# Continuous-Time Quantum Walks on Dynamic Graphs

## TL;DR

This paper extends continuous-time quantum walks to dynamic graphs, demonstrating their potential for universal quantum computation and proposing physical implementations using quantum optical waveguides.

## Contribution

It introduces a framework for CTQWs on dynamic graphs, enabling universal quantum gate implementation and providing explicit examples and simulations.

## Key findings

- Dynamic graphs can implement universal quantum gates.
- Numerical simulations validate quantum teleportation and addition circuits.
- Potential physical realization with quantum optical waveguides.

## Abstract

Continuous-time quantum walks (CTQWs) on static graphs provide efficient methods for search and sampling as well as a model for universal quantum computation. We consider an extension of CTQWs to the case of dynamic graphs, in which an ordered sequence of graphs governs free evolution of the quantum walk. We then consider how perfect state transfer during the quantum walk can be used to design dynamic graphs that implement a universal set of quantum logic gates. We give explicit examples for a complete logical basis, and we validate implementations using numerical simulations for quantum teleportation and addition circuits. Finally, we discuss the potential for realizing CTQWs on dynamic graphs using actively controlled quantum optical waveguides.