Journal
PHYSICAL REVIEW LETTERS
Volume 106, Issue 17, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevLett.106.170501
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Funding
- ERC
- European grant Quevadis
- FWF SFB
- NSERC
- FQRNT
- NSF through CCF
- LANL
- Division of Computing and Communication Foundations
- Direct For Computer & Info Scie & Enginr [1016689] Funding Source: National Science Foundation
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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.
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