Implementation of Leaking Quantum Walks on a Photonic Processor

TL;DR

This work investigates how partially absorbing boundaries affect a discrete-time quantum walk (DTQW) implemented on a photonic processor. By combining theory with an on-chip programmable platform, it introduces a boundary with tunable strength $r^2$ and a fully reflective edge on an 8-mode lattice realized over up to $N=20$ steps, enabling non-Hermitian, boundary-controlled quantum dynamics. The results show that weak leakage largely preserves coherence and interference patterns similar to a lossless QW, while strong leakage accelerates mean propagation and increases spreading, breaking certain symmetries and emulating decoherence effects. Overall, the study demonstrates programmable open-quantum-system simulations on integrated photonics, with boundary engineering offered as a versatile tool to tune transport and coherence in quantum devices.

Abstract

Quantum walks represent pillars of quantum dynamics and information processing. They provide a powerful framework for simulating quantum transport, designing search algorithms, and achieving universal quantum computation. Several physical platforms have been employed to implement QWs, such as trapped atoms, trapped ions, nuclear magnetic resonance systems and photonic quantum systems either in bulk optics or waveguide structures and fiber-loop networks. Here we focus on the most promising approach, that is photonic integrated circuits. We will review how the employment of this versatile experimental platform has allowed to explore several phenomena related to QW-based protocols, e.g. 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.

Figures (8)

• Figure 1: Scheme of the confined leaking QW with $2M=8$ modes, implemented as a cascade of MZ interferometers. The pale-blue waveguide at the upper edge of the lattice (input mode 1, corresponding to the position $x=-3.5$) represents the leaking boundary, where photon are partially lost. The dark-blue waveguide at the bottom edge (input mode 8, corresponding to $x=3.5$ along the position axis) depicts hard-confinement boundary, where photons are totally reflected back into the lattice. The internal gray waveguides (input modes 2-7) implement Hadamard coin operation with balanced BS. Light is injected from one of the input modes as described in the text.
• Figure 2: Scheme of the experimental setup. Attenuated coherent light plays the role of the walker which is injected into the tunable photonic processor via a polarization maintaining fiber (PMF). The processor implements the QW unitary and the output is sent to the measurement stage through single mode fibers (SMF). The measurement apparatus consists of a photodiode used to retrieve the probability distributions across the output modes. Thanks to a computer-driven reconfigurability of the processor, we implemented various leaking configurations.
• Figure 3: Simulated mean position (left column, panels (a) and (c)) and variance of the mean position (right column, panels (b) and (d)) as a function of the number of steps: comparison between the four selected input modes for $r^2 = 0.2$ (panels (a) and (b)) and $r^2=0.8$ (panels (c) and (d)), corresponding to low- and high-leakage regime, respectively.
• Figure 4: Mean position (left) and variance of the mean position (right) as a function of the number of steps in the case of $r^2=0.8$ corresponding to a strongly leaking boundary for different initial sites of the walk, namely site 2 corresponding to position $x=-2.5$ (blue dots), site 3 ($x=1.5$ orange squares), site 6 ($x=1.5$, violet triangles) and site 7 ($x=2.5$, cyan diamonds). Symbols correspond to experimental data, lines to theoretical behaviors.
• Figure 5: Mean position (left) and variance of the mean position (right) as a function of the number of steps in the case of $r^2=0.2$ corresponding to a weakly leaking boundary for different initial sites of the walk, namely site 2 corresponding to position $x=-2.5$ (cyan circles) and site 6 ($x=1.5$, pink triangles). Symbols correspond to experimental data, lines to theoretical behaviors.