A duplication-free quantum neural network for universal approximation

TL;DR

This paper introduces a duplication-free quantum neural network that is universal, resource-efficient, noise-robust, and suitable for near-term quantum devices, capable of solving diverse classical and quantum learning tasks.

Contribution

It presents a novel quantum neural network design that is universal, requires fewer qubits, has a shallower circuit, and is more noise-resistant than existing models.

Findings

Proved the universality of the proposed model.

Achieved significant reduction in qubits and circuit depth.

Demonstrated effectiveness on classical and quantum learning problems.

Abstract

The universality of a quantum neural network refers to its ability to approximate arbitrary functions and is a theoretical guarantee for its effectiveness. A non-universal neural network could fail in completing the machine learning task. One proposal for universality is to encode the quantum data into identical copies of a tensor product, but this will substantially increase the system size and the circuit complexity. To address this problem, we propose a simple design of a duplication-free quantum neural network whose universality can be rigorously proved. Compared with other established proposals, our model requires significantly fewer qubits and a shallower circuit, substantially lowering the resource overhead for implementation. It is also more robust against noise and easier to implement on a near-term device. Simulations show that our model can solve a broad range of classical and quantum learning problems, demonstrating its broad application potential.