Benchmarking Neural Networks For Quantum Computations.

The power of quantum computers is still somewhat speculative. Although they are certainly faster than classical ones at some tasks, the class of problems they can efficiently solve has not been mapped definitively onto known classical complexity theory. This means that we do not know for which calculations there will be a "quantum advantage," once an algorithm is found. One way to answer the question is to find those algorithms, but finding truly quantum algorithms turns out to be very difficult. In previous work, over the past three decades, we have pursued the idea of using techniques of machine learning to develop algorithms for quantum computing. Here, we compare the performance of standard real- and complex-valued classical neural networks with that of one of our models for a quantum neural network, on both classical problems and on an archetypal quantum problem: the computation of an entanglement witness. The quantum network is shown to need far fewer epochs and a much smaller network to achieve comparable or better results.

Reinforcement and backpropagation training for an optical neural network using self-lensing effects.

The optical bench training of an optical feedforward neural network, developed by the authors, is presented. The network uses an optical nonlinear material for neuron processing and a trainable applied optical pattern as the network weights. The nonlinear material, with the applied weight pattern, modulates the phase front of a forward propagating information beam by dynamically altering the index of refraction profile of the material. To verify that the network can be trained in real time, six logic gates were trained using a reinforcement training paradigm. More importantly, to demonstrate optical backpropagation, three gates were trained via optical error backpropagation. The output error is optically backpropagated, detected with a CCD camera, and the weight pattern is updated and stored on a computer. The obtained results lay the ground work for the implementation of multilayer neural networks that are trained using optical error backpropagation and are able to solve more complex problems.

Neural network implementation using self-lensing media.

An all-optical implementation of a feed-forward artificial neural network is presented that uses self-lensing materials in which the index of refraction is irradiance dependent. Many of these types of material have ultrafast response times and permit both weighted connections and nonlinear neuron processing to be implemented with only thin material layers separated by free space. Both neuron processing and weighted interconnections emerge directly from the physical optics of the device. One creates virtual neurons and their connections simply by applying patterns of irradiance to thin layers of the nonlinear media. This is a result of a variation of the refractive-index profile of the self-lensing nonlinear media in response to the applied irradiance. An optical-backpropagation training method for this network is presented. The optical backpropagation is a training method that can be implemented potentially within the same optical device as the forward calculations, although several issues crucial to this po sibility remain to be addressed. Such a network was numerically simulated and trained to solve many benchmark classification problems, and some of these results are presented. To demonstrate the feasibility of building such a network, we also describe experimental work in the construction of an optical network trained to perform a logic XNOR function. This network, as a proof of concept, uses a relatively slow thermal nonlinear material with ~1-s response time.