Continuous time limit of the DTQW in 2D+1 and plasticity

A Plastic quantum walk admits both continuous time and continuous spacetime. The model has been recently proposed by one of the authors in Di Molfetta and Arrighi (Quant Inf Process 19(2): 47, 2020), leading to a general quantum simulation scheme for simulating fermions in the relativistic and non-r...

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Bibliographic Details
Published in:Quantum information processing 2021-02, Vol.20 (2), Article 76
Main Authors: Manighalam, Michael, Di Molfetta, Giuseppe
Format: Article
Language:English
Subjects:
Data Structures and Information Theory
Fermions
Hamiltonian functions
Mathematical Physics
Operators (mathematics)
Parameters
Physics
Physics and Astronomy
Plastic properties
Quantum Computing
Quantum Information Technology
Quantum Physics
Relativistic effects
Series expansion
Spintronics
Taylor series
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Summary:A Plastic quantum walk admits both continuous time and continuous spacetime. The model has been recently proposed by one of the authors in Di Molfetta and Arrighi (Quant Inf Process 19(2): 47, 2020), leading to a general quantum simulation scheme for simulating fermions in the relativistic and non-relativistic regimes. The extension to two physical dimensions is still missing and here, as a novel result, we demonstrate necessary and sufficient conditions concerning which discrete time quantum walks can admit plasticity, showing the resulting Hamiltonians. We consider coin operators as general 4 parameter unitary matrices, with parameters which are functions of the lattice step size ε . This dependence on ε encapsulates all functions of ε for which a Taylor series expansion in ε is well defined, making our results very general.
ISSN:1570-0755
1573-1332
DOI:10.1007/s11128-021-03011-5