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Quantitative Universal Approximation for Noisy Quantum Neural Networks

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  • Lukas Gonon
  • Antoine Jacquier
  • Marcel Mordarski

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.

Suggested Citation

  • Lukas Gonon & Antoine Jacquier & Marcel Mordarski, 2026. "Quantitative Universal Approximation for Noisy Quantum Neural Networks," Papers 2604.02064, arXiv.org, revised May 2026.
    • Handle: RePEc:arx:papers:2604.02064
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    1. Samson Wang & Enrico Fontana & M. Cerezo & Kunal Sharma & Akira Sone & Lukasz Cincio & Patrick J. Coles, 2021. "Noise-induced barren plateaus in variational quantum algorithms," Nature Communications, Nature, vol. 12(1), pages 1-11, December.
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