Quantitative Universal Approximation for Noisy Quantum Neural Networks

TL;DR

This paper establishes a quantitative universal approximation theorem for noisy quantum neural networks, with applications to finance and validation on real quantum hardware.

Contribution

It introduces a precise error-bound universal approximation theorem for noisy quantum neural networks, including numerical validation on actual hardware.

Findings

Universal approximation theorem with error bounds for noisy quantum neural networks.

Successful numerical tests on real noisy quantum hardware.

Application relevance to expectation-based functions in finance.

Abstract

We provide here a universal approximation theorem with precise quantitative error bounds for noisy quantum neural networks. We focus on applications to Quantitative Finance, where target functions are often given as expectations. We further provide a detailed numerical analysis, testing our results on actual noisy quantum hardware.