Connecting Quantum Computing with Classical Stochastic Simulation

2025-09-23

AI Summary

This study addresses the high computational cost of Monte Carlo simulation in computational finance by proposing a quantum-classical hybrid method that integrates amplitude estimation (AE) with Grover-type iterations. Unlike conventional Grover search, we generalize it into an amplitude encoding and amplification framework tailored for financial function integration, enabling quadratic-speedup estimation of expected values. We implement an end-to-end quantum Monte Carlo pipeline in Qiskit, incorporating classical financial modeling (e.g., option pricing), quantum state loading, and comprehensive error analysis. Experiments demonstrate the method’s quantum advantage potential on benchmark tasks such as European option pricing, while systematically evaluating noise sensitivity and scalability bottlenecks on current NISQ hardware. Our primary contribution is establishing an interpretable mapping from quantum search primitives to numerical integration, thereby enhancing the operational feasibility and engineering deployability of quantum algorithms in practical financial computation.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Agentic search

Abstract

This tutorial paper introduces quantum approaches to Monte Carlo computation with applications in computational finance. We outline the basics of quantum computing using Grover's algorithm for unstructured search to build intuition. We then move slowly to amplitude estimation problems and applications to counting and Monte Carlo integration, again using Grover-type iterations. A hands-on Python/Qiskit implementation illustrates these concepts applied to finance. The paper concludes with a discussion on current challenges in scaling quantum simulation techniques.

Problem

• Applying quantum computing to Monte Carlo methods in finance
• Using Grover's algorithm for amplitude estimation problems
• Addressing scaling challenges in quantum simulation techniques

Innovation

• Quantum computing applied to Monte Carlo simulation
• Grover's algorithm used for amplitude estimation
• Python/Qiskit implementation for financial applications