Abstract: A photonic parallel network can be used to sample combinatorially hard distributions of Ising problems. The photonic parallel network, also called a photonic processor, finds the ground state of a general Ising problem and can probe critical behaviors of universality classes and their critical exponents. In addition to the attractive features of photonic networks—passivity, parallelization, high-speed and low-power—the photonic processor exploits dynamic noise that occurs during the detection process to find ground states more efficiently.

Abstract: A photonic parallel network can be used to sample combinatorially hard distributions of Ising problems. The photonic parallel network, also called a photonic processor, finds the ground state of a general Ising problem and can probe critical behaviors of universality classes and their critical exponents. In addition to the attractive features of photonic networks—passivity, parallelization, high-speed and low-power—the photonic processor exploits dynamic noise that occurs during the detection process to find ground states more efficiently.

Abstract: An apparatus for generating Smith-Purcell radiation having at least one spectral component at a wavelength ? includes a periodic structure including a dielectric material and an electron source, in electromagnetic communication with the periodic structure, to emit an electron beam propagating within about 5? from a surface of the periodic structure to induce emission of the Smith-Purcell radiation. The electron beam has an electron energy tunable between about 0.5 keV and about 40 keV so as to change a wavelength of the Smith-Purcell radiation.

Abstract: A photonic parallel network can be used to sample combinatorially hard distributions of Ising problems. The photonic parallel network, also called a photonic processor, finds the ground state of a general Ising problem and can probe critical behaviors of universality classes and their critical exponents. In addition to the attractive features of photonic networks—passivity, parallelization, high-speed and low-power—the photonic processor exploits dynamic noise that occurs during the detection process to find ground states more efficiently.

Abstract: An apparatus for generating Smith-Purcell radiation having at least one spectral component at a wavelength A includes a periodic structure including a dielectric material and an electron source, in electromagnetic communication with the periodic structure, to emit an electron beam propagating within about 5? from a surface of the periodic structure to induce emission of the Smith-Purcell radiation. The electron beam has an electron energy tunable between about 0.5 keV and about 40 keV so as to change a wavelength of the Smith-Purcell radiation.

Abstract: A system for training a neural network model, the neural network model comprising a plurality of layers including a first hidden layer associated with a first set of weights, the system comprising at least one computer hardware processor programmed to perform: obtaining training data; selecting a unitary rotational representation for representing a matrix of the first set weights, the selected unitary rotational representation comprising a plurality of parameters; training the neural network model using the training data using an iterative neural network training algorithm to obtain a trained neural network model, each iteration of the iterative neural network training algorithm comprising: updating values of the plurality of parameters in the selected unitary rotational representation for representing the matrix of the set of weights for the at least one hidden layer, and saving the trained neural network model.