Quantum walk based Monte Carlo simulation for photon interaction cross sections

TL;DR

This paper presents a quantum-enhanced Monte Carlo simulation framework using quantum walks and amplitude estimation to model photon interactions, achieving quadratic speedup and high fidelity in high-energy physics simulations.

Contribution

It introduces a novel quantum algorithm integrating quantum walks with amplitude estimation for photon interaction modeling, demonstrating significant speedup over classical methods.

Findings

Quadratic speedup in amplitude estimation compared to classical Monte Carlo.

High fidelity reproduction of classical probability distributions.

Feasibility of quantum algorithms for complex particle physics simulations.

Abstract

High-energy physics simulations traditionally rely on classical Monte Carlo methods to model complex particle interactions, often incurring significant computational costs. In this paper, we introduce a novel quantum-enhanced simulation framework that integrates discrete-time quantum walks with quantum amplitude estimation to model photon interaction cross sections. By mapping the probabilistic transport process of 10 MeV photons in a water medium onto a quantum circuit and focusing on Compton scattering as the dominant attenuation mechanism, we demonstrate that our approach reproduces classical probability distributions with high fidelity. Simulation results obtained via the IBM Qiskit quantum simulator reveal a quadratic speedup in amplitude estimation compared to conventional Monte Carlo methods. Our framework not only validates the feasibility of employing quantum algorithms for high-energy physics simulations but also offers a scalable pathway toward incorporating multiple interaction channels and secondary particle production. These findings underscore the potential of quantum-enhanced methods to overcome the computational bottlenecks inherent in large-scale particle physics simulations.