From curved spacetime to spacetime-dependent local unitaries over the honeycomb and triangular Quantum Walks

Arrighi, Pablo; Molfetta, Giuseppe Di; Márquez-Martín, Iván; Perez, A.

doi:10.48550/arxiv.1812.02601

Cited by 2 publications

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“…One should first extend the procedure to include arbitrary Yang-Mills and gravitational fields, thus producing QWs which model the Dirac equation in curved spacetime coupled to arbitrary gauge fields. Also, DQWs with spinors living on the edges of a graph have been introduced recently in [28,30]. The method we present in this article should thus be extended to take this possibility into account, as well as wave-functions with a higher number of components [14] than the number of spinor components of irreducible representations of the Lorentz group.…”

Section: Discussionmentioning

confidence: 99%

A new method to building Dirac quantum walks coupled to electromagnetic fields

Jay,

Debbasch,

Wang

2018

Preprint

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A quantum walk whose continuous limit coincides with Dirac equation is usually called a Dirac Quantum Walk (DQW). A new systematic method to build DQWs coupled to electromagnetic (EM) fields is introduced and put to test on several examples of increasing difficulty. It is first used to derive the EM coupling of a well-known 3D walk on the cubic lattice. Recently introduced DQWs on the triangular and honeycomb lattice are then re-derived, showing for the first time that these are the only DQWs that can be defined with spinors living on the vertices of these lattices. As a third example of the method's effectiveness, a new 3D walk on a parallelepiped lattice is derived. As a fourth, negative example, it is shown that certain lattices like the rhombohedral lattice cannot be used to build DQWs. The effect of changing representation in the Dirac equation is also discussed.

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Section: Discussionmentioning

confidence: 99%

A new method to building Dirac quantum walks coupled to electromagnetic fields

Jay,

Debbasch,

Wang

2018

Preprint

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“…In the present work we show how to overcome this issue considering more general graphs, while keeping a homogeneous evolution rule. We point out that generally inhomogeneous models (like the Staggered QW one) find their relevance on the side of the experimental implementation, or also to mimic a curved space-time [52].…”

Section: The Operatormentioning

confidence: 94%

Chirality from quantum walks without a quantum coin

2019

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Quantum walks (QWs) describe the evolution of quantum systems on graphs. An intrinsic degree of freedom-called the coin and represented by a finite-dimensional Hilbert space-is associated to each node. Scalar quantum walks are QWs with a one-dimensional coin. We propose a general strategy allowing one to construct scalar QWs on a broad variety of graphs, which admit embedding in Eulidean spaces, thus having a direct geometric interpretation. After reviewing the technique that allows one to regroup cells of nodes into new nodes, transforming finite spatial blocks into internal degrees of freedom, we prove that no QW with a two-dimensional coin can be derived from an isotropic scalar QW in this way. Finally we show that the Weyl and Dirac QWs can be derived from scalar QWs in spaces of dimension up to three, via our construction.

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From curved spacetime to spacetime-dependent local unitaries over the honeycomb and triangular Quantum Walks

Cited by 2 publications

References 0 publications

A new method to building Dirac quantum walks coupled to electromagnetic fields

A new method to building Dirac quantum walks coupled to electromagnetic fields

Chirality from quantum walks without a quantum coin

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