"\u0158e\u0161iteln\u00E9 modely kvantov\u00FDch proch\u00E1zek a jejich aplikace" . . . "http://www.isvav.cz/projectDetail.do?rowId=GP14-02901P"^^ . . "2014-04-07+02:00"^^ . "Kvantov\u00E1 proch\u00E1zka je zobecn\u011Bn\u00EDm n\u00E1hodn\u00E9 proch\u00E1zky na unit\u00E1rn\u00ED v\u00FDvoj kvantov\u00E9 \u010D\u00E1stice na diskr\u00E9tn\u00ED m\u0159\u00ED\u017Ece. Nach\u00E1z\u00ED uplatn\u011Bn\u00ED v kvantov\u00E9 informaci, nap\u0159\u00EDklad v algoritmu pro prohled\u00E1v\u00E1n\u00ED neuspo\u0159\u00E1dan\u00FDch datab\u00E1z\u00ED. Je to tak\u00E9 vhodn\u00FD n\u00E1stroj pro kvantov\u00E9 simulace. Abychom mohli kvantovou proch\u00E1zku efektivn\u011B vyu\u017E\u00EDt, mus\u00EDme rozum\u011Bt jej\u00EDmu chov\u00E1n\u00ED. C\u00EDlem t\u00E9to grantov\u00E9 aplikace je roz\u0161\u00ED\u0159it na\u0161e znalosti o vlivu oper\u00E1tor\u016F mince a po\u010D\u00E1te\u010Dn\u00EDch podm\u00EDnek na dynamiku kvantov\u00E9 proch\u00E1zky. Prvn\u00EDm t\u00E9matem je vysv\u011Btlen\u00ED z\u00E1vislosti rozd\u011Blen\u00ED grupov\u00FDch rychlost\u00ED kvantov\u00E9 proch\u00E1zky na po\u010D\u00E1te\u010Dn\u00EDm stavu mince. C\u00EDle dos\u00E1hneme vhodnou zm\u011Bnou b\u00E1ze prostoru mince. To n\u00E1m umo\u017En\u00ED naj\u00EDt extrem\u00E1ln\u00ED re\u017Eimy chov\u00E1n\u00ED kvantov\u00E9 proch\u00E1zky. Druh\u00FDm c\u00EDlem projektu je nal\u00E9zt t\u0159\u00EDdy minc\u00ED, pro kter\u00E9 m\u016F\u017Eeme nal\u00E9zt analytick\u00FD tvar disperzn\u00EDch relac\u00ED. P\u0159edev\u0161\u00EDm se chceme zam\u011B\u0159it na mince, kter\u00E9 vedou na lokalizaci, a zkoumat vlastnosti odpov\u00EDdaj\u00EDc\u00EDch v\u00E1zan\u00FDch stav\u016F. D\u00E1le chceme vytvo\u0159it protokol pro p\u0159enos stavu zalo\u017Een\u00FD na kvantov\u00E9 proch\u00E1zce, kter\u00FD vy\u017Eaduje jen minim\u00E1ln\u00ED kontrolu nad syst\u00E9mem." . "2015-02-09+01:00"^^ . "quantum walk, coin operator, perfect state transfer"@en . . " coin operator" . . "Solvable models of quantum walks and their applications"@en . "1"^^ . . "GP14-02901P" . . . . . "0"^^ . "2"^^ . "2"^^ . . "2014-01-01+01:00"^^ . . "0"^^ . . . . . "quantum walk" . "Quantum walk is a generalization of a random walk to a unitary evolution of a quantum particle on a discrete lattice. It can be applied to quantum information tasks such as search of an unsorted database. To use the quantum walk efficiently one has to understand its properties. The aim of this grant application is to extend our knowledge of the role of coin operators and initial states on the quantum walk dynamics. First topic is to clarify the dependence of the group velocity density of the quantum walk on the initial coin state. We achieve this goal by a suitable change of the basis of the coin space. This allows us to analyze in full detail the extremal regimes of the quantum walk. The second part of the proposal aims to find classes of coins for which the dispersion relations can be found analytically. In particular, we want to determine coins leading to localization and analyze the properties of the resulting bound states. Finally, we want to develop a quantum walk based protocol for perfect state transfer which requires only minimal control over the system."@en . . "2016-12-31+01:00"^^ .