Quantum walk state transfer on a hypercube

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.

Automated summary

In this study, state transfer on a hypercube through quantum walk is investigated. The search for a single marked vertex is analyzed first, demonstrating the possibility of state transfer between arbitrary vertices. The transfer of state between antipodal vertices is then considered, showing that high-fidelity transfer can be achieved in a shorter time by adjusting the weight of the loop. Finally, state transfer between vertices of arbitrary distance is investigated, with results for antipodal vertices being applicable when the distance is at least 2.