Quantum activation functions for quantum neural networks

Abstract

The field of artificial neural networks is expected to strongly benefit from recent developments of quantum computers. In particular, quantum machine learning, a class of quantum algorithms which exploit qubits for creating trainable neural networks, will provide more power to solve problems such as pattern recognition, clustering and machine learning in general. The building block of feed-forward neural networks consists of one layer of neurons connected to an output neuron that is activated according to an arbitrary activation function. The corresponding learning algorithm goes under the name of Rosenblatt perceptron. Quantum perceptrons with specific activation functions are known, but a general method to realize arbitrary activation functions on a quantum computer is still lacking. Here, we fill this gap with a quantum algorithm which is capable to approximate any analytic activation functions to any given order of its power series. Unlike previous proposals providing irreversible measurement–based and simplified activation functions, here we show how to approximate any analytic function to any required accuracy without the need to measure the states encoding the information. Thanks to the generality of this construction, any feed-forward neural network may acquire the universal approximation properties according to Hornik’s theorem. Our results recast the science of artificial neural networks in the architecture of gate-model quantum computers.

Neural Field Continuum Limits and the Structure–Function Partitioning of Cognitive–Emotional Brain Networks

“…A quantum neuron, e.g., Ref. [ 110 ], also may be developed from Equations (4) and (5) with the activation function z : where classical orthogonal variables from Equation (5) are represented as quantum state vectors having modifiable probability amplitude coefficients residing in matrices or on quantum spheres [ 111 ]. For the hybrid classical-quantum model, which may involve classical and quantum neurons, the rate at which a node increases its network links proceeds via a power law established from the exponent, where μ equals the chemical potential associated with free energy, and helps define energy states, gradients, and transition or switching thresholds between cognitive-emotional states, macrocircuits, microcircuits, and nodes.…”

Casting Rubik’s Group into a Unitary Representation for Reinforcement Learning

“…Furthermore, we have applied both supervised learning by quantum tensor networks [4] and an unsupervised learning algorithm on a quantum hardware, expressed as a QUBO problem [5]. Reinforcement Learning has been applied also in the field of quantum compiling, to apply a set of logic gates [6,7] on a quantum hardware [8,9,10]. RL algorithms have been also employed in order to tackle problems of combinatorial optimization, such as solving the Rubik's Cube [11,12] or finding out the native configuration for a protein from a sequence of amino acids [13,14,15].…”

Quantum Simulation of Tunable Neuron Activation

“…In the classical computer, this nonlinear effect can be realized by bringing in various nonlinear activation functions. It deserves a deep study DOI: 10.1002/andp.202200546 how to realize the nonlinear activation function in the quantum manner, [14][15][16][17][18][19][20] serving quantum neural networks. [21] In this work, we propose to simulate the activation of the neuron and realize the nonlinearity by the quantum operation.…”