Navigating Between the Classical and the Quantum Worlds

Eduardo Sánchez-Burillo, Jordi Duch, Jesús Gómez‐Gardeñes +1 more

Complex networks are formal frameworks capturing the interdependencies between the elements of large systems and databases. This formalism allows to use network navigation methods to rank the importance that each constituent has on the global organization of the system. A key example is Pagerank navigation which is at the core of the most used search engine of the World Wide Web. Inspired in this classical algorithm, we define a quantum navigation method providing a unique ranking of the elements of a network. We analyze the convergence of quantum navigation to the stationary rank of networks and show that quantumness decreases the number of navigation steps before convergence. In addition, we show that quantum navigation allows to solve degeneracies found in classical ranks. By implementing the quantum algorithm in real networks, we confirm these improvements and show that quantum coherence unveils new hierarchical features about the global organization of complex systems.

CHRISTOF WETTERICH

Jeffrey Bub

Shuyin Xia, Xiaojiang Tian, Suzhen Yuan +1 more

High time complexity is one of the biggest challenges faced by k-Nearest Neighbors (kNN). Although current classical and quantum kNN algorithms have made some improvements, they still have a speed bottleneck when facing large amounts of data. To address this issue, we propose an innovative algorithm called Granular-Ball based Quantum kNN(GB-QkNN). This approach achieves higher efficiency by first employing granular-balls, which reduces the data size needed to processed. The search process is then accelerated by adopting a Hierarchical Navigable Small World (HNSW) method. Moreover, we optimize the time-consuming steps, such as distance calculation, of the HNSW via quantization, further reducing the time complexity of the construct and search process. By combining the use of granular-balls and quantization of the HNSW method, our approach manages to take advantage of these treatments and significantly reduces the time complexity of the kNN-like algorithms, as revealed by a comprehensive complexity analysis.

Kaj Börge Hansen

Brutchsama Jean-Louis

A research prototype showing a weakly quantum-inspired sensing channel (a globally-leaked Bohmian-style pilot wave plus Penrose-style observation collapse) helps a swarm of local agents find routes a deterministic local-greedy classical baseline structurally cannot, in a 128x128 grid world. Null rejected in 4 of 5 scenarios; mechanism is global route discovery via the leaked pilot wave (not wall penetration). Includes a calibrated baseline-forensics evaluation method and a ranked Applications section. Code & scripts: https://github.com/BrutchsamaJeanLouis/quantum-inspired-sensor-navigation