Quantum Walks in Periodic and Quasiperiodic Fibonacci Fibers

Abstract

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 have 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 offdiagonal 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.

Localization of Light in Photonics Lattices for All-Optical Representation of Binaries

“…The results from our previous works, in particular, the very good agreements between experiments and theoretical results on QWs [16], suggest that a photonics lattice composed with different waveguides that break periodicity of the normal lattices can create localizations of light in the system. Localization of light in arrays of waveguides have been investigated both with coherent [16][17][18][19] and quantum sources20 [20][21][22][23]. We have expanded our investigation to different structures, and among them, we found new structures-the binary photonics lattices (BPLs) that are simple but can be used for ORB that doesn't require optical nonlinearity--a long sought component for optical digital computing.…”

“…We have extended the method to simulate single photons QWs in periodic and quasiperiodic photonics lattices [13][14][15]. Furthermore, using the same approach, we have recently simulated and designed for fabrication of the first quasiperiodic Fibonacci MCRFs for realizing localized quantum walks (LQWs) [16]. Our simulation results are in very good agreement with experiments of quantum walks (QWs) and LQWs in periodic and quasiperiodic MCRFs, respectively, [16].…”

“…It is worth noting that the concept of binary photonics lattices originates from our previous works on quantum walks (QWs) in arrays of waveguides, especially the localization in quasi-periodic Fibonacci arrays of waveguides [13][14][15], and in our quasiperiodic Fibonacci multicore ring fiber (MCRF) [16]. The results from our previous works, in particular, the very good agreements between experiments and theoretical results on QWs [16], suggest that a photonics lattice composed with different waveguides that break periodicity of the normal lattices can create localizations of light in the system. Localization of light in arrays of waveguides have been investigated both with coherent [16][17][18][19] and quantum sources20 [20][21][22][23].…”

“…The output of photon distribution from the system is then very sensitive to the tolerance of propagation distance where the measurement is taken. It is shown in our previous works on both theory and experiment of single photon quantum walks in periodic and quasiperiodic photonics lattices, a reasonably large number of WGs are needed so that the distributions of photons are meaningful [13][14][15], especially for experimental implementations [16]. It is worth noting that the problem of single photon quantum walks is equivalent to the problem of propagation of coherent light in photonics lattices which is the one under consideration in this work [13][14][15][16][17][18][19].…”

“…It is shown in our previous works on both theory and experiment of single photon quantum walks in periodic and quasiperiodic photonics lattices, a reasonably large number of WGs are needed so that the distributions of photons are meaningful [13][14][15], especially for experimental implementations [16]. It is worth noting that the problem of single photon quantum walks is equivalent to the problem of propagation of coherent light in photonics lattices which is the one under consideration in this work [13][14][15][16][17][18][19]. This fact dictates us to construct BPLs that compose a reasonably large number of WGs, and at the same time the mapping BAW N ↔BR N with 1↔A, 0↔B is always satisfied so that BAW N can be used to represent the BR N of number N. Clearly, the expressions of BRs with adding "0s" described above helps us to construct photonics lattices with large numbers of WGs Bs added on the left of the last WG in these BAWs.…”