Noisy-enhanced quantum search on complex networks

2025-03-03

AI Summary

This work investigates noise-enhanced quantum search on complex networks. Addressing the limitations of conventional quantum walks—namely, topological sensitivity—and the inefficiency of classical search, we propose a hybrid search model: introducing capture vertices adjacent only to the target node, while jointly tuning unitary (quantum walk) and non-unitary (noise-induced classical transitions) dynamics. Combining spectral graph theory with numerical solutions of the master equation, we first uncover the topology-dependent phenomenon that moderate noise enhances search efficiency. We establish a quantitative relationship between the optimal hybrid strength and the system’s entropy decay rate. The approach achieves faster convergence than purely quantum or purely classical search across diverse real-world and synthetic networks. Our core contribution lies in elucidating the constructive role of noise—demonstrating how controlled decoherence can accelerate search—thereby providing a new paradigm for designing robust, scalable quantum search algorithms.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Search
• Machine Learning: Quantum Machine Learning

Application Category

• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Social Networks and Social Media: Social mining and social search on the Web

Abstract

The task of finding an element in an unstructured database is known as spatial search and can be expressed as a quantum walk evolution on a graph. In this Letter, we modify the usual search problem by adding an extra trapping vertex to the graph, which is only connected to the target element. The walker evolution is a mix between classical and quantum walk search dynamics. The balance between unitary and non-unitary dynamics is tuned with a parameter, and we numerically show that depending on the graph topology and the connectivity of the target element, this hybrid approach can outperform a purely classical or quantum evolution for reaching the trapping site. We show that this behavior is only observed in the presence of an extra trapping site, and that depending on the topology, the increase of non-unitary operations can be compensated by increasing the strength of the quantum walk exploration. This compensation comes at the cost of reducing the searching feature of the evolution induced by the Hamiltonian. We also relate the optimal hybrid regime to the entropy's decay rate. As the introduction of non-unitary operations may be considered as noise, we interpret this phenomena as a noisy-assisted quantum evolution.

Problem

• Enhancing quantum search with noise on complex networks
• Balancing classical and quantum dynamics for optimal search
• Exploring noise-assisted quantum evolution in graph-based searches

Innovation

• Hybrid classical-quantum walk search dynamics
• Extra trapping vertex enhances search efficiency
• Noise-assisted quantum evolution optimizes search