Quantum Information Processing

, Volume 15, Issue 8, pp 3467–3486 | Cite as

Quantum walking in curved spacetime

Article

Abstract

A discrete-time quantum walk (QW) is essentially a unitary operator driving the evolution of a single particle on the lattice. Some QWs admit a continuum limit, leading to familiar PDEs (e.g., the Dirac equation). In this paper, we study the continuum limit of a wide class of QWs and show that it leads to an entire class of PDEs, encompassing the Hamiltonian form of the massive Dirac equation in (\(1+1\)) curved spacetime. Therefore, a certain QW, which we make explicit, provides us with a unitary discrete toy model of a test particle in curved spacetime, in spite of the fixed background lattice. Mathematically, we have introduced two novel ingredients for taking the continuum limit of a QW, but which apply to any quantum cellular automata: encoding and grouping.

Keywords

Paired QWs Lattice quantum field theory Quantum simulation 

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Pablo Arrighi
    • 1
  • Stefano Facchini
    • 2
  • Marcelo Forets
    • 2
  1. 1.LIFAix-Marseille UniversityMarseilleFrance
  2. 2.LIGUniversity of Grenoble AlpesGrenobleFrance

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