Physics

Qubit

Mathematics

Algorithm

Statistical physics

Artificial intelligence

Multilayer perceptron

Geometry

Computer science

Quantum computer

Quantum mechanics

Theoretical computer science

Scalability

Artificial neural network

Perceptron

Database

Quantum

Dissipative system

Scaling

Physical Review Letters

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 call 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. Our work represents the first rigorous analysis of the scalability of a perceptron-based QNN.

Trainability of Dissipative Perceptron-Based Quantum Neural Networks