Trojan Quantum Walks

TL;DR

This paper explores how specific initial states and quantum gates in one-dimensional quantum walks can produce non-spreading, Trojan wave packets, revealing new insights into quantum transport and entanglement.

Contribution

It introduces the concept of Trojan wave packets in quantum walks, showing how initial delocalization and gate operations can control wave packet spreading.

Findings

Delocalized initial states enable non-spreading wave packets.

NOT gate reflection can extinguish interference patterns.

Trojan wave packets maintain propagation without dispersion.

Abstract

We investigate the transport properties and entanglement between spin and position of one-dimensional quantum walks starting from a qubit over position states following a delta-like (local state) and Gaussian (delocalized state) distributions. We find out that if the initial state is delocalized enough and a NOT gate reflects this state backwards, then the interference pattern extinguishes the position dispersion without preventing the propagation of the state. This effect allows the creation of a Trojan wave packet, a non-spreading and non-stationary double-peak quantum state.