Implementation of Leaking Quantum Walks on a Photonic Processor

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.

💡 Research Summary

This paper presents a comprehensive study of discrete‑time quantum walks (DTQWs) on a one‑dimensional lattice implemented with a reconfigurable integrated photonic processor. The authors focus on the effect of a partially absorbing (leaking) boundary on the walker’s dynamics, a scenario that has received limited attention despite its relevance for simulating open quantum systems and for engineering loss‑based quantum information protocols.

The theoretical model adopts the standard coined DTQW formalism: a Hadamard coin operator followed by a conditional shift. The walk evolves on a finite lattice of 2M = 8 sites, with one edge acting as a hard reflective boundary (r² = 0) and the opposite edge as a tunable leaking boundary characterized by a transmission coefficient r². Two regimes are explored: low leakage (r² = 0.2) and high leakage (r² = 0.8). Because the leaking edge introduces non‑unitary dynamics, the total probability inside the lattice decays over time; the authors therefore analyse the normalized probability distribution that remains confined after each step. Key observables are the mean position ⟨x⟩ and the variance σ², which reveal oscillatory behavior due to repeated reflections and partial losses at the boundaries.

Numerical simulations are performed for up to N = 100 steps, considering four injection sites: two near the leaking edge (positions –2.5 and –1.5) and two near the reflective edge (positions +1.5 and +2.5). In the low‑leakage case the walker’s interference pattern is only mildly perturbed; ⟨x⟩ stays close to the injection site and σ² exhibits the characteristic linear growth of a coherent quantum walk, albeit with small amplitude modulations caused by the asymmetric boundaries. In the high‑leakage regime the dynamics change dramatically: walkers injected close to the leaking edge lose probability rapidly, the mean position drifts toward the reflective side, and the variance growth is strongly suppressed. Walkers injected near the reflective edge experience many reflections, retain a larger fraction of their probability, and display a more symmetric evolution.

Experimentally, the authors implement the model on the Quix Quantum Alquor20 processor, a silicon‑nitride (Si₃N₄) chip comprising 190 Mach‑Zehnder interferometers (MZIs) that can realize arbitrary 20‑port linear optical transformations. The device exhibits an insertion loss of ≈ 3.6 dB and an average amplitude fidelity of 98.8 % across Haar‑random unitaries. A weak coherent beam at λ = 942 nm is injected via a polarization‑maintaining fiber into a selected input port, and the processor is programmed to realize the unitary corresponding to a given number of walk steps and a specific leakage coefficient. Output intensities are collected with single‑mode fiber‑coupled photodiodes, calibrated against an identity operation to correct for port‑to‑port variations, and normalized to unit total probability.

The measured probability distributions for 4 ≤ n ≤ 20 steps match the simulated profiles closely. In the low‑leakage configuration the experimental mean position and variance follow the predicted oscillatory patterns, confirming that quantum interference survives despite modest losses. In the high‑leakage configuration the data show a pronounced shift of the probability mass away from the leaking side and a reduction of the variance, in agreement with theory. The overall probability remaining inside the lattice decreases with step number, reflecting the controlled loss at the boundary, yet the internal distribution retains non‑classical features such as asymmetry and interference fringes.

The authors conclude that integrated photonic platforms enable precise engineering of boundary conditions, allowing deterministic simulation of open quantum dynamics. Moreover, controlled loss can be turned from a detrimental error into a functional resource for designing quantum walks that mimic energy transport in biological complexes, for implementing decoherence‑assisted algorithms, or for studying loss‑induced topological phenomena. Future directions include extending the scheme to higher‑dimensional lattices, time‑dependent loss profiles, and multi‑photon interactions, thereby broadening the applicability of photonic quantum walks in quantum simulation and quantum information processing.