TY  - JOUR
AU  - Arrighi, P.
AU  - Di Molfetta, G.
AU  - Marquez-Martin, I.
AU  - Perez, A.
PY  - 2019
DA  - 2019//
TI  - From curved spacetime to spacetime-dependent local unitaries over the honeycomb and triangular Quantum Walks
T2  - Sci Rep
JO  - Scientific Reports
SP  - 10904
EP  - 10pp
VL  - 9
PB  - Nature Publishing Group
AB  - A discrete-time Quantum Walk (QW) is an operator driving the evolution of a single particle on the lattice, through local unitaries. In a previous paper, we showed that QWs over the honeycomb and triangular lattices can be used to simulate the Dirac equation. We apply a spacetime coordinate transformation upon the lattice of this QW, and show that it is equivalent to introducing spacetime-dependent local unitaries-whilst keeping the lattice fixed. By exploiting this duality between changes in geometry, and changes in local unitaries, we show that the spacetime-dependent QW simulates the Dirac equation in (2 + 1)-dimensional curved spacetime. Interestingly, the duality crucially relies on the non linear-independence of the three preferred directions of the honeycomb and triangular lattices: The same construction would fail for the square lattice. At the practical level, this result opens the possibility to simulate field theories on curved manifolds, via the quantum walk on different kinds of lattices.
SN  - 2045-2322
UR  - https://arxiv.org/abs/1812.02601
UR  - https://doi.org/10.1038/s41598-019-47535-4
DO  - 10.1038/s41598-019-47535-4
LA  - English
N1  - WOS:000477701800007
ID  - Arrighi_etal2019
ER  -