Noisy dynamics of confined quantum walks on a chip

TL;DR

The paper addresses how boundary confinement and realistic dynamic noise shape discrete-time quantum walks implemented on an on-chip photonic platform. By combining numerical simulations of unbounded and confined lattices with experiments on an 8-site lattice using a 20-port photonic processor, it reveals how boundary reflections generate oscillatory interference patterns and how time-dependent phase noise can either hinder or preserve coherence depending on its strength and temporal structure. The study identifies regimes where relatively low dynamic noise yields robust, quasi-coherent dynamics despite confinement, suggesting approaches for noise-resilient, scalable integrated photonic quantum devices. Overall, the work demonstrates rich interplay between confinement and noise in photonic QWs and provides quantitative benchmarks (variance dynamics, TVD) for theory-experiment agreement.

Abstract

Quantum walks represent an excellent testbed for investigating the interplay between unitary coherent and incoherent dissipative processes. Thanks to photonic quantum interferometers of considerable size, experimental studies could be performed, devoted to investigating the consequences of different sorts of realistic noise in these systems. In this work we employ a 20x20 on-chip multimode interferometer to introduce another key aspect in the problem: the presence of edges in the walker lattice, enforcing a confined evolution. We show how noise can disrupt translational symmetry and reshape interference patterns. The non trivial probability distributions obtained along the temporal evolution of the system demonstrate how speed up effects, localization and coherent oscillations are pillar concepts to be fully characterized and understood when applied in realistic quantum dynamics.

Figures (11)

• Figure 1: Top: scheme of a confined 8-site QW in the photonic processor built as a cascade of Mach-Zehender interferometers. Light is injected from the two central input waveguides (red arrows). Colored ovals on the waveguides represent phase shifters. Bottom: probability distribution of a confined 8-site Hadamard QW up to 20 steps.
• Figure 2: Time evolution of variance of the walkers' mean position (calculated with respect to the middle point of the spatial axis) in three different scenarios for QW in unbounded lattice: noise-free configuration (red line), QW with dynamic noise (green line), and QW with time-sorted dynamic noise (purple line). The dashed line in the inset indicates the quadratic trend followed by the variance when disorder increases with the time steps: after the first $\sim60-70$ steps, the dynamic of the QW starts to deviate from the ballistic regime, which is typically observed in the absence of noise. Probability distributions are averaged over 100 random configurations for each kind of noisy QW. The standard deviation of data points are represented by colored bands.
• Figure 3: Time evolution of the variance of the mean position for a disorder-free QW: comparison between the propagation of walkers in confined (red circles) and unbounded (dark cyan triangles) lattice. Colored lines are shown as guides to the eye.
• Figure 4: Variance of the mean position as a function of the number of steps for a confined QW with dynamic weak noise (colored lines are shown as guides to the eye). Probability distributions are averaged over 100 random configurations for each kind of noisy QW. Errors are shown as colored bands. (a) Dynamic noise with stepwise increasing phases (time-sorted disorder). (b) Dynamic time-unsorted noise.
• Figure 5: Variance of the mean position as a function of the number of steps for a confined QW with dynamic strong noise (colored lines are shown as guides to the eye). Probability distributions are averaged over 100 random configurations for each kind of noisy QW. Errors are shown as colored bands. (a) Dynamic noise with stepwise increasing phases (time-sorted disorder). (b) Dynamic time-unsorted noise.