Abstract
AbstractFinding the solution to a large category of optimization problems, known as the NP-hard class, requires an exponentially increasing solution time using conventional computers. Lately, there has been intense efforts to develop alternative computational methods capable of addressing such tasks. In this regard, spin Hamiltonians, which originally arose in describing exchange interactions in magnetic materials, have recently been pursued as a powerful computational tool. Along these lines, it has been shown that solving NP-hard problems can be effectively mapped into finding the ground state of certain types of classical spin models. Here, we show that arrays of metallic nanolasers provide an ultra-compact, on-chip platform capable of implementing spin models, including the classical Ising and XY Hamiltonians. Various regimes of behavior including ferromagnetic, antiferromagnetic, as well as geometric frustration are observed in these structures. Our work paves the way towards nanoscale spin-emulators that enable efficient modeling of large-scale complex networks.
Highlights
Enhancing the efficiency of various computational tasks has always been a major challenge in many and diverse fields
It has been shown that solving NP-hard problems can be effectively mapped into finding the ground state of certain types of classical spin models
In all the cases discussed in our study, the relevant exchange interactions Jij can be adjusted via tuning the metallic gaps between adjacent nanocavities
Summary
Enhancing the efficiency of various computational tasks has always been a major challenge in many and diverse fields. These magnetic materials lack the required versatility to be used for computational optimization To address this issue, ultracold atoms in optical lattices have been employed to emulate magnetic spins [9,10,11,12,13] and most recently, active photonic platforms have been pursued as a viable means for experimental realization of spin Hamiltonians. Ultracold atoms in optical lattices have been employed to emulate magnetic spins [9,10,11,12,13] and most recently, active photonic platforms have been pursued as a viable means for experimental realization of spin Hamiltonians In this regard, unlike passive implementations, such optical systems can identify the ground state of the corresponding Hamiltonian by their natural tendency to operate in the global minimum loss. One can find the total EM loss associated with the TM modes to be
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