Qubit state transfer via discrete-time quantum walks

We propose a scheme for perfect transfer of an unknown qubit state via the discrete-time quantum walk on a line or a circle. For this purpose, we introduce an additional coin operator which is applied at the end of the walk. This operator does not depend on the state to be transferred. We show that perfect state transfer over an arbitrary distance can be achieved only if the walk is driven by an identity or a flip coin operator. Other biased coin operators and Hadamard coin allow perfect state transfer over finite distances only. Furthermore, we show that quantum walks ending with a perfect state transfer are periodic.Comment: 13 pages, 5 figure

Two-dimensional quantum walk under artificial magnetic field

We introduce the Peierls substitution to a two-dimensional discrete-time quantum walk on a square lattice to examine the spreading dynamics and the coin-position entanglement in the presence of an artificial gauge field. We use the ratio of the magnetic flux through the unit cell to the flux quantum as a control parameter. For a given flux ratio, we obtain faster spreading for a small number of steps and the walker tends to be highly localized around the origin. Moreover, the spreading of the walk can be suppressed and decreased within a limited time interval for specific rational values of flux ratio. When the flux ratio is an irrational number, even for a large number of steps, the spreading exhibit diffusive behavior rather than the well-known ballistic one as in the classical random walk and there is a significant probability of finding the walker at the origin. We also analyze the coin-position entanglement and show that the asymptotic behavior vanishes when the flux ratio is different from zero and the coin-position entanglement become nearly maximal in a periodic manner in a long time range.Comment: 7 pages, 5 figures, sections 3 and 4 revise

Spreading and transport properties of quantum walks

Quantum computing aims to harness and exploit the quantum mechanical phenomena such as superposition, entanglement and contextuality in order to encode and process information. In this context, quantum walks, which has been suggested as the quantum counterpart of classical random walks, is an emerging topic in quantum computing that provides powerful techniques for developing new quantum algorithms, quantum simulation and quantum state transfer. This thesis intends to investigate the properties of quantum walks which may potentially promote further work in such techniques in quantum computation. We first propose a novel method for transferring arbitrary unknown qubit state between two points in space with quantum walk architecture. We determine the cases providing perfect state transfers over both finite and infinite lattices with different boundary conditions and we introduce recovery operators assisting the transfer process. Next, by modeling the incoherent and coherent transport with classical random walks and quantum walks, respectively, we calculate the transport efficiencies over an explosive percolation lattice. We show that the minimal correlation between discrete clusters leads to maximal localizations which originating from random scatterings. These localization effects, however, are rather small when compared to the supportive effect of the abrupt growth of the largest cluster on transport efficiency, which eventually allows us to obtain more efficient transports in case of minimal correlations. We support our results with further calculations on whether the eigenstates of the systems we study are localized or not. Lastly, we turn our attention to the spreading dynamics and the coin-position entanglement for two-dimensional quantum walks under an artificial magnetic fields by introducing Peierls phases to the system. In particular, we show that the spreading of the quantum walk is diffusive rather than ballistic when the ratio of the magnetic flux through unit cell - where the walk takes place - to the flux quantum is an irrational number. On the contrary, the walk recovers its original ballistic behavior when this ratio is chosen to be a rational number. Furthermore, we demonstrate that coin-position entanglement is nearly maximum under an artificial magnetic field, even for large number of steps

Synchronization and Non-Markovianity in open quantum systems

Detuned systems can spontaneously achieve a synchronous dynamics and display robust quantum correlations in different local and global dissipation regimes. Beyond the Markovian limit, information backflow form the environment becomes a crucial mechanism whose interplay with spontaneous synchronization is unknown. Considering a model of two coupled qubits, one of which interacts with a dissipative environment, we show that non-Markovianity is highly detrimental for the emergence of synchronization, for the latter can be delayed and hindered because of the presence of information backflow. The results are obtained considering both a master equation approach and a collision model based on repeated interactions, which represents a very versatile tool to tailor the desired kind of environment.Comment: 6+2 pages, 5+1 figure

The Sariçiçek Howardite Fall in Turkey: Source Crater of HED Meteorites on Vesta and İmpact Risk of Vestoids

The Sariçiçek howardite meteorite shower consisting of 343 documented stones occurred on 2 September 2015 in Turkey and is the first documented howardite fall. Cosmogenic isotopes show that Sariçiçek experienced a complex cosmic ray exposure history, exposed during ~12–14 Ma in a regolith near the surface of a parent asteroid, and that an ~1 m sized meteoroid was launched by an impact 22 ± 2 Ma ago to Earth (as did one third of all HED meteorites). SIMS dating of zircon and baddeleyite yielded 4550.4 ± 2.5 Ma and 4553 ± 8.8 Ma crystallization ages for the basaltic magma clasts. The apatite U-Pb age of 4525 ± 17 Ma, K-Ar age of ~3.9 Ga, and the U,Th-He ages of 1.8 ± 0.7 and 2.6 ± 0.3 Ga are interpreted to represent thermal metamorphic and impact-related resetting ages, respectively. Petrographic, geochemical and O-, Cr- and Tiisotopic studies confirm that Sariçiçek belongs to the normal clan of HED meteorites. Petrographic observations and analysis of organic material indicate a small portion of carbonaceous chondrite material in the Sariçiçek regolith and organic contamination of the meteorite after a few days on soil. Video observations of the fall show an atmospheric entry at 17.3 ± 0.8 kms-1 from NW, fragmentations at 37, 33, 31 and 27 km altitude, and provide a pre-atmospheric orbit that is the first dynamical link between the normal HED meteorite clan and the inner Main Belt. Spectral data indicate the similarity of Sariçiçek with the Vesta asteroid family (V-class) spectra, a group of asteroids stretching to delivery resonances, which includes (4) Vesta. Dynamical modeling of meteoroid delivery to Earth shows that the complete disruption of a ~1 km sized Vesta family asteroid or a ~10 km sized impact crater on Vesta is required to provide sufficient meteoroids ≤4 m in size to account for the influx of meteorites from this HED clan. The 16.7 km diameter Antonia impact crater on Vesta was formed on terrain of the same age as given by the 4He retention age of Sariçiçek. Lunar scaling for crater production to crater counts of its ejecta blanket show it was formed ~22 Ma ago

Coherent transport over an explosive percolation lattice

We investigate coherent transport over a finite square lattice in which the growth of bond percolation clusters are subjected to an Achlioptas type selection process, i.e., whether a bond will be placed or not depends on the sizes of clusters it may potentially connect. Different than the standard percolation where the growth of discrete clusters are completely random, clusters in this case grow in correlation with one another. We show that certain values of correlation strength, if chosen in a way to suppress the growth of the largest cluster which actually results in an explosive growth later on, may lead to more efficient transports than in the case of standard percolation, satisfied that certain fraction of total possible bonds are present in the lattice. In this case transport efficiency obeys a power law in the vicinity of bond fraction where effective transport begins. It turns out that the higher correlation strengths may also reduce the efficiency as well. We also compare our results with those of the incoherent transport and examine the spreading of eigenstates of corresponing structures. We demonstrate that structural differences of discrete clusters due to different correlations result in different localization properties

Synchronization and Non-Markovianity in open quantum systems

Detuned systems can spontaneously achieve a synchronous dynamics and display robust quantum correlations in different local and global dissipation regimes. Beyond the Markovian limit, information backflow from the environment becomes a crucial mechanism whose interplay with spontaneous synchronization is unknown. Considering a model of two coupled qubits, one of which interacts with a dissipative environment, we show that non-Markovianity is highly detrimental for the emergence of synchronization, for the latter can be delayed and hindered because of the presence of information backflow. The results are obtained considering both a master equation approach and a collision model based on repeated interactions, which represents a very versatile tool to tailor the desired kind of environment.G. K. is supported by the BAGEP Award of the Science Academy, the TUBA-GEBIP Award of the Turkish Academy of Sciences, and also by the Technological Research Coun-cil of Turkey (TUBITAK) under Grant No. 117F317. ̇I. Y.is supported by MSMT under Grant No. RVO 14000. B. C ̧ .is supported by the BAGEP Award of the Science Academy,the TUBITAK under Grant No. 117F317, and also by the Research Fund of Bahc ̧es ̧ehir University (BAUBAP) under project no: BAP.2019.02.03. R.Z. and G.L.G. acknowledge financial support from MINECO/AEI/FEDER through projects PID2019-109094GB-C21, the Severo Ochoa and María de Maeztu Program for Centers and Units of Excellence in R&D (MDM-2017-0711), CSIC Research Platform PTI-001 andPIE 202050E098, and the QUAREC project funded by CAIB (PRD2018/47). GLG is funded by the Spanish Ministerio deEducación y Formación Profesional/Ministerio de Universidades and co-funded by the University of the Balearic Islandsthrough the Beatriz Galindo program (BG20/00085).N