Quantum Simulation of TimeDependent Hamiltonians and the Convenient Illusion of Hilbert Space
Abstract
We consider the manifold of all quantum manybody states that can be generated by arbitrary timedependent 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 timedependent generalization of the SuzukiTrotter expansion, followed by a wellknown 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.
 Publication:

Physical Review Letters
 Pub Date:
 April 2011
 DOI:
 10.1103/PhysRevLett.106.170501
 arXiv:
 arXiv:1102.1360
 Bibcode:
 2011PhRvL.106q0501P
 Keywords:

 03.67.Ac;
 03.65.Ud;
 89.70.Eg;
 Quantum algorithms protocols and simulations;
 Entanglement and quantum nonlocality;
 Computational complexity;
 Quantum Physics
 EPrint:
 Presented at QIP 2011