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Networks of non-equilibrium condensates for global optimisation of spin Hamiltonians

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The majority of optimisation problems are computationally impractical for conventional classical computers and known as NP-hard optimisation problems. Such problems deal with scheduling, the dynamic analysis of neural networks and financial markets, the prediction of new chemical materials, and machine learning. Incredibly, it is possible to reformulate these optimisation problems into the problem of finding the ground state of a particular spin Hamiltonian. In my talk I will address various physical platforms that can simulate such spin Hamiltonians in order to solve optimisation problems orders of magnitude faster than can be achieved on a classical computer. In particular, the spin Hamiltonians can be simulated experimentally with polariton condensates. These are effectively comprised of a “mix” of the states of light and matter, and can be explicitly mapped into problems such as the travelling salesman problem. Using such mappings, one can study physical systems experimentally and effectively “read out” the solution to an optimisation problem one wishes to solve. A possible speedup opens a path to global minimisation of large-scale, real-world problems not accessible by classical simulations.

This talk is part of the Trinity Mathematical Society series.

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