High-expressibility Quantum Neural Networks using only classical resources

TL;DR

This paper demonstrates that high-expressibility quantum neural networks can be simulated using classical resources by analyzing the properties of matrix-product states and Clifford-enhanced states, challenging the necessity of quantum hardware.

Contribution

The study shows that classical simulations of quantum neural network properties are feasible, revealing that high expressibility does not require quantum resources.

Findings

CMPS approach the Haar distribution faster than MPS in entanglement and magic.

Classical states can replicate properties attributed to quantum neural networks.

High expressibility in QNNs can be achieved without quantum hardware.

Abstract

Quantum neural networks (QNNs), as currently formulated, are near-term quantum machine learning architectures that leverage parameterized quantum circuits with the aim of improving upon the performance of their classical counterparts. In this work, we show that some desired properties attributed to these models can be efficiently reproduced without necessarily resorting to quantum hardware. We indeed study the expressibility of parametrized quantum circuit commonly used in QNN applications and contrast it to those of two classes of states that can be efficiently simulated classically: matrix-product states (MPS), and Clifford-enhanced MPS (CMPS), obtained by applying a set of Clifford gates to MPS. In addition to expressibility, we assess the level of primary quantum resources, entanglement and non-stabilizerness (a.k.a. "magic"), in random ensembles of such quantum states, tracking their convergence towards the Haar distribution. While MPS require a large number of parameters to effectively reproduce an arbitrary quantum state, we find that CMPS approach the Haar distribution more rapidly, in terms of both entanglement and magic. Our results on states with up to 20 qubits indicate that high expressibility in QNNs is attainable with purely classical resources.