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Photonics for Quantum (PfQ)

Quantum walks in two-dimension arrays of waveguides

Dan Trung Nguyen, Kam C. Ng, Santanu Basu, Daniel A. Nolan, David A. S. Loeber

Published Jul 19, 2022• 1 citation
Publisher

Abstract

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.

DOI
10.1117/12.2638193

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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.
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.
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.
We report on our latest findings on photonic Quantum Walks (QW) of entangled particles in several quantum transport regimes as for instance in photonic Bloch lattices or disordered lattices. Furthermore, the discrete fractional Fourier transform of quantum states is presented in the context of QWs. The propagation of a classical single walker on a random graph is an important field in statistics and can be applied on many domains in nature reaching from a foraging animals over Brownian molecular motion towards the evolution of lead changes in competitive team sports. Its quantum mechanical counterpart, the Quantum Walk (QW), features genuine quantum objects to walk on a random graph and hence, leading to non-classical quantum interference, in particular when considering two or more walkers. Their great potential lies i.a. in their ability to exponentially speed up a multitude of algorithms, as for instance the data bank search algorithm from L. Grover. In this regard, photonic lattices of evanescently coupled waveguides represent an ideal platform to study QW dynamics, since they feature advantages in stability, robustness and miniaturization. Our waveguide lattices were fabricated by means the direct laser inscription technique. In doing so, three dimensional waveguide geometries are realizable, enabling the implementation of various QW graphs. Along these lines, we study QWs of entangled photon pairs in disordered lattices. There we observe Anderson co-localization, meaning that neither the individual photons nor the pair localizes, rather their distance does. It turns out that both photons tend to bunch as they will be found together in the same lattice site, implying that their original correlation remains while performing a QW in a disordered lattice. Further, we investigate QWs of non-local two-photon EPR-states in Bloch-lattices. The experimental results reveal the strong dependence of the correlation output statistics (bosonic-, anyonicor fermionic-like) on the input states' symmetry. Finally, the discrete fractional Fourier transform of quantum states is realized through a discrete QW lattice. The results demonstrate the enormous potential of waveguide lattices in the field of quantum photonics and give rise to further investigations like the Fourier suppression law.
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.
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.
Abstract Quantum walks (QWs) are one of the fundamental concepts in quantum information science, being an essential component for various new applications. Implementing QWs using integrated photonic waveguide lattices allows for realizing long evolution times, for exploring novel lattice geometries, and even for controllable coupling to the environment. This tutorial gives an introduction to the field of on-chip QWs of single photons and photon pairs featuring non-classical two-photon correlations.