Quantum algorithms for spin models and simulable gate sets for quantum computation

verfasst von: M. Van Den Nest, W. Dür, R. Raussendorf, H. J. Briegel
Abstract: We present simple mappings between classical lattice models and quantum circuits, which provide a systematic formalism to obtain quantum algorithms to approximate partition functions of lattice models in certain complex-parameter regimes. We, e.g., present an efficient quantum algorithm for the six-vertex model as well as a two-dimensional Ising-type model. We show that classically simulating these (complex-parameter) spin models is as hard as simulating universal quantum computation, i.e., BQP complete (BQP denotes bounded-error quantum polynomial time). Furthermore, our mappings provide a framework to obtain efficiently simulable quantum gate sets from exactly solvable classical models. We, e.g., show that the simulability of Valiant's match gates can be recovered by using the solvability of the free-fermion eight-vertex model.
Externe Organisation(en): Max-Planck-Institut für Quantenoptik (MPQ)
Austrian Academy of Sciences
Universität Innsbruck
University of British Columbia
Typ: Artikel
Journal: Physical Review A - Atomic, Molecular, and Optical Physics
Band: 80
ISSN: 1050-2947
Publikationsdatum: 30.11.2009
Publikationsstatus: Veröffentlicht
Peer-reviewed: Ja
ASJC Scopus Sachgebiete: Atom- und Molekularphysik sowie Optik
Elektronische Version(en): https://doi.org/10.48550/arXiv.0805.1214 (Zugang: Offen)
https://doi.org/10.1103/PhysRevA.80.052334 (Zugang: Geschlossen)

BibTeX

@article{ab1cb5cb2985435d9531efd9de422375,
title = "Quantum algorithms for spin models and simulable gate sets for quantum computation",
abstract = "We present simple mappings between classical lattice models and quantum circuits, which provide a systematic formalism to obtain quantum algorithms to approximate partition functions of lattice models in certain complex-parameter regimes. We, e.g., present an efficient quantum algorithm for the six-vertex model as well as a two-dimensional Ising-type model. We show that classically simulating these (complex-parameter) spin models is as hard as simulating universal quantum computation, i.e., BQP complete (BQP denotes bounded-error quantum polynomial time). Furthermore, our mappings provide a framework to obtain efficiently simulable quantum gate sets from exactly solvable classical models. We, e.g., show that the simulability of Valiant's match gates can be recovered by using the solvability of the free-fermion eight-vertex model.",
author = "{Van Den Nest}, M. and W. D{\"u}r and R. Raussendorf and Briegel, {H. J.}",
year = "2009",
month = nov,
day = "30",
doi = "10.48550/arXiv.0805.1214",
language = "English",
volume = "80",
journal = "Physical Review A - Atomic, Molecular, and Optical Physics",
issn = "1050-2947",
publisher = "American Physical Society",
number = "5",
}