Équipe de Recherche en Physique de l'Information Quantique


Author = {David Poulin and Angie Quarry and Rolando D. Somma and Frank Verstraete},
Eprint = {arXiv:1102.1360},
Journal = {Phys. Rev. Lett.},
Volume = {106},
Pages = {170501},
Title = {Quantum simulation of time-dependent Hamiltonians and the convenient illusion of Hilbert space},
Local-Url = {PQSV11b1.pdf},
Year = {2011},
Abstract = {We consider the manifold of all quantum many-body states that can be generated by arbitrary time-dependent local Hamiltonians in a time that scales polynomially in the system size, and showthat it occupies an exponentially small volume in Hilbert space. This implies that the overwhelming majority of states in Hilbert space are not physical as they can only be produced after an exponentially long time. We establish this fact by making use of a time-dependent generalization of the Suzuki-Trotter expansion, followed by a well-known counting argument. This also demonstrates that a computational model based on arbitrarily}}