A. Nayak and A. Vishwanath, "Quantum walk on the line", quant-ph/0010117. Home/Search Document Not in Database Summary Related Articles Check |
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Quantum Walks On Graphs - Aharonov, Ambainis, Kempe, Vazirani (2000) (4 citations) (Correct)
....De nition 2.3 Dispersion Time: minfT j 8t T ; D 0 ; X V : D t (X) 1 ) X)g. The mixing time is related to the gap between the (unique) largest eigenvalue 1 = 1 of the stochastic matrix P , and the second largest eigenvalue 2 . Theorem 2. 4 Mixing time and spectral gap: [6] 2 (1 2 ) log 2 M 1 (1 2 ) max i log 1 i log 1 ) 1) The mixing time of a random walk on a graph is strongly related to a geometric property of the graph, the conductance, denoted by . De nition 2.5 Let the capacity CX and the ow FX of a subset X G of the graph ....
A. Nayak and A. Vishwanath, Quantum walk on a line, Private Communication, October 2000.
One-Dimensional Quantum Walks - Ambainis, Bach, Nayak, Vishwanath.. (3 citations) Self-citation (Nayak Vishwanath) (Correct)
....basis, where it can easily be solved, and at the end revert back to the real space description by inverting the Fourier transformation. This and the following two subsections represent a preliminary exposition of an analysis of the two way infinite timed Hadamard walk to be given in more detail in [26]. The dynamics for q in the Hadamard walk is given by the following transformation (cf. Figure 1) t i) 1 1 (n i, t) w (n i, t) M (n i,t) M (n i,t) for matrices M , M defined appropriately. Since the particle starts at the origin with chirality state RIGHT, we have the ....
A. Nayak and A. Vishwanath. Quantum walk on the line. In prepaxation. Preliminaxy version available from the Los Alamos Preprint Archive, quant-ph/0010117.
One-Dimensional Quantum Walks - Ambainis, Bach, Nayak, Vishwanath.. (3 citations) Self-citation (Nayak Vishwanath) (Correct)
....basis, where it can easily be solved, and at the end revert back to the real space description by inverting the Fourier transformation. This and the following two subsections represent a preliminary exposition of an analysis of the two way in nite timed Hadamard walk to be given in more detail in [26]. The dynamics for in the Hadamard walk is given by the following transformation (cf. Figure 1) n; t 1) 0 0 1 p 2 1 p 2 (n 1; t) 1 p 2 1 p 2 0 0 (n 1; t) M (n 1; t) M (n 1; t) for matrices M ; M de ned appropriately. Since the particle starts ....
A. Nayak and A. Vishwanath. Quantum walk on the line. In preparation. Preliminary version available from the Los Alamos Preprint Archive, quant-ph/0010117.
Parrondo Games As Lattice Gas Automata - Meyer, Blumer (2001) (1 citation) (Correct)
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A. Nayak and A. Vishwanath, "Quantum walk on the line", quant-ph/0010117.
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