A Quantum Information Theoretic View On A Deep Quantum Neural Network

TL;DR

This paper explores a quantum deep neural network model where qubits and unitaries replace neurons and weights, analyzing its learning process through quantum information theory and questioning the fundamental limits imposed by quantum uncertainty.

Contribution

It introduces a quantum neural network framework using qubits and unitaries, and investigates the impact of quantum uncertainty on its learning dynamics.

Findings

Heisenberg uncertainty bounds influence gradient changes

Quantum non-commutativity does not limit neural network optimization

Quantum information perspective provides new insights into quantum neural learning

Abstract

We discuss a quantum version of an artificial deep neural network where the role of neurons is taken over by qubits and the role of weights is played by unitaries. The role of the non-linear activation function is taken over by subsequently tracing out layers (qubits) of the network. We study two examples and discuss the learning from a quantum information theoretic point of view. In detail, we show that the lower bound of the Heisenberg uncertainty relations is defining the change of the gradient descent in the learning process. We raise the question if the limit by Nature to two non-commuting observables, quantified in the Heisenberg uncertainty relations, is ruling the optimization of the quantum deep neural network. We find a negative answer.