180 citations · 542 across the 13 of their papers we have counts for
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Relation between Random Walks and Quantum Walks
Stefan Boettcher, Stefan Falkner, Renato Portugal
Based on studies on four specific networks, we conjecture a general relation between the walk dimensions of discrete-time random walks and quantum walks with the (self-inve…
One-Dimensional Coinless Quantum Walks
Renato Portugal, Stefan Boettcher, Stefan Falkner
A coinless, discrete-time quantum walk possesses a Hilbert space whose dimension is smaller compared to the widely-studied coined walk. Coined walks require the direct product of t…
Weak Limit of the 3-State Quantum Walk on the Line
Stefan Falkner, Stefan Boettcher
We revisit the one dimensional discrete time quantum walk with 3 states and the Grover coin. We derive analytic expressions for observed the localization, an long time approximatio…