Connecting Quantum Computing with Classical Stochastic Simulation

ArXiv ID: 2509.18614 “View on arXiv”

Authors: Jose Blanchet, Mark S. Squillante, Mario Szegedy, Guanyang Wang

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.

Keywords: Quantum Monte Carlo, Amplitude Estimation, Grover’s Algorithm, Qiskit Implementation, Monte Carlo Integration, General Computational Finance

Complexity vs Empirical Score

• Math Complexity: 6.5/10
• Empirical Rigor: 4.0/10
• Quadrant: Lab Rats
• Why: The paper discusses advanced quantum algorithms like amplitude estimation and error correction with substantial mathematical formalism, but the implementation is a proof-of-concept tutorial (Python/Qiskit) without backtests or large-scale data, placing it in the lab research domain.

  flowchart TD
    A["Research Goal:<br/>Bridge Quantum & Classical<br/>Monte Carlo"] --> B["Data/Inputs:<br/>Financial Payoff Functions<br/>(e.g., Option Pricing)"]
    B --> C["Methodology:<br/>Grover's Algorithm<br/>(Unstructured Search)"]
    C --> D["Computational Process:<br/>Amplitude Estimation<br/>(Phase Estimation on Grover)"]
    D --> E["Output:<br/>Quantum Monte Carlo<br/>Integration"]
    E --> F["Implementation:<br/>Python/Qiskit Simulation"]
    F --> G["Key Findings:<br/>Potential Speedup &<br/>Current Scaling Challenges"]