The Traveling Salesperson Problem (TSP), a quintessential NP-hard combinatorial optimisation challenge, is vital for logistics and network design but limited by exponential complexity in large instances. We propose a hybrid quantum-classical framework integrating variational quantum eigensolver (VQE) optimisation with classical machine learning, using K-means clustering for problem decomposition and a RandomForestRegressor for path refinement. Evaluated on 80 European cities (from 4 to 80 cities, 38,500 samples in total) via Qiskit's AerSimulator and ibm_kyiv 127-qubit backend, the hybrid approach outperforms quantum-only methods, achieving an approximation ratio of 1.0287 at 80 cities, a 47.5% improvement over quantum-only's 1.9614, nearing the classical baseline. Machine learning reduces variability in tour distances (interquartile range, IQR - the spread of the middle 50% of results relative to the median - from 0.06 to 0.04), enhancing stability despite noisy intermediate-scale quantum (NISQ) noise. This framework underscores hybrid strategies' potential for scalable TSP optimisation, with future hardware advancements promising practical quantum advantages.

The robot takeover will start in the smaller cities. Towns and small cities have a smaller proportion of jobs that will be resilient to automation than larger urban centres, according to a new study. By looking at the jobs that are most susceptible to automation and their distribution across different US cities, Iyad Rahwan at the Massachusetts Institute of Technology Media Lab and his team have found a trend between the size of a city and the impact we should expect artificial intelligence and robots to have on human workers. Roughly speaking, cities with fewer than 100,000 inhabitants are more at risk. The East Coast cities are full of jobs that should be resilient to automation. Washington DC, for example, has many government-related roles that are hard to automate, and New York, with its population of 8.5 million, is able to support many specialist jobs too.