Polaritonic networks as a route to unconventional computing
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Polariton ic networks for large scale hard optimisation Natalia G. Berloff Department of Applied Mathematics and Theoretical Physics, University of Cambridge and Skolkovo Institute of Science and Technology Recently several gain - dissipative platforms based on the networks of optical parametric oscillators , coupled lasers  and various non - equilibrium Bose - Einstein condensates such as exciton - polariton, atomic  and photon  condensates have been proposed as analogue Hamiltonian simulators for solving large - scale hard optimisation problems. Such platforms use an approach to finding the global minimum of spin Hamiltonians which is different from quantum annealers or quantum computers. However, in general, the parameters of such spin Hamiltonians when realised by gain - dissipative simulators depend on the no de occupancies that are not known a priori , which limits the simulators applicability to the classes of problems easily solvable by classical computations. I show how to overcome this difficulty and formulate algorithms for solving the NP - hard large - scale optimisation problems such as constant modulus continuous quadratic optimisation  and quadratic binary optimisation for any general matrix  . T o solve such problems any gain - dissipative simulator has to implement a feedback mechanism for the dynamical adjustment of the gain and coupling strengths , so that occupancy of each node is the same. I will illustrate the work of such a simulator using the polariton graph platform that we recently realised in experiments . The estimates of the time operation of the physical implementation of the gain - dissipative simulato rs for large matrices s uggest the speed - up of the several orders of magnitude in comparison with classical computations  . Besides acting as analog Hamiltonian optimizers, the networks of exciton - polaritons are a flexible universal platform to realise a vast array of known and extensively studied systems of coupled oscillators such as Kuramoto, Sakaguchi - Kuramot o, Stuart - Landau, Lang - Kobayashi oscillators and beyond [9 ]. The networks of polariton condensates are therefore capable of implementing various regimes producing Chimera states, exotic spin glasses and large scale secondary synchronization of oscillations , probe new exotic dynamical regimes and to create novel states of matter.
References:  Marandi, A., et al. Network of time - multiplexed optical parametric oscillators as a coherent Ising machine . Nat. Phot. 8 , 937 - 942 (2014).  Nixon, M., et al. Observing geometric frustration with thousands of coupled lasers. Phys. Rev. Lett. 110 , 184102 (2013).  Berloff, N. G. et al. Realizing the classical XY Hamiltonian in polariton simulators. Nat. Mat . 16 (11), 1120 (2017).  Vaidya, D. V. et al. Tunable - range, photon - mediated atomic interactions in multimode cavity QED. Phys. Rev. X 8 (1), 011002 (2018).  Dung, D. et al. Variable potentials for thermalized light and coupled condensates. Nat. Phot. 11 (9), 565 (2017)  Kalinin K.P. and N.G. Berloff "Networks of non - equilibrium condensates for global optimization" New J . of Phys ., 20 113023 (2018)  Kalinin K. P. and N.G.Berloff "Simulating Ising and Potts models and external fields with non - equilibrium condensates," Phys . Rev . Lett s ., 121 , 235302 (2018) [ 8 ] Kalinin K.P. and N.G.Berloff "Global optimization of spin Hamiltonians with gain - dissipative systems," Sci . Rep ., 8 ,17791 (2018)  Kalinin K.P. and N.G.Berloff “ Polaritonic network as a paradigm for dynamics of coupled oscillators ” , arXiv:1902.09142 Download PDF
Physics Theatre C
November 8, 2019
From: 10h00 To: 11h00
University of St Andrews
The oldest university in Scotland, with international renown for both research and education of undergraduates and postgraduates.