Coined Quantum Walks on Complex Networks for Quantum Computers

TL;DR

This paper presents a quantum circuit design for implementing coined quantum walks on complex networks, demonstrating scalable performance and experimental validation on current quantum hardware.

Contribution

The authors introduce a dual-register encoding method that simplifies circuit construction for complex networks and evaluate its performance through simulations and real quantum hardware.

Findings

Circuit depth scales as approximately N^{1.9} regardless of network topology.

Hardware-aware optimization improves performance metrics on larger networks.

Current NISQ devices are limited but the framework is scalable for fault-tolerant quantum computing.

Abstract

We propose a quantum circuit design for implementing coined quantum walks on complex networks. In complex networks, the coin and shift operators depend on the varying degrees of the nodes, which makes circuit construction more challenging than for regular networks. To address this issue, we use a dual-register encoding to enable a simplified shift operator and reduces the resource overhead. We implement the circuit using Qmod, a high-level quantum programming language, and evaluated the performance through numerical simulations on Erd\H{o}s-R\'enyi, Watts-Strogatz, and Barab\'asi-Albert models. The results show that the circuit depth scales as approximately $N^{1.9}$ regardless of the network topology. Furthermore, we execute the proposed circuits on the ibm\_torino superconducting quantum processor for Watts-Strogatz models with $N=4$ and $N=8$. The experiments show that hardware-aware optimization slightly improved the variation distance and Hellinger fidelity for the larger network, whereas connectivity constraints imposed overhead for the smaller one. These results indicate that while current NISQ devices are limited to small-scale validations, the polynomial scaling of our framework makes it suitable for larger-scale implementations in the fault-tolerant quantum computing era.