Scrambling Ability of Quantum Neural Networks Architectures

TL;DR

This paper introduces a principle linking quantum information scrambling to the learning efficiency of quantum neural networks, demonstrating that architectures with higher scrambling ability perform better in learning tasks.

Contribution

It proposes a novel measure of quantum information scrambling for neural network architectures and links it to their learning efficiency, supported by computational examples.

Findings

Higher averaged operator size correlates with faster loss reduction.

Architectures with greater scrambling ability achieve higher accuracy faster.

The approach can be extended to complex quantum machine learning algorithms.

Abstract

In this letter we propose a general principle for how to build up a quantum neural network with high learning efficiency. Our stratagem is based on the equivalence between extracting information from input state to readout qubit and scrambling information from the readout qubit to input qubits. We characterize the quantum information scrambling by operator size growth, and by Haar random averaging over operator sizes, we propose an averaged operator size to describe the information scrambling ability for a given quantum neural network architectures, and argue this quantity is positively correlated with the learning efficiency of this architecture. As examples, we compute the averaged operator size for several different architectures, and we also consider two typical learning tasks, which are a regression task of a quantum problem and a classification task on classical images, respectively. In both cases, we find that, for the architecture with a larger averaged operator size, the loss function decreases faster or the prediction accuracy in the testing dataset increases faster as the training epoch increases, which means higher learning efficiency. Our results can be generalized to more complicated quantum versions of machine learning algorithms.