document: Simulating fermions on a quantum computer The real-time probabilistic simulation of quantum systems in classical computers is known to be limited by the so-called dynamical sign problem , a problem leading to exponential complexity . In 1981 Richard Feynman raised some provocative questions in connection to the `` exact imitation '' of such systems using a special device named a `` quantum computer '' . Feynman hesitated about the possibility of imitating fermion systems using such a device . Here we address some of his concerns and , in particular , investigate the simulation of fermionic systems . We show how quantum computers avoid the sign problem in some cases by reducing the complexity from exponential to polynomial . Our demonstration is based upon the use of isomorphisms of algebras . We present specific quantum algorithms that illustrate the main points of our algebraic approach
doc_bio_tags: O O O O B I O O O O O O O O B I O O O O O O O O B I I O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O B O B O O O O O O O O O O O O O O O
extractive_keyphrases: quantum computer classical computers dynamical sign problem exponential complexity fermion systems sign problem isomorphisms algebras
abstractive_keyphrases: fermions simulation real-time probabilistic simulation