Managing rogue quantum amplitudes: a control perspective in quantum walks

TL;DR

This paper explores how phase disorder influences rogue wave events in discrete-time quantum walks, revealing regimes where quantum coin choices and disorder levels can be controlled to manage extreme quantum amplitudes.

Contribution

It provides a detailed analysis of the interplay between quantum coins and disorder in generating rogue waves, offering insights into controlling extreme quantum amplitudes in DTQWs.

Findings

Rogue wave probability increases with quantum coins near Pauli-Z.

Rogue events are scarce near Pauli-X coins unless disorder is weak.

A threshold exists between rare and high-probability rogue wave regimes.

Abstract

We investigate the emergence of rogue quantum amplitudes in discrete-time quantum walks (DTQWs) influenced by phase disorder. Our study reveals the statistics of occupation probability amplitudes in space and time, uncovering optimal disorder regimes that favor rogue wave events. Through numerical simulations, we demonstrate that the probability of rogue waves increases with quantum coins close to the Pauli-Z choice, regardless the disorder degree. Conversely, for coins near Pauli-X rogue events are scarce, except under weak disorder. A monotonic threshold is observed between rare- and high-probability rogue wave regimes, depending on the quantum coin. We provide a comprehensive analysis of the coin-disorder interplay to rogue wave events. Our findings shed light on the possible control of extreme quantum amplitudes through quantum coins in disordered DTQWs.