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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Simulations of two particle dynamics employing dynamic coin control in 2D quantum walks

Andreas Schreiber, Fabian Katzschmann, A. Gábris, Peter P. Rohde, Kaisa Laiho, M. Štefaňák, Václav Potoček, Craig S. Hamilton, Igor Jex, Christine Silberhorn

Published May 1, 2013• 0 citations
Publisher

Abstract

There has been constantly rising interest in quantum walks in recent years, as they are a well-snited framework to study quantum algorithms, for example [1, 2] or to use them as a simulator for other quantum systems, which are not as readily accessible [3]. A key element for a versatile simulator is the ability to dynamically control the quantum-coin, which is the main entity responsible for the evolution of the quantum walk.

DOI
10.1109/cleoe-iqec.2013.6801681

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There has been constantly rising interest in quantum walks in recent years, as they are a well-snited framework to study quantum algorithms, for example [1, 2] or to use them as a simulator for other quantum systems, which are not as readily accessible [3]. A key element for a versatile simulator is the ability to dynamically control the quantum-coin, which is the main entity responsible for the evolution of the quantum walk.
Abstract Photonic implementations of unitary processes on lattice structures, such as quantum walks, have been demonstrated across various architectures. However, few platforms offer the combined advantages of scalability, reconfigurability, and the ability to simulate dynamics on lattices with periodic boundary conditions, such as cyclic or toroidal geometries. Here, we employ a recently developed platform that enables the implementation of arbitrary translationally invariant unitary operations on one- and two-dimensional lattices, and demonstrate a natural mechanism for introducing periodic boundary conditions. Our approach leverages direct access to the reciprocal lattice, where discrete sampling of the unitary evolution effectively enforces the desired topology. We program our platform to realize quantum walks on 1D cyclic lattices and 2D lattices with cylindrical or toroidal topologies. The lattice size can be readily tuned by adjusting the sampling density in reciprocal space. By controlling reciprocal-space occupancy, we investigate the dynamics of localized states and wavepackets, observing refocusing behavior, breathing modes modulated by reciprocal-space discretizations, and wavepacket trajectories that reflect the underlying topology. We further demonstrate a form of dimensional reduction by mapping a 2D quantum walk on a cylinder to a 1D walk with a high-dimensional coin. These results establish a versatile platform for realizing a broad class of optical mode transformations within bounded Hilbert spaces.
Quantum walk research has mainly focused on evolutions due to repeated applications of time-independent unitary coin operators. However, the idea of controlling the single particle evolution using time-dependent unitary coins has still been a subject of multiple studies as it not only hosts interesting possibilities for quantum information processing but also opens a much richer array of phenomena including static and dynamic localizations. So far, such studies have been performed only for single quantum walkers. In case of multi-walker systems, time-dependent coins may generate measurable phenomena not described by the single-particle model, due to entanglement and interaction among the walkers. In this context, we present here a thorough numerical study of an one dimensional system of two quantum walkers exhibiting rich collective dynamics controlled by simple time-dependent unitary coins proposed in [Phys. Rev. A \textbf{80}, 042332(2009)] and [Phys. Rev. A \textbf{73},062304(2006)]. We study how the interplay of coin time-dependence, simple interaction schemes, entanglement and the relative phase between the coin states of the particles influences the evolution of the quantum walk. The results show that the system offers a rich variety of collective dynamical behavior while being controlled by time dependent coins. In particular, we find and characterize fascinating two-body localization phenomena with tunable quasiperiodic dynamics of correlations and entanglements which are quantities of quantum origin.
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.