The defect-induced localization in many positions of the quantum random walk.

作者: Tian Chen , Xiangdong Zhang

DOI: 10.1038/SREP25767

关键词: Statistical physicsAmplitudeQuantum walkProbability distributionPhase (waves)Operator (physics)Eigenvalues and eigenvectorsPhysicsChain (algebraic topology)Position (vector)

摘要: We study the localization of probability distribution in a discrete quantum random walk on an infinite chain. With phase defect introduced any position (QRW), we have found that QRW emerges. Different localized behaviors are presented when occupies different positions. Given coefficients stationary eigenstates relies coin operator, reveal positions, amplitude exhibits non-trivial dependence operator.

参考文章(78)
Zafer Gedik, İskender Yalçınkaya, Qubit state transfer via discrete-time quantum walks Journal of Physics A. ,vol. 48, pp. 225302- ,(2015) , 10.1088/1751-8113/48/22/225302
Norio Konno, Etsuo Segawa, Localization of discrete-time quantum walks on a half line via the CGMV method Quantum Information & Computation. ,vol. 11, pp. 485- 495 ,(2011) , 10.26421/QIC11.5-6-9
Andrew M. Childs, Sam Gutmann, Edward Farhi, An Example of the Difference Between Quantum and Classical Random Walks Quantum Information Processing. ,vol. 1, pp. 35- 43 ,(2002) , 10.1023/A:1019609420309
Ho Tat Lam, Kwok Yip Szeto, Ramsauer effect in a one-dimensional quantum walk with multiple defects Physical Review A. ,vol. 92, pp. 012323- ,(2015) , 10.1103/PHYSREVA.92.012323
Clement Ampadu, Localization of Two-Dimensional Five-State Quantum Walks arXiv: Quantum Physics. ,(2011)
Clement Ampadu, Localization of M-Particle Quantum Walks arXiv: Quantum Physics. ,(2011)
Y. Aharonov, L. Davidovich, N. Zagury, Quantum random walks Physical Review A. ,vol. 48, pp. 1687- 1690 ,(1993) , 10.1103/PHYSREVA.48.1687
Antoni Wójcik, Tomasz Łuczak, Paweł Kurzyński, Andrzej Grudka, Małgorzata Bednarska, Quasiperiodic Dynamics of a Quantum Walk on the Line Physical Review Letters. ,vol. 93, pp. 180601- ,(2004) , 10.1103/PHYSREVLETT.93.180601
Edward Farhi, Sam Gutmann, Quantum computation and decision trees Physical Review A. ,vol. 58, pp. 915- 928 ,(1998) , 10.1103/PHYSREVA.58.915
Z. J. Li, J. A. Izaac, J. B. Wang, Position-defect-induced reflection, trapping, transmission, and resonance in quantum walks Physical Review A. ,vol. 87, pp. 012314-1- 012314-9 ,(2013) , 10.1103/PHYSREVA.87.012314