4.6 Article

Complete classification of trapping coins for quantum walks on the two-dimensional square lattice

期刊

PHYSICAL REVIEW A
卷 102, 期 1, 页码 -

出版社

AMER PHYSICAL SOC
DOI: 10.1103/PhysRevA.102.012207

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资金

  1. Czech Grant Agency [17-00844S]
  2. MSMT [RVO 14000]
  3. project Centre for Advanced Applied Sciences - Operational Programme Research, Development and Education [CZ.02.1.01/0.0/0.0/16_ 019/0000778]
  4. European Structural and Investment Funds
  5. state budget of the Czech Republic
  6. National Research, Development and Innovation Office of Hungary [K124351, 2017-1.2.1-NKP-2017-00001]
  7. ERC Consolidator Grant QPROGRESS
  8. QuantERA project QuantAlgo [680-91-034]
  9. Institute for Quantum Information and Matter, an NSF Physics Frontiers Center (NSF) [PHY-1733907]
  10. Technical University of Ostrava [SP2018/44]

向作者/读者索取更多资源

One of the unique features of discrete-time quantum walks is called trapping, meaning the inability of the quantum walker to completely escape from its initial position, although the system is translationally invariant. The effect is dependent on the dimension and the explicit form of the local coin. A four-state discrete-time quantum walk on a square lattice is defined by its unitary coin operator, acting on the four-dimensional coin Hilbert space. The well-known example of the Grover coin leads to a partial trapping, i.e., there exists some escaping initial state for which the probability of staying at the initial position vanishes. On the other hand, some other coins are known to exhibit strong trapping, where such an escaping state does not exist. We present a systematic study of coins leading to trapping, explicitly construct all such coins for discrete-time quantum walks on the two-dimensional square lattice, and classify them according to the structure of the operator and the manifestation of the trapping effect. We distinguish three types of trapping coins exhibiting distinct dynamical properties, as exemplified by the existence or nonexistence of the escaping state and the area covered by the spreading wave packet.

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