Möbius quantum walk
Majid Moradi, Mostafa Annabestani · Journal of Physics A Mathematical and Theoretical · 2017
Abstract By adding an extra Hilbert space to the Hadamard quantum walk on cycle (QWC), we present a new type of QWC, the Möbius quantum walk (MQW). The new space configuration enables the particle to rotate around the axis of movement. We define the factor α as the Möbius factor, which is the number of rotations per cycle. So, by α = 0 we have a normal QWC, while α ≠ 0 defines a new type of QWC (namely the MQW). In particular, α = 1 2 defines a structure similar to the Möbius strip. We analytically investigate this new type of QWC and found that by tuning the parameter α we can reach uniform distribution for any number of nodes, while it is impossible for a normal QWC. The effects of α on the limiting distribution are investigated and an explicit formula for non-uniform cases is also derived.