Abstract
We present the single-particle sector of a quantum cellular automaton, namely a quantum walk, on a simple dynamical triangulated 2 - manifold. The triangulation is changed through Pachner moves, induced by the walker density itself, allowing the surface to transform into any topologically equivalent one. This model extends the quantum walk over triangular grid, introduced in a previous work, by one of the authors, whose space-time limit recovers the Dirac equation in (2+1)-dimensions. Numerical simulations show that the number of triangles and the local curvature grow as t α e − β t 2 , where α and β parametrize the way geometry changes upon the local density of the walker, and that, in the long run, flatness emerges. Finally, we also prove that the global behavior of the walker, remains the same under spacetime random fluctuations.
Subject
Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)
Cited by
4 articles.
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1. Geodesic quantum walks;Physical Review A;2022-06-13
2. Quantum control using quantum memory;Scientific Reports;2020-12
3. Growing Random Graphs with Quantum Rules;Electronic Proceedings in Theoretical Computer Science;2020-04-03
4. Proceedings 9th International Conference on Quantum Simulation and Quantum Walks;Electronic Proceedings in Theoretical Computer Science;2020-04-03