Quantum Simulation of Time-Dependent Hamiltonians and the Convenient Illusion of Hilbert Space

Autor(en)

David Poulin, Angie Qarry, Rolando Somma, Frank Verstraete

Abstrakt

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 show that 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 rapidly changing Hamiltonians is no more powerful than the standard quantum circuit model.

Organisation(en)

Quantenoptik, Quantennanophysik und Quanteninformation

Externe Organisation(en)

University of Sherbrooke, Los Alamos National Laboratory

Journal

Physical Review Letters

Band

106

Anzahl der Seiten

4

ISSN

0031-9007

DOI

https://doi.org/10.1103/PhysRevLett.106.170501

Publikationsdatum

04-2011

Peer-reviewed

Ja

ÖFOS 2012

103025 Quantenmechanik

Schlagwörter

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/7344f585-0843-4890-aca9-f18b7b4f4971