Quantum Random Walks in One Dimension

@article{Konno2002QuantumRW,
  title={Quantum Random Walks in One Dimension},
  author={Norio Konno},
  journal={Quantum Information Processing},
  year={2002},
  volume={1},
  pages={345-354}
}
  • N. Konno
  • Published 2002
  • Physics, Computer Science
  • Quantum Information Processing
AbstractThis letter treats the quantum random walk on the line determined by a 2 × 2 unitary matrix U. A combinatorial expression for the mth moment of the quantum random walk is presented by using 4 matrices, P, Q, R and S given by U. The dependence of the mth moment on U and initial qubit state ϕ is clarified. A new type of limit theorems for the quantum walk is given. Furthermore necessary and sufficient conditions for symmetry of distribution for the quantum walk is presented. Our results… Expand
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