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IEEE/LEOS Summer Topical Meetings

Quantum Walks in Quasi-Periodic Photonics Lattices

Dan Trung Nguyen, Daniel A. Nolan, Nicholas F. Borrelli

Published Jul 1, 2019• 2 citations
Publisher

Abstract

We present construction rules for a new class of quasi-periodic photonics lattices to realize localized quantum walks deterministically. The new quasi-periodic structures are constructed symmetrically with Fibonacci, Thue-Morse sequences. Our simulations show that localized quantum walks in these quasi-periodic lattices are symmetrical and highly controllable.

DOI
10.1109/phosst.2019.8794963

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We present construction rules for a new class of quasi-periodic photonics lattices to realize localized quantum walks deterministically. The new quasi-periodic structures are constructed symmetrically with Fibonacci, Thue-Morse sequences. Our simulations show that localized quantum walks in these quasi-periodic lattices are symmetrical and highly controllable.
New quasi-periodic arrays of waveguides (AWs) constructed with Fibonacci sequences are proposed to realize localized quantum walks (LQWs). The proposed Fibonacci arrays of waveguides (FAWs) are simple and straightforward to make, but have a rich set of properties that are of potential use for applications in quantum communication. Our simulations show that, in contrast with randomly disordered AWs, LQWs in FAWs are highly controllable due to the deterministic disorder nature of quasi-periodic systems. Furthermore, unique LQWs with symmetrical probability distribution can be conveniently realized in the FAWs.
Quantum walk is a key operation in quantum computing, simulation, communication and information. Here, we report for the first time the demonstration of quantum walks and localized quantum walks in a new type of optical fibers having a ring of cores constructed with both periodic and quasiperiodic Fibonacci sequences, respectively. Good agreement between theoretical and experimental results has been achieved. The new multicore ring fibers provide a new platform for experiments of quantum effects in low-loss optical fibers which is critical for scalability of real applications with large-size problems. Furthermore, our new quasiperiodic Fibonacci multicore ring fibers provide a new class of quasiperiodic photonics lattices possessing both on- and off-diagonal deterministic disorders for realizing localized quantum walks deterministically. The proposed Fibonacci fibers are simple and straightforward to fabricate and have a rich set of properties that are of potential use for quantum applications. Our simulation and experimental results show that, in contrast with randomly disordered structures, localized quantum walks in new proposed quasiperiodic photonics lattices are highly controllable due to the deterministic disordered nature of quasiperiodic systems.
In this paper, we present results of numerical investigation of quantum walks (QWs) in different type arrays of single-mode waveguides: (i) regular arrays of identical waveguides (AIW), (ii) periodic arrays of two different waveguides (PAW), (iii) quasi-periodic arrays of waveguides with Fibonacci sequences (FAW), (iv) quasi-periodic arrays of waveguides with Thue-Morse sequences (TMAW). Our simulations show in contrast with randomly disordered systems, localized QWs in quasi-periodic arrays of waveguides FAWs and TMAWs are predictable and controllable due to the deterministic disorder nature of the quasi-periodic systems.
Quantum walks (QWs) have emerged from fundamental research to be one of key processes in quantum information technology including quantum computing and quantum communication. In this paper, we present results of our numerical investigation of quantum walks (QWs) in different types of 2D arrays of waveguides. We show (i) the localized QWs in quasiperiodic arrays based on Fibonacci sequences are highly controllable due to the deterministically disordered nature of quasiperiodic photonic lattices, (ii) 2D arrays of waveguides can also be used as platforms to realize important effects for special applications such as exponential speedup in quantum search and quantum topology photonics and finally, (iii) results of multiple photons QWs in 2D programable directional couplers can be useful for designing quantum photonics gates.