Abstract
The authors develop an experimental platform to realize walks with four-dimensional coins using a looped Michelson interferometer based on the time-multiplexing technique. They are able to show walks on nontrivial finite structures, such as circles and figure-eight graphs. This paves the way to experimental implementations of important applications, e.g. quantum search, graph problems, quantum transport and magnetic walks.
Highlights
During the past two decades, quantum walks [1,2,3], the quantum mechanical analog of random walks, have become an established basis for quantum algorithms [4,5,6,7,8] and quantum simulations [9,10,11,12,13]
A marked feature of the Discrete time quantum walks (DTQWs) is an internal degree of freedom—the coin space—that conditions the spatial shift of the walker, in the same way as a coin toss determines the movement of a classical random walker
It is the dynamics in the coin space that is argued to provide the key ingredient to the complex behavior of the DTQW [6]
Summary
During the past two decades, quantum walks [1,2,3], the quantum mechanical analog of random walks, have become an established basis for quantum algorithms [4,5,6,7,8] and quantum simulations [9,10,11,12,13]. These protocols simulate higherdimensional coins by splitting up each step into multiple coin and shift operations acting on a two-dimensional coin space They have found use in realizing dynamics on graphs embedded in higher dimensions, and in 1D quantum walks on more sophisticated graphs, such as on percolation graphs or circles [45,46]. DTQWs with genuine four-dimensional coins on structures embedded in the two-dimensional (2D) space admit phases analogous to the quantum spin Hall (QSH) phases [50,51], offering significantly new applications over the phases accessible in 1D [50,52] Another example is that of the Grover walk on a 2D grid, exhibiting dynamics composed of a spreading and a localized part [53,54], of which only the spreading part can be reproduced by two-dimensional coins [55].
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