Polylogarithmic-depth controlled-NOT gates without ancilla qubits

Autor: Baptiste Claudon, Julien Zylberman, César Feniou, Fabrice Debbasch, Alberto Peruzzo, Jean-Philip Piquemal

Publikováno v: Nature Communications, Vol 15, Iss 1, Pp 1-8 (2024)

Abstract Controlled operations are fundamental building blocks of quantum algorithms. Decomposing n-control-NOT gates (C n (X)) into arbitrary single-qubit and CNOT gates, is a crucial but non-trivial task. This study introduces C n (X) circuits outp

Externí odkaz: https://doaj.org/article/f22d341fbda84e79a92f86a0d1442b38

Dirac Spatial Search with Electric Fields

Autor: Julien Zylberman, Fabrice Debbasch

Publikováno v: Entropy, Vol 23, Iss 11, p 1441 (2021)

Electric Dirac quantum walks, which are a discretisation of the Dirac equation for a spinor coupled to an electric field, are revisited in order to perform spatial searches. The Coulomb electric field of a point charge is used as a non local oracle t

Externí odkaz: https://doaj.org/article/5ef49fb5b7634d6b9020d97e725fbc73

Minimal quantum walk simulation of Dirac fermions in curved space-times

Autor: Fabrice Debbasch

The problem of simulating through quantum walks Dirac fermions in arbitrary curved space-times and coordinates is revisited, taking (1 + 1)D space-times as an example. A new shift or translation operator on the grid is introduced, to take into accoun

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8545434b2088f2b8fbcc355467919023
http://arxiv.org/abs/2202.11181

Dirac quantum walks with conserved angular momentum

Autor: Fabrice Debbasch, Gareth Jay, Pablo Arnault

Publikováno v: Quantum Studies: Mathematics and Foundations
Quantum Studies: Mathematics and Foundations, 2021, 8 (4), pp.419-430. ⟨10.1007/s40509-021-00253-x⟩

A quantum walk (QW) simulating the flat $$(1 + 2)$$ D Dirac equation on a spatial polar grid is constructed. Because fermions are represented by spinors, which do not constitute a representation of the rotation group $${\mathrm{SO}}(3)$$ , but rather

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::292ffdcf7ba1355b334975fdd5a7587a
https://hal.science/hal-03577256

Action principles for quantum automata and Lorentz invariance of discrete time quantum walks

Autor: Fabrice Debbasch

Publikováno v: Annals Phys.
Annals Phys., 2019, 405, pp.340-364. ⟨10.1016/j.aop.2019.03.005⟩

A discrete action principle for general quantum automata is proposed. This action principle is particularized to Discrete Time Quantum Walks (DTQWs) and then extended into an energy and momentum preserving, manifestly covariant formulation. Space-tim

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1336ac214492c186ba61eb91051c60db
https://doi.org/10.1016/j.aop.2019.03.005