Quantum walk state transfer on a hypercube

TL;DR

This paper explores quantum walk-based state transfer on a hypercube, demonstrating high-fidelity transfer between arbitrary vertices by tuning loop weights, with improved efficiency over switching methods.

Contribution

It introduces a method to achieve high-fidelity quantum state transfer on a hypercube using weighted loops, optimizing run-time compared to traditional switching techniques.

Findings

High-fidelity state transfer between arbitrary vertices achieved.

Tuning loop weights shortens transfer run-time.

Method effective for vertices at various distances, including neighbors.

Abstract

We investigate state transfer on a hypercube by means of a quantum walk where the sender and the receiver vertices are marked by a weighted loops. First, we analyze search for a single marked vertex, which can be used for state transfer between arbitrary vertices by switching the weighted loop from the sender to the receiver after one run-time. Next, state transfer between antipodal vertices is considered. We show that one can tune the weight of the loop to achieve state transfer with high fidelity in shorter run-time in comparison to the state transfer with a switch. Finally, we investigate state transfer between vertices of arbitrary distance. It is shown that when the distance between the sender and the receiver is at least 2, the results derived for the antipodes are well applicable. If the sender and the receiver are direct neighbours the evolution follows a slightly different course. Nevertheless, state transfer with high fidelity is achieved in the same run-time.