@article{BarthelKlieschEisert2010,
  author    = {Barthel, Thomas and Kliesch, Martin and Eisert, Jens},
  title     = {Real-space renormalization yields finite correlations},
  issn      = {0031-9007},
  doi       = {10.1103/Physrevlett.105.010502},
  year      = {2010},
  abstract  = {Real-space renormalization approaches for quantum lattice systems generate certain hierarchical classes of states that are subsumed by the multiscale entanglement renormalization Ansatz (MERA). It is shown that, with the exception of one spatial dimension, MERA states are actually states with finite correlations, i.e., projected entangled pair states (PEPS) with a bond dimension independent of the system size. Hence, real-space renormalization generates states which can be encoded with local effective degrees of freedom, and MERA states form an efficiently contractible class of PEPS that obey the area law for the entanglement entropy. It is further pointed out that there exist other efficiently contractible schemes violating the area law.},
  language  = {en}
}
@article{KlieschBarthelGogolinetal.2011,
  author    = {Kliesch, Martin and Barthel, Thomas and Gogolin, C. and Kastoryano, M. and Eisert, J.},
  title     = {Dissipative quantum church-turing theorem},
  series = {Physical review letters},
  volume    = {107},
  journal   = {Physical review letters},
  number    = {12},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {0031-9007},
  doi       = {10.1103/PhysRevLett.107.120501},
  pages     = {5},
  year      = {2011},
  abstract  = {We show that the time evolution of an open quantum system, described by a possibly time dependent Liouvillian, can be simulated by a unitary quantum circuit of a size scaling polynomially in the simulation time and the size of the system. An immediate consequence is that dissipative quantum computing is no more powerful than the unitary circuit model. Our result can be seen as a dissipative Church-Turing theorem, since it implies that under natural assumptions, such as weak coupling to an environment, the dynamics of an open quantum system can be simulated efficiently on a quantum computer. Formally, we introduce a Trotter decomposition for Liouvillian dynamics and give explicit error bounds. This constitutes a practical tool for numerical simulations, e.g., using matrix-product operators. We also demonstrate that most quantum states cannot be prepared efficiently.},
  language  = {en}
}
@article{BarthelKliesch2012,
  author    = {Barthel, Thomas and Kliesch, Martin},
  title     = {Quasilocality and efficient simulation of Markovian Quantum Dynamics},
  series = {Physical review letters},
  volume    = {108},
  journal   = {Physical review letters},
  number    = {23},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {0031-9007},
  doi       = {10.1103/PhysRevLett.108.230504},
  pages     = {5},
  year      = {2012},
  abstract  = {We consider open many-body systems governed by a time-dependent quantum master equation with short-range interactions. With a generalized Lieb-Robinson bound, we show that the evolution in this very generic framework is quasilocal; i.e., the evolution of observables can be approximated by implementing the dynamics only in a vicinity of the observables' support. The precision increases exponentially with the diameter of the considered subsystem. Hence, time evolution can be simulated on classical computers with a cost that is independent of the system size. Providing error bounds for Trotter decompositions, we conclude that the simulation on a quantum computer is additionally efficient in time. For experiments and simulations in the Schrodinger picture, our result can be used to rigorously bound finite-size effects.},
  language  = {en}
}