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Applied Optics and Photonics China: Optoelectronics and Micro/Nano-Optics (AOPC)

Simulating continuous-time and discrete-time quantum walks with self-collimated light

Qingyan Ma, Yufei Wang, Zhishuang Liu, Wanhua Zheng

Published Oct 24, 2017• 0 citations
Publisher

Abstract

Quantum walks (QWs) have been proposed as powerful tools in a broad range of fields. Discrete-time QW (DTQW) is an extension of the classical random walk, where the walker goes back and forth along a line and the direction at each step depends on the result of a fair coin flip. Continuous-time QW (CTQW) can be shown as a limit of DTQW. Many objects, such as atoms, trapped ions etc., have been used to simulate QW. But photon, with the wave-particle duality, is easy to generate and can be easily manipulated in many platforms, such as space light circuits and integrated optical platforms. Silicon-on-insulator (SOI) integrated optics have been widely used, among these self-collimation photonic crystal shows a great potential. In this paper we propose the simulation of CTQWs and DTQWs with self-collimation photonic crystal chip fabricated on 830 nm thick top silicon SOI. Similarity between theory results and simulations are analyzed.

DOI
10.1117/12.2284914

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Quantum walks (QWs) have been proposed as powerful tools in a broad range of fields. Discrete-time QW (DTQW) is an extension of the classical random walk, where the walker goes back and forth along a line and the direction at each step depends on the result of a fair coin flip. Continuous-time QW (CTQW) can be shown as a limit of DTQW. Many objects, such as atoms, trapped ions etc., have been used to simulate QW. But photon, with the wave-particle duality, is easy to generate and can be easily manipulated in many platforms, such as space light circuits and integrated optical platforms. Silicon-on-insulator (SOI) integrated optics have been widely used, among these self-collimation photonic crystal shows a great potential. In this paper we propose the simulation of CTQWs and DTQWs with self-collimation photonic crystal chip fabricated on 830 nm thick top silicon SOI. Similarity between theory results and simulations are analyzed.
In self-collimated photonic crystal, periodically arranged air holes of sub-wavelength scale provide flattened equi-frequency curves perpendicular to the ΓM direction, which allow light or photons propagating in a quasi-uniform medium without diffraction. Here we for the first time experimentally simulate four-step single-photon discrete time quantum walks with classical light in such a photonic crystal chip fabricated on silicon-on-insulator. Similarities between theoretical expectations and experimental results are higher than 0.98. The functional area is compact and can be extended to construct more complicated linear quantum circuits.
We present a review of photonic implementations of discrete-time quantum walks (DTQW) in the spatial and temporal domains, based on spatial- and time-multiplexing techniques, respectively. Additionally, we propose a detailed novel scheme for photonic DTQW, using transverse spatial modes of single photons and programmable spatial light modulators (SLM) to manipulate them. Unlike all previous mode-multiplexed implementations, this scheme enables simulation of an arbitrary step of the walker, only limited, in principle, by the SLM resolution. We discuss current applications of such photonic DTQW architectures in quantum simulation of topological effects and the use of non-local coin operations based on two-photon hybrid entanglement.
Quantum walks (QWs) simulate particle behaviors in the quantum mechanical regime, which exhibit time evolutions completely different from the classical (probabilistic) random works [1]. QWs offer quantum physical simulations and the novel approach to build quantum computers. Currently on-chip photonic devices implementing QWs have been intensively developed. QW photonic chips were realized using photonic circuits based on silica (SiO2) waveguide platforms [1,2]. Here, we demonstrate a QW chip based on the other waveguide platform, namely the long-range surface plasmon polariton (LR-SPP) waveguide [3]. The LR-SPP waveguide allows a single-polarization mode, and has relatively low optical losses. Moreover, the LR-SPP waveguide platform will realize two-dimensional waveguide lattice structures with a high reliability. Thus, the LR-SPP waveguide is the potential platform to construct large-scale and high-dimension QW simulators.
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.
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, which is photonic integrated circuits. In this work, we review how the employment of this versatile experimental platform has allowed exploring several phenomena related to QW-based protocols, such as evolution in the 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 the 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 suggest 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.