Quantum Walk with Jumps

We analyze a special class of 1-D quantum walks (QWs) realized using optical multi-ports. We assume non-perfect multi-ports showing errors in the connectivity, i.e. with a small probability the multi- ports can connect not to their nearest neighbor but to another multi-port at a fixed distance - we call this a jump. We study two cases of QW with jumps where multiple displacements can emerge at one timestep. The first case assumes time-correlated jumps (static disorder). In the second case, we choose the positions of jumps randomly in time (dynamic disorder). The probability distributions of position of the QW walker in both instances differ significantly: dynamic disorder leads to a Gaussian-like distribution, while for static disorder we find two distinct behaviors depending on the parity of jump size. In the case of even-sized jumps, the distribution exhibits a three-peak profile around the position of the initial excitation, whereas the probability distribution in the odd case follows a Laplace-like discrete distribution modulated by additional (exponential) peaks for long times. Finally, our numerical results indicate that by an appropriate mapping an universal functional behavior of the variance of the long-time probability distribution can be revealed with respect to the scaled average of jump size.Comment: 11 pages, 13 figure

Quantum walks: a comprehensive review

Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation. Quantum walks is now a solid field of research of quantum computation full of exciting open problems for physicists, computer scientists, mathematicians and engineers. In this paper we review theoretical advances on the foundations of both discrete- and continuous-time quantum walks, together with the role that randomness plays in quantum walks, the connections between the mathematical models of coined discrete quantum walks and continuous quantum walks, the quantumness of quantum walks, a summary of papers published on discrete quantum walks and entanglement as well as a succinct review of experimental proposals and realizations of discrete-time quantum walks. Furthermore, we have reviewed several algorithms based on both discrete- and continuous-time quantum walks as well as a most important result: the computational universality of both continuous- and discrete- time quantum walks.Comment: Paper accepted for publication in Quantum Information Processing Journa

Programmable holographic technique for implementing unitary and nonunitary transformations

Beyond the possibilities of linear transformations in polarization space, whose dimensionality is constrained by limited orthogonal states, we propose a technique for implementing both unitary and nonunitary transformations with higher dimensionality. Any high-dimensional matrix can be decomposed into a product of two processes realizable by utilizing spatial phase modulation and free-space propagation, in a simple, fixed, and scalable setup. Given that perfect power transmission for an arbitrary matrix may not be possible, the method is optimized to reach the theoretical best. Projected applications of the method described here include a means of restricting the infinite-dimensional Hilbert space to a finite-dimensional basis for information processing purposes, simultaneous multichannel optical routing, and a method of optical orbital angular momentum sorting and generation

Simulations of two-particle interactions with 2D quantum walks in time

© 2014 AIP Publishing LLC. We present the experimental implementation of a quantum walk on a two-dimensional lattice and show how to employ the optical system to simulate the quantum propagation of two interacting particles. Our quantum walk in time transfers the spatial spread of a quantum walk into the time domain, which guarantees a high stability and scalability of the setup. We present with our device quantum walks over 12 steps on a 2D lattice. By changing the properties of the driving quantum coin, we investigate different kinds of two-particle interactions and reveal their impact on the occurring quantum propagation

Photons walking the line:A quantum walk with adjustable coin operations

We present the first robust implementation of a coined quantum walk over five steps using only passive optical elements. By employing a fiber network loop we keep the amount of required resources constant as the walker’s position Hilbert space is increased. We observed a non-Gaussian distribution of the walker’s final position, thus characterizing a faster spread of the photon wave packet in comparison to the classical random walk. The walk is realized for many different coin settings and initial states, opening the way for the implementation of a quantum-walk-based search algorithm

Quantum simulations with a two-dimensional quantum walk

We present an experimental implementation of a quantum walk in two dimensions, employing an optical fiber network. We simulated entangling operations and nonlinear multi-particle interactions revealing phenomena such as bound states. © 2012 OSA

Vývoj radiačního poškození v čistém W a slitině W-Cr-Hf způsobené 5 MeV Au ionty v širokém rozsahu dpa

Čistý W a slitina W-Cr-Hf, které jsou perspektivními materiály pro jaderné fúzní reaktory, jako je DEMO, byly ozářeny při pokojové teplotě 5 MeV ionty Au2+ s dávkami mezi 4 × 10e14 a 1,3 × 10e16 ionty.cm-2 za účelem vytvoření různých úrovní poškození mřížky od jednotek až po desítky dpa. Odlišný charakter akumulace radiačního poškození, mikrostruktura a povaha defektů byly pozorovány u čistého W i slitin W-Cr-Hf, přičemž tyto slitiny vykazovaly zajímavou schopnost reorganizace poškození a snížení velikosti defektu při vyšších dávkách iontů, jak bylo stanoveno pozitronovou anihilační spektroskopií. (PAS). Vysoká míra radiačního poškození v ozařované vrstvě byla prokázána ve vzorcích W již při nižších dávkách Au-iontů ve srovnání se vzorky W-Cr-Hf, kde se poškození stupňovitě zvyšovalo s rostoucí dávkou Auiontů. Zřetelná akumulace defektů byla doprovázena odlišnou distribucí implantovaných Au-iontů v ozařované vrstvě stanovenou sekundární iontovou hmotnostní spektrometrií (SIMS), stejně jako tepelné vlastnosti ukázaly následné zhoršení hloubky v dobré shodě s Au koncentračními hloubkovými profily. TEM potvrdila výše uvedená zjištění, kde podpovrchová vrstva vykazovala po ozáření uvolnění defektů, maximum hustoty dislokační smyčky bylo identifikováno v hloubce podle predikovaného maxima dpa (posun částic na atom) pro nižší dávku Au-iontů. Kromě toho TEM ukazuje, že struktura pásu hustoty dislokací se objevila ve vzorcích W-Cr-Hf vykazujících pásmo defektů s vysokou hustotou podle projektovaného rozsahu Au-iontů současně s další vrstvou s většími izolovanými dislokacemi vyjádřenými ve větší hloubce jako rostoucí funkce dávky Au-iontů. Takový jev nebyl u W vzorků pozorován.Pure W and W-Cr-Hf alloy which are prospective materials for nuclear fusion reactors, such as DEMO, were irradiated at room temperature with 5 MeV Au2+ ions with fluences between 4 × 10e14 and 1.3 × 10e16 ions.cm-2 to generate various levels of lattice damage from about units up to tens of dpa. The distinct character of radiation damage accumulation, microstructure and defect nature have been observed in both pure W and W-Cr-Hf alloys, the latter exhibited interesting ability of damage reorganisation and defect size decrease at the higher ion fluences as determined by positron annihilation spectroscopy (PAS). High radiation damage rate in the irradiated layer has been evidenced in the W samples already at the lower Au-ion fluences compared to W-Cr-Hf samples, where the damage increased in steps with the increasing Au-ion fluence. The distinct defect accumulation was accompanied with the different Au-ion implanted distribution in the irradiated layer determined by Secondary Ion Mass Spectrometry (SIMS) as well as the thermal properties have shown the consequent worsening in the depth in good agreement with the Au-depth concentration profiles. TEM corroborated above mentioned findings, where the sub-surface layer exhibited defect release after the irradiation, the maximum of dislocation loop density has been identified in the depth according the predicted dpa (displacement particles per atom) maximum for the lower Au-ion fluences. Moreover, TEM shows the dislocation density band structure appeared in W-Cr-Hf samples exhibiting the high density defect band according the projected range of the Au-ions simultaneously with the additional layer with larger isolated dislocations pronounced in the higher depth as a growing function of Au-ion fluence. Such phenomenon was not observed in W samples