Quantum walk approach to simulating parton showers

TL;DR

This paper introduces a quantum walk-based algorithm for simulating parton showers on quantum computers, offering improved efficiency and scalability over previous methods, and demonstrating its potential for more realistic simulations.

Contribution

It presents a novel quantum walk framework for simulating parton showers, significantly increasing the number of steps and efficiency compared to prior quantum algorithms.

Findings

Successfully simulated a 31-step toy model of a parton shower

Quantum walk approach scales exponentially with qubits

Circuit depth grows linearly with the number of steps

Abstract

This paper presents a novel quantum walk approach to simulating parton showers on a quantum computer. We demonstrate that the quantum walk paradigm offers a natural and more efficient approach to simulating parton showers on quantum devices, with the emission probabilities implemented as the coin flip for the walker, and the particle emissions to either gluons or quark pairs corresponding to the movement of the walker in two dimensions. A quantum algorithm is proposed for a simplified, toy model of a 31-step, collinear parton shower, hence significantly increasing the number of steps of the parton shower that can be simulated compared to previous quantum algorithms. Furthermore, it scales efficiently: the number of possible shower steps increases exponentially with the number of qubits, and the circuit depth grows linearly with the number of steps. Reframing the parton shower in the context of a quantum walk therefore brings dramatic improvements, and is a step towards extending the current quantum algorithms to simulate more realistic parton showers.