Quantitative Universal Approximation for Noisy Quantum Neural Networks
This work addresses the challenge of applying quantum neural networks in practical, noisy environments, specifically for quantitative finance, representing an incremental advancement in the field.
The paper tackles the problem of approximating target functions, particularly expectations in quantitative finance, using noisy quantum neural networks, and provides a universal approximation theorem with precise quantitative error bounds, validated through numerical analysis on actual noisy quantum hardware.
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.