Randomness-enhanced expressivity of quantum neural networks

TL;DR

This paper introduces a method to improve quantum neural networks by adding randomness, enabling them to better approximate complex functions and perform various learning tasks on noisy quantum devices.

Contribution

The authors propose a novel randomness-based enhancement to QNNs, increasing their expressivity and applicability in quantum machine learning tasks.

Findings

Randomness improves QNN expressivity across tasks

Enhanced QNNs accurately approximate target operators

Demonstrated success in image recognition and entropy measurement

Abstract

As a hybrid of artificial intelligence and quantum computing, quantum neural networks (QNNs) have gained significant attention as a promising application on near-term, noisy intermediate-scale quantum (NISQ) devices. Conventional QNNs are described by parametrized quantum circuits, which perform unitary operations and measurements on quantum states. In this work, we propose a novel approach to enhance the expressivity of QNNs by incorporating randomness into quantum circuits. Specifically, we introduce a random layer, which contains single-qubit gates sampled from an trainable ensemble pooling. The prediction of QNN is then represented by an ensemble average over a classical function of measurement outcomes. We prove that our approach can accurately approximate arbitrary target operators using Uhlmann's theorem for majorization, which enables observable learning. Our proposal is demonstrated with extensive numerical experiments, including observable learning, R\'enyi entropy measurement, and image recognition. We find the expressivity of QNNs is enhanced by introducing randomness for multiple learning tasks, which could have broad application in quantum machine learning.