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

authored by

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.

External Organisation(s)

Max Planck Institute of Quantum Optics (MPQ)
Austrian Academy of Sciences
University of Innsbruck
University of British Columbia

Type

Article

Journal

Physical Review A - Atomic, Molecular, and Optical Physics

Volume

80

ISSN

1050-2947

Publication date

30.11.2009

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Atomic and Molecular Physics, and Optics

Electronic version(s)

https://doi.org/10.48550/arXiv.0805.1214 (Access: Open)
https://doi.org/10.1103/PhysRevA.80.052334 (Access: Closed)