specific focus on incorporating a partial diffusion operator. Grover's search algorithm is a well-known quantum algorithm that provides a quadratic speedup for searching an unsorted database. However, its performance can be further enhanced by modifying its diffusion operator. In this work, we aim to identify a parameterized quantum circuit that can effectively learn and optimize Grover's search algorithm, incorporating a partial diffusion operator. The key idea behind this approach is to use variational learning, a technique that employs parameterized quantum circuits to optimize the algorithm's performance. By adjusting the parameters of the quantum circuit, the algorithm can be tailored to better solve the search problem. Variational learning is employed to determine the optimal parameters for the partial diffusion operator, enabling the quantum circuit to adapt to different problem instances. Our experimental results demonstrate that the optimized quantum circuit outperforms the traditional Grover’s algorithm that uses the standard partial diffusion operator. The results suggest that the proposed approach offers significant improvements in terms of algorithmic efficiency and performance. This advancement could have important implications for the development of quantum algorithms, particularly in applications related to database search and optimization problems. In conclusion, this paper presents a promising new method to enhance Grover's search algorithm, utilizing variational learning and a partial diffusion operator, with results showing improved performance over the original algorithm.This paper introduces a new approach to improve Grover's search algorithm by utilizing variational learning, with a specific focus on incorporating a partial diffusion operator. Grover's search algorithm is a well-known quantum algorithm that provides a quadratic speedup for searching an unsorted database. However, its performance can be further enhanced by modifying its diffusion operator. In this work, we aim to identify a parameterized quantum circuit that can effectively learn and optimize Grover's search algorithm, incorporating a partial diffusion operator. The key idea behind this approach is to use variational learning, a technique that employs parameterized quantum circuits to optimize the algorithm's performance. By adjusting the parameters of the quantum circuit, the algorithm can be tailored to better solve the search problem. Variational learning is employed to determine the optimal parameters for the partial diffusion operator, enabling the quantum circuit to adapt to different problem instances. Our experimental results demonstrate that the optimized quantum circuit outperforms the traditional Grover’s algorithm that uses the standard partial diffusion operator. The results suggest that the proposed approach offers significant improvements in terms of algorithmic efficiency and performance. This advancement could have important implications for the development of quantum algorithms, particularly in applications related to database search and optimization problems. In conclusion, this paper presents a promising new method to enhance Grover's search algorithm, utilizing variational learning and a partial diffusion operator, with results showing improved performance over the original algorithm.

Transactions on Machine IntelligenceNov 25, 20180 citations

Entanglement in the Quantum Search Algorithm

Shantanav Chakraborty

May 1, 20130 citations

Enhanced Quantum Search via Partial Diffusion and Entanglement with Linear Optics

Ahmed S. El Fiky, Ahmed Younes, A. R. Abdulghany +2 more

Searching for specific items in an unstructured database presents a vital computational problem. While the best-known classical search algorithm in a database of size $N$ has a complexity $\mathrm{O}(N)$ , Grover's quantum search algorithm exhibits a complexity $\mathrm{O}(\sqrt{N})$ , featuring a quadratic speed-up. In this paper, we present an optical system that implements an enhanced version of the search algorithm proposed by Younis et al. The system uses linear optical components such as beam splitters, phase shifters, and wave plates, along with a single-photon source and photodetectors.Searching for specific items in an unstructured database presents a vital computational problem. While the best-known classical search algorithm in a database of size$N$has a complexity$\mathrm{O}(N)$, Grover's quantum search algorithm exhibits a complexity$\mathrm{O}(\sqrt{N})$, featuring a quadratic speed-up. In this paper, we present an optical system that implements an enhanced version of the search algorithm proposed by Younis et al. The system uses linear optical components such as beam splitters, phase shifters, and wave plates, along with a single-photon source and photodetectors.

National Radio Science ConferenceMay 6, 20250 citations

Understanding Entanglement as a Resource for Quantum Information Processing

Scott M. Cohen

Bulletin of the American Physical SocietyMar 17, 20091 citation

Circuit-depth optimization of quantum partial-search algorithms

Yan-Bo Jiang, Xiao-Hui Wang, Kun Zhang +1 more

Grover's algorithm is optimal in terms of oracle queries. We can trade accuracy for speed, which gives rise to the quantum partial-search algorithm. The partial-search algorithm is implemented using two kinds of Grover operators, global and local, where the former is the standard Grover operator for full search and the latter has a diffusion operator acting on the search subspace. The global-local-global sequence, also known as the Grover-Radhakrishnan-Korepin (GRK) algorithm, has been proved optimal in the oracle-query metric. In this work, we show that the alternating sequence of global and local Grover operators, formed by repeatedly applying a fixed product of global and local Grover operators, can achieve a lower expected circuit depth than the GRK algorithm. Through systematic analysis, we obtain its exact success probability, expected depth, and asymptotically optimal parameters. We derive the boundary, characterized by the ratio between the depths of the oracle and the global diffusion operator, separating the depth-optimal and oracle-optimal partial-search algorithms. When the depths of the oracle and the global diffusion operator are comparable, our proposed alternating partial-search sequence can reduce the minimum expected circuit depth by more than 20\% compared with the GRK algorithm.Grover's algorithm is optimal in terms of oracle queries. We can trade accuracy for speed, which gives rise to the quantum partial-search algorithm. The partial-search algorithm is implemented using two kinds of Grover operators, global and local, where the former is the standard Grover operator for full search and the latter has a diffusion operator acting on the search subspace. The global-local-global sequence, also known as the Grover-Radhakrishnan-Korepin (GRK) algorithm, has been proved optimal in the oracle-query metric. In this work, we show that the alternating sequence of global and local Grover operators, formed by repeatedly applying a fixed product of global and local Grover operators, can achieve a lower expected circuit depth than the GRK algorithm. Through systematic analysis, we obtain its exact success probability, expected depth, and asymptotically optimal parameters. We derive the boundary, characterized by the ratio between the depths of the oracle and the global diffusion operator, separating the depth-optimal and oracle-optimal partial-search algorithms. When the depths of the oracle and the global diffusion operator are comparable, our proposed alternating partial-search sequence can reduce the minimum expected circuit depth by more than 20\% compared with the GRK algorithm.

quant-pharXiv:2609.28147Sep 24, 20260 citations

Searching for specific items in an unstructured database presents a vital computational problem. While the best-known classical search algorithm in a database of size

N

has a complexity

\mathrm{O}(N)

, Grover's quantum search algorithm exhibits a complexity

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

, featuring a quadratic speed-up. In this paper, we present an optical system that implements an enhanced version of the search algorithm proposed by Younis et al. The system uses linear optical components such as beam splitters, phase shifters, and wave plates, along with a single-photon source and photodetectors.