Trainability of Dissipative Perceptron-Based Quantum Neural Networks

TL;DR

This paper investigates the trainability of dissipative quantum neural networks (DQNNs), revealing that they can suffer from barren plateaus with exponentially vanishing gradients, and provides bounds on their gradient scaling under various conditions.

Contribution

The study offers the first rigorous analysis of gradient scaling in DQNNs, highlighting conditions where trainability may be compromised.

Findings

DQNNs can exhibit barren plateaus with exponentially vanishing gradients.

Provided quantitative bounds on gradient scaling for DQNNs.

Trainability of DQNNs depends on circuit depth and cost functions.

Abstract

Several architectures have been proposed for quantum neural networks (QNNs), with the goal of efficiently performing machine learning tasks on quantum data. Rigorous scaling results are urgently needed for specific QNN constructions to understand which, if any, will be trainable at a large scale. Here, we analyze the gradient scaling (and hence the trainability) for a recently proposed architecture that we called dissipative QNNs (DQNNs), where the input qubits of each layer are discarded at the layer's output. We find that DQNNs can exhibit barren plateaus, i.e., gradients that vanish exponentially in the number of qubits. Moreover, we provide quantitative bounds on the scaling of the gradient for DQNNs under different conditions, such as different cost functions and circuit depths, and show that trainability is not always guaranteed.