Enhanced quantum transport in chiral quantum walks

TL;DR

The paper tackles enhancing quantum transport on chain-like graphs by leveraging chiral continuous-time quantum walks with edge phases. It introduces a framework of phase degrees of freedom, defines chain units (P, C, DiC), and applies Krylov reduction alongside spectral analysis to understand transport optimization. The main findings identify three optimal chain units—C3, C4, and DiC4—that yield strong long-distance transport, with C4 chains behaving like sped-up paths and C3/DiC4 relying on chirality; a phase configuration that optimizes the first transport maximum emerges as a robust design principle. The work demonstrates that phase engineering combined with topology can produce directional, high-fidelity quantum transport and offers practical avenues for quantum routing and entanglement transfer in networked quantum systems.

Abstract

Quantum transport across discrete structures is a relevant topic of solid state physics and quantum information science, which can be suitably studied in the context of continuous-time quantum walks. The addition of phases degrees of freedom, leading to chiral quantum walks, can also account for directional transport on graphs with loops. We discuss criteria for quantum transport and study the enhancement that can be achieved with chiral quantum walks on chain-like graphs, exploring different topologies for the chain units and optimizing over the phases. We select three candidate structures with optimal performance and investigate their transport behaviour with Krylov reduction. While one of them can be reduced to a weighted line with minor couplings modulation, the other two are truly chiral quantum walks, with enhanced transport probability over long chain structures.

Figures (16)

• Figure 1: A numbered graph (a) and its Laplacian matrix (b)
• Figure 2: Three representatives of the three phase configurations addressed in this paper. From left to right: P4, C5, DiC8(1-5). Start and end sites are highlighted.
• Figure 3: Evolution of localization probability on target site for C7 as a function of time (x) and phase applied to the cycle (y). The two plot represent the same evolution on 2 different time window, $\nu$ (see below) is respectively set to 2 (a) and 12 (b). It is evident how difference in applied phase may result in two completely unrelated evolutions.
• Figure 4: Transport time (corresponding to the first maximum of the transport probability) for a sample of graphs from the three classes P(black), C(blue) and h(C)(orange), plotted as function of endpoint distance. The search time-window for each graph scales linearly with distance. We set $\nu=1$ (a), $\nu=5$ (b), and $\nu=20$ (c).
• Figure 5: Transport time of first maxima (as obtained with the optimal phase value) for chains composed by 3 different units: C3, C4, DiC4(1,3). The black solid line represents the behaviour observed for P (for reference). As it is apparent from the plot, all the conisdered chain topologies provide a speedup with respect to the reference. The horizontal axis displays the topological distance (directly related to the number of units), while the vertical axis represents the transport times of first maxima.