Work

Deterministic Search on Complete Bipartite Graphs by Continuous-Time Quantum Walk

Year: 2024

Type: article

Abstract: How to design deterministic spatial search algorithms is a difficult but important problem. This paper presents a deterministic search algorithm on complete bipartite graphs with optimal runtime scaling. Our algorithm adopts the simple form of alternating iterations of an oracle and a continuous-time quantum walk operator, which is a generalization of Grover's search algorithm. To address the case of the number of marked vertices being unknown, we construct a quantum counting algorithm based on the spectrum structure of the search operator. This is a non-trivial example of quantum counting for spatial search. To implement the continuous-time quantum walk operator, we perform Hamiltonian simulation in the quantum circuit model and simulate it on the IBM quantum computing platform Qiskit.

Source: Quantum Information and Computation

DOI: 10.2478/qic-2024-0001

Authors: Honghong Lin, Yun Shang

Institutions: Chinese Academy of Sciences, Academy of Mathematics and Systems Science, University of Chinese Academy of Sciences, National Center for Mathematics and Interdisciplinary Sciences

Language: English

Topic: Quantum Computing Algorithms and Architecture

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Funders: National Natural Science Foundation of China, National Key Research and Development Program of China

Awards: G1101892756, G2680642259, G2896165731