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

Author(s): D. Poulin, A. Qarry, R. Somma, F. Verstraete

Journal: Physical Review Letters

Volume: 106

Page(s): 4

Year: 2011

DOI Number: 10.1103/PhysRevLett.106.170501

Link: Link to publication

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 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.

Note: http://arxiv.org/abs/1102.1360

File: Link to PDF

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