Option Pricing on Noisy Intermediate-Scale Quantum Computers: A Quantum Neural Network Approach

2026-04-20

AI Summary

This work addresses the challenge of efficiently and accurately pricing options on noisy intermediate-scale quantum (NISQ) devices within the multi-hundred-trillion-dollar derivatives market. The authors propose a quantum neural network (QNN) approach that leverages the geometric structure of Hilbert space to approximate option pricing functions, benchmarked against the Black–Scholes–Merton model. For the first time, a minimal two-qubit QNN architecture is deployed across multiple leading NISQ processors—including IBM Fez, IQM Garnet, IonQ Forte, and Rigetti Ankaa-3—demonstrating consistently high accuracy in reproducing option prices across diverse hardware platforms. These empirical results validate the cross-platform efficacy of QNNs under stringent hardware constraints and lay a foundation for the quantum implementation of more complex financial models.

Technology Category

Machine Learning: Quantum Machine LearningSearch and Optimization: Learning to SearchNatural Language Processing: Learning & Optimization for NLP

Application Category

Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactionsGraph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphsUser Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

In a global derivatives market with notional values in the hundreds of trillions of dollars, the accuracy and efficiency of pricing models are of fundamental importance, with direct implications for risk management, capital allocation, and regulatory compliance. In this work, we employ the Black-Scholes-Merton (BSM) framework not as an end in itself, but as a controlled benchmark environment in which to rigorously assess the capabilities of quantum machine learning methods. We propose a fully quantum approach to option pricing based on Quantum Neural Networks (QNNs), and, to the best of our knowledge, present one of the first implementations of such a methodology on currently available quantum hardware. Specifically, we investigate whether QNNs, by exploiting the geometric structure of Hilbert space, can effectively approximate option pricing functions. Our implementation utilizes a compact 2-qubit QNN architecture evaluated across multiple state-of-the-art quantum processors, including IBM Fez, IQM Garnet, IonQ Forte, and Rigetti Ankaa-3. This cross-platform study reveals distinct hardware-dependent performance characteristics while demonstrating that accurate pricing approximations can be achieved consistently across different devices despite the constraints of Noisy Intermediate-Scale Quantum (NISQ) hardware. The results provide empirical evidence that QNN-based approaches constitute a viable framework for derivative pricing. While the analysis is conducted within the BSM setting, the broader significance lies in the potential extension of these methods to more realistic and computationally demanding models, including local volatility, stochastic volatility, and interest rate frameworks commonly used in practice.

Problem

• Option Pricing
• Noisy Intermediate-Scale Quantum
• Quantum Neural Networks
• Derivatives
• Quantum Machine Learning

Innovation

• Quantum Neural Networks
• Option Pricing
• NISQ
• Cross-platform Quantum Hardware
• Black-Scholes-Merton