Skip to Main content Skip to Navigation
Journal articles

Quantum walking in curved spacetime: (3+1) dimensions, and beyond

Abstract : A discrete-time Quantum Walk (QW) is essentially an operator driving the evolution of a single particle on the lattice, through local unitaries. Some QWs admit a continuum limit, leading to familiar PDEs (e.g. the Dirac equation). Recently it was discovered that prior grouping and encoding allows for more general continuum limit equations (e.g. the Dirac equation in (1 + 1) curved spacetime). In this paper, we extend these results to arbitrary space dimension and internal degree of freedom. We recover an entire class of PDEs encompassing the massive Dirac equation in (3 + 1) curved spacetime. This means that the metric field can be represented by a field of local unitaries over a lattice.
Document type :
Journal articles
Complete list of metadata

Cited literature [25 references]  Display  Hide  Download
Contributor : Kévin Perrot <>
Submitted on : Monday, May 7, 2018 - 3:39:17 PM
Last modification on : Thursday, January 23, 2020 - 6:22:10 PM
Long-term archiving on: : Monday, September 24, 2018 - 7:34:00 PM


Files produced by the author(s)


  • HAL Id : hal-01785463, version 1



Pablo Arrighi, F. Facchini. Quantum walking in curved spacetime: (3+1) dimensions, and beyond. Quantum Information & Computation, Rinton Press, 2017, 17 (9-10), pp.0810--0824. ⟨hal-01785463⟩



Record views


Files downloads