A Quantum Information Theoretic View On A Deep Quantum Neural Network

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.

arXiv comment8 pages, 5+2 new figures

References in corpus (8)

• Entanglement of a Pair of Quantum Bits
• Barren plateaus in quantum neural network training landscapes
• Efficient Learning for Deep Quantum Neural Networks
• The Bitter Truth About Quantum Algorithms in the NISQ Era
• Entropic Uncertainty Relations in Quantum Physics
• Composite parameterization and Haar measure for all unitary and special unitary groups
• BEINIT: Avoiding Barren Plateaus in Variational Quantum Algorithms
• Evaluating the performance of sigmoid quantum perceptrons in quantum neural networks