Quantum walk processes in quantum devices

TL;DR

This paper investigates how to efficiently simulate quantum walk processes on quantum computers by exploring their relationship with quantum circuits, focusing on hypercube and arbitrary graphs to improve quantum algorithms.

Contribution

It introduces methods to represent quantum walks as quantum circuits, enhancing simulation efficiency for NISQ devices and advancing quantum algorithm implementation.

Findings

Methods to obtain graphs from quantum circuits

Techniques to represent quantum walks as quantum circuits

Potential for improved quantum walk simulations on quantum computers

Abstract

Simulation and programming of current quantum computers as Noisy Intermediate-Scale Quantum (NISQ) devices represent a hot topic at the border of current physical and information sciences. The quantum walk process represents a basic subroutine in many quantum algorithms and plays an important role in studying physical phenomena. Simulating quantum walk processes is computationally challenging for classical processors. With an increasing improvement in qubits fidelity and qubits number in a single register, there is a potential to improve quantum walks simulations substantially. However, efficient ways to simulate quantum walks in qubit registers still have to be explored. Here, we explore the relationship between quantum walk on graphs and quantum circuits. Firstly, we discuss ways to obtain graphs provided quantum circuit. We then explore techniques to represent quantum walk on a graph as a quantum circuit. Specifically, we study hypercube graphs and arbitrary graphs. Our approach to studying the relationship between graphs and quantum circuits paves way for the efficient implementation of quantum walks algorithms on quantum computers.