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Title: Quantum simulation of time-dependent hamiltonians and the convenient illusion of hilbert space
Authors: Poulin, D.
Qarry, A. 
Somma, R.
Verstraete, F.
Issue Date: 29-Apr-2011
Citation: Poulin, D., Qarry, A., Somma, R., Verstraete, F. (2011-04-29). Quantum simulation of time-dependent hamiltonians and the convenient illusion of hilbert space. Physical Review Letters 106 (17) : -. ScholarBank@NUS Repository.
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. © 2011 American Physical Society.
Source Title: Physical Review Letters
ISSN: 00319007
DOI: 10.1103/PhysRevLett.106.170501
Appears in Collections:Staff Publications

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