Quantum simulation of time-dependent Hamiltonians and the convenient illusion of Hilbert space.

@article{Poulin2011QuantumSO,
  title={Quantum simulation of time-dependent Hamiltonians and the convenient illusion of Hilbert space.},
  author={David Poulin and Angie Qarry and Rolando D. Somma and Frank Verstraete},
  journal={Physical review letters},
  year={2011},
  volume={106 17},
  pages={170501}
}
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… CONTINUE READING
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