Year: 2025
Type: article
Abstract: Quantum walks are a powerful framework for simulating complex quantum systems and designing quantum algorithms, particularly for spatial search on graphs, where the goal is to find a marked vertex efficiently. In this work, we present efficient quantum circuits that implement the evolution operator of continuous-time quantum-walk-based search algorithms for three graph families: complete graphs, complete bipartite graphs, and hypercubes. For complete and complete bipartite graphs, our circuits exactly implement the evolution operator. For hypercubes, we propose an approximate implementation that closely matches the exact evolution operator as the number of vertices increases. Our Qiskit simulations demonstrate that even for low-dimensional hypercubes, the algorithm effectively identifies the marked vertex. Furthermore, the approximate implementation developed for hypercubes can be extended to a broad class of graphs, enabling efficient quantum search in scenarios where exact implementations are impractical.
Source: Entropy
DOI: 10.3390/e27050454
Authors: Renato Portugal, Jalil Khatibi Moqadam
Institution: Laboratório Nacional de Computação Científica
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,137
OpenAlex ID: W4409729900