Quantum Search Algorithm with more Reliable Behaviour using Partial Diffusion

Abstract

In this paper, we will use a quantum operator which performs the inversion about the mean operation only on a subspace of the system ({\it Partial Diffusion Operator}) to propose a quantum search algorithm runs in $O(\sqrt N/M})$ for searching unstructured list of size $N$ with $M$ matches such that, $1\le M\le N$. We will show that the performance of the algorithm is more reliable than known quantum search algorithms especially for multiple matches within the search space. A performance comparison with Grover's algorithm will be provided.

27 pages, 9 figures

References in corpus (5)

• Elementary gates for quantum computation
• Quantum Amplitude Amplification and Estimation
• A Family of Grover's Quantum Searching Algorithms
• Searching in Grover's Algorithm
• A Hybrid Quantum Search Engine: A Fast Quantum Algorithm for Multiple Matches

Cited by in corpus (10)

• A different kind of quantum search
• Quantum Searching via Entanglement and Partial Diffusion
• Fixed Phase Quantum Search Algorithm
• Synthesis and Optimization of Reversible Circuits for Homogeneous Boolean Functions
• Database Manipulation on Quantum Computers
• Complementary-multiphase quantum search for all numbers of target items
• Quantum Algorithms with Fixed Points: The Case of Database Search
• Approximate Phase Search and Eigen Estimation using Modified Grover's Algorithm
• Constant-Time Quantum Algorithm For The Unstructured Search Problem
• Exact quantum search based on analytical multiphase matching for known number of target items and the experimental demonstration on IBM Q