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arXiv:2510.16204 · Physical Review A

Decoherence-free subspaces in the noisy dynamics of discrete-step quantum walks in a photonic lattice

Rajesh Asapanna, Clément Hainaut, Alberto Amo, Álvaro Gómez-León

Published Mar 31, 2026• 0 citations
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Abstract

We study the noisy dynamics of periodically driven, discrete-step quantum walks in a one-dimensional photonic lattice. We find that in the bulk, temporal noise that is constant within a Floquet period leads to decoherence-free momentum subspaces, whereas fully random noise destroys coherence in a few time steps. When considering topological edge states, we observe decoherence no matter the type of temporal noise. To explain these results, we derive a non-perturbative master equation to describe the system's dynamics. We experimentally confirm our findings in a time multiplexed photonic lattice implemented in a double-fiber ring setup subject to laser pulse input states, in which we engineer different types of temporal noise.

DOI
10.1103/dxjw-bmng

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We study the noisy dynamics of periodically driven, discrete-step quantum walks in a one-dimensional photonic lattice. We find that in the bulk, temporal noise that is constant within a Floquet period leads to decoherence-free momentum subspaces, whereas fully random noise destroys coherence in a few time steps. When considering topological edge states, we observe decoherence no matter the type of temporal noise. To explain these results, we derive a non-perturbative master equation to describe the system's dynamics. We experimentally confirm our findings in a time multiplexed photonic lattice implemented in a double-fiber ring setup subject to laser pulse input states, in which we engineer different types of temporal noise.
The dynamics of a discrete-time quantum walk subject to time-correlated noise is studied in this paper. The noise, which goes beyond the usual telegraph noise with random variables 1 and $\ensuremath{-}1$, is modeled as a unitary coin-type operator and it is generated by a sample path of the Ornstein-Uhlenbeck process. Up to the first order in the amplitude of noise, a master equation to describe the walk is derived. The dynamics governed by the master equation is in good agreement with those given by numerical simulations within a certain number of steps, depending on the parameters of noise. Two remarkable features of long-time dynamics are observed in the numerical simulations. (1) In the slow noise regime, with the increase of the noise amplitude, the quantum coherence is suppressed, and the dynamics of noisy discrete-time quantum walk gradually transits to that of classical random walk. (2) In the fast noise regime, the walker is confined into a few lattice sites, and the width of the wave packet is much narrower compared with that in the slow noise regime.
We analyze the decoherence in quantum walks in two-dimensional lattices generated by broken-link-type noise. In this type of decoherence, the links of the lattice are randomly broken with some given constant probability. We obtain the evolution equation for a quantum walker moving on two-dimensional (2D) lattices subject to this noise, and we point out how to generalize for lattices in more dimensions. In the nonsymmetric case, when the probability of breaking links in one direction is different from the probability in the perpendicular direction, we have obtained a nontrivial result. If one fixes the link-breaking probability in one direction, and gradually increases the probability in the other direction from 0 to 1, the decoherence initially increases until it reaches a maximum value, and then it decreases. This means that, in some cases, one can increase the noise level and still obtain more coherence. Physically, this can be explained as a transition from a decoherent 2D walk to a coherent 1D walk.
We investigate the impact of decoherence and static disorder on the dynamics of quantum particles moving in a periodic lattice. Our experiment relies on the photonic implementation of a one-dimensional quantum walk. The pure quantum evolution is characterized by a ballistic spread of a photon's wave packet along 28 steps. By applying controlled time-dependent operations we simulate three different environmental influences on the system, resulting in a fast ballistic spread, a diffusive classical walk, and the first Anderson localization in a discrete quantum walk architecture.
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.
The topological phases of periodically driven, or Floquet systems, rely on a perfectly periodic modulation of system parameters in time. Even the smallest deviation from periodicity leads to decoherence, causing the boundary (end) states to leak into the system's bulk. Here, we show that in one dimension this decay of topologically protected end states depends fundamentally on the nature of the bulk states: a dispersive bulk results in an exponential decay, while a localized bulk slows the decay down to a diffusive process. The localization can be due to disorder, which remarkably counteracts decoherence even when it breaks the symmetry responsible for the topological protection. We derive this result analytically, using a novel, discrete-time Floquet-Lindblad formalism and confirm our findings with the help of numerical simulations. Our results are particularly relevant for experiments, where disorder can be tailored to protect Floquet topological phases from decoherence.
Quantum walks (QWs) represent pillars of quantum dynamics and information processing. They provide a powerful framework for simulating quantum transport, designing search algorithms, and enabling universal quantum computation. Several physical platforms have been employed for their implementation, such as trapped atoms and ions, nuclear magnetic resonance systems, and photonic quantum architectures either in bulk optics or waveguide structures and fiber-loop networks. Here we focus on the most promising and versatile approach, that is photonic integrated circuits. In this work, we review how the employment of this versatile experimental platform has allowed to explore several phenomena related to QW-based protocols as, for instance, the evolution in presence of different kinds of noise. In this landscape, to the best of our knowledge, few examples report on the introduction of absorbing centers and their effects on the coherence of the dynamics. Here we present and discuss the results related to absorbing boundaries in QWs obtained through theoretical simulations and experiments conducted with the universal photonic quantum processors realized by Quix Quantum. We analyze how localized absorption along one lattice edge affects the walker dynamics depending on both the leakage probability and the initial injection site. Our results show that the presence of controlled losses modifies interference patterns and coherence, without fully destroying quantum features and providing an effective resource for engineering on-chip QWs and simulating open quantum systems.