Neural networks with quantum architecture and quantum learning

Abstract

A method is proposed for solving the two key problems facing quantum neural networks: introduction of nonlinearity in the neuron operation and efficient use of quantum superposition in the learning algorithm. The former is indirectly solved by using suitable Boolean functions. The latter is based on the use of a suitable nonlinear quantum circuit. The resulting learning procedure does not apply any optimization method. The optimal neural network is obtained by applying an exhaustive search among all the possible solutions. The exhaustive search is carried out by the proposed quantum circuit composed of both linear and nonlinear components. © 2009 John Wiley & Sons, Ltd

The quest for a Quantum Neural Network

“…Neurons are macroscopic objects with dynamics on the timescale of microseconds, and a quron's theoretically introduced two quantum states refer to a process involving millions of ions in a confined space, leading to estimated decoherence times in the order of 10 −13 sec and less [6], thus making quantum effects unlikely to play a role in neural information processing. However, QNNs promise to be very powerful computing devices [10,11]. Their potential lies in the fact that they exploit the advantages of superposition-based quantum computing and parallel-processed neural computing at the same time.…”

Weightless neural network parameters and architecture selection in a quantum computer

“…In [8,11] quantum neural models are pure abstract mathematical devices and in [12] quantum neural networks are described as a physical device. In this paper we follow the first approach where a neural network is a mathematical model.…”

“…Learning algorithms for quantum neural networks are also proposed in [8,11] where a superposition of neural networks with a fixed architecture is created and a quantum search is performed to recover the best neural network architecture. In this paper we propose a variation of this methodology to train quantum weightless neural networks.…”

“…Attempts to bring quantum computing power to a greater range of problems are the development of quantum machine-learning algorithms as decision trees [6], evolutionary algorithms [7] and artificial neural networks [8,9,10,11,12,13,14,15,16]. In this paper, we are concerned in the field of quantum weightless neural networks.…”

“…For instance, quantum weightless neural networks [13], neural networks with quantum architecture [8] and a simple quantum neural network [11]. In all these works [13,8,11] a quantum neural network configuration is represented by a string of qubits and quantum learning algorithms are proposed within a common framework. The main idea of the learning algorithms in [13,8,11] is to present input data to all possible neural networks for a given architecture in superposition and perform a quantum search in the resulting superposition.…”