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When working with quantum walks in other dimensions (1D – 2D – 3D...) do your results tend to be different from what is proposed in theory with the probability density? The results obtained in the qiskit for a quantum walk differ from those seen in theory, as proposed in the image below, is there any research or explanation for this difference?

4 step of the discrete-time quantum walk in a cycle of 4 knots

4 steps of the discrete-time quantum walk in a cycle of 4-node

5 steps discrete-time quantum walk in a 6-node cycle

5 steps discrete-time quantum walk in a 6-node cycle along with the graph described in theory

Circuit for 4-node cycle enter image description here

Circuit for 6-node cycle enter image description here

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  • $\begingroup$ what are you asking precisely? Whether/why quantum walks differ from classical random walks (they do)? Or whether/why the results you got from the IBM device differ from what you'd have expected from the theory of quantum walks? These are rather different questions. You should probably also further specify what kind of quantum walk you're considering. Looks like a discrete-time one, but what's the coin operation, and how do you define the walk operation precisely? $\endgroup$
    – glS
    May 24 at 7:54
  • $\begingroup$ It would be because the results I got differ from what I expected in theory. Yes it's a walk in discrete time, I'm using the IBM standard hadamard currency, the walk generation would be the application of the currency operator, along with the rotations to the right and left of the cycle, which would be the operator shift (increment and decrement gates) $\endgroup$
    – Ikky R
    May 27 at 13:02

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