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IntechOpen eBooks

Quantum Walks in Quasi-Periodic Photonics Lattices

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

Published Jul 22, 2019• 4 citations
Publisher

Abstract

We present construction rules for a new class of quasiperiodic photonics lattices (QPL) to realize localized quantum walks (LQWs) deterministically.The new quasiperiodic structures are constructed symmetrically with Fibonacci, Thue-Morse, and other quasiperiodic sequences.Our construction rules allow us to build the symmetrical quasiperiodic photonics lattices.As a result, LQWs with symmetrical probability distributions can be realized in these QPLs.Furthermore, the proposed QPLs are composed with different waveguides providing both on-and off-diagonal deterministic disorders.We show LQWs in the proposed QPLs are highly programmable and controllable.

DOI
10.5772/intechopen.87758

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We present construction rules for a new class of quasiperiodic photonics lattices (QPL) to realize localized quantum walks (LQWs) deterministically.The new quasiperiodic structures are constructed symmetrically with Fibonacci, Thue-Morse, and other quasiperiodic sequences.Our construction rules allow us to build the symmetrical quasiperiodic photonics lattices.As a result, LQWs with symmetrical probability distributions can be realized in these QPLs.Furthermore, the proposed QPLs are composed with different waveguides providing both on-and off-diagonal deterministic disorders.We show LQWs in the proposed QPLs are highly programmable and controllable.
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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.
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