Quantum advantage of Monte Carlo option pricing

Abstract

Quantum computers have the potential to provide quadratic speedup for Monte Carlo methods currently used in various classical applications. In this work, we examine the advantage of quantum computers for financial option pricing with the Monte Carlo method. Systematic and statistical errors are handled in a joint framework, and a relationship to quantum gate error is established. New metrics are introduced for the assessment of quantum advantage based on sample count and optimized error handling. We implement and analyze a Fourier series based approach and demonstrate its benefit over the more traditional rescaling method in function approximation. Our numerical calculations reveal the unpredictable nature of systematic errors, making consistent quantum advantage difficult with current quantum hardware. Our results indicate that very low noise levels, a two-qubit gate error rate below 10−6, are necessary for the quantum method to outperform the classical one, but a low number of logical qubits (ca. 20) may be sufficient to see quantum advantage already.