@article{OhligerNesmeEisert2013,
  author    = {Ohliger, Matthias and Nesme, V. and Eisert, J.},
  title     = {Efficient and feasible state tomography of quantum many-body systems},
  series = {New journal of physics : the open-access journal for physics},
  volume    = {15},
  journal   = {New journal of physics : the open-access journal for physics},
  number    = {5},
  publisher = {IOP Publ. Ltd.},
  address   = {Bristol},
  issn      = {1367-2630},
  doi       = {10.1088/1367-2630/15/1/015024},
  pages     = {19},
  year      = {2013},
  abstract  = {We present a novel method for performing quantum state tomography for many-particle systems, which are particularly suitable for estimating the states in lattice systems such as of ultra-cold atoms in optical lattices. We show that the need to measure a tomographically complete set of observables can be overcome by letting the state evolve under some suitably chosen random circuits followed by the measurement of a single observable. We generalize known results about the approximation of unitary two-designs, i.e. certain classes of random unitary matrices, by random quantum circuits and connect our findings to the theory of quantum compressed sensing. We show that for ultra-cold atoms in optical lattices established experimental techniques such as optical super-lattices, laser speckles and time-of-flight measurements are sufficient to perform fully certified, assumption-free tomography. This is possible without the need to address single sites in any step of the procedure. Combining our approach with tensor network methods-in particular, the theory of matrix product states-we identify situations where the effort of reconstruction is even constant in the number of lattice sites, allowing, in principle, to perform tomography on large-scale systems readily available in present experiments.},
  language  = {en}
}
@article{TrotzkyChenFleschetal.2012,
  author    = {Trotzky, S. and Chen, Y-A. and Flesch, A. and McCulloch, I. P. and Schollw{\"o}ck, U. and Eisert, J. and Bloch, I.},
  title     = {Probing the relaxation towards equilibrium in an isolated strongly correlated one-dimensional Bose gas},
  series = {Nature physics},
  volume    = {8},
  journal   = {Nature physics},
  number    = {4},
  publisher = {Nature Publ. Group},
  address   = {London},
  issn      = {1745-2473},
  doi       = {10.1038/NPHYS2232},
  pages     = {325 -- 330},
  year      = {2012},
  abstract  = {The problem of how complex quantum systems eventually come to rest lies at the heart of statistical mechanics. The maximum-entropy principle describes which quantum states can be expected in equilibrium, but not how closed quantum many-body systems dynamically equilibrate. Here, we report the experimental observation of the non-equilibrium dynamics of a density wave of ultracold bosonic atoms in an optical lattice in the regime of strong correlations. Using an optical superlattice, we follow its dynamics in terms of quasi-local densities, currents and coherences-all showing a fast relaxation towards equilibrium values. Numerical calculations based on matrix-product states are in an excellent quantitative agreement with the experimental data. The system fulfills the promise of being a dynamical quantum simulator, in that the controlled dynamics runs for longer times than present classical algorithms can keep track of.},
  language  = {en}
}
@article{MariEisert2012,
  author    = {Mari, A. and Eisert, J.},
  title     = {Opto- and electro-mechanical entanglement improved by modulation},
  series = {New journal of physics : the open-access journal for physics},
  volume    = {14},
  journal   = {New journal of physics : the open-access journal for physics},
  publisher = {IOP Publ. Ltd.},
  address   = {Bristol},
  issn      = {1367-2630},
  doi       = {10.1088/1367-2630/14/7/075014},
  pages     = {12},
  year      = {2012},
  abstract  = {One of the main milestones in the study of opto- and electromechanical systems is to certify entanglement between a mechanical resonator and an optical or microwave mode of a cavity field. In this work, we show how a suitable time-periodic modulation can help to achieve large degrees of entanglement, building upon the framework introduced in Mari and Eisert (2009 Phys. Rev. Lett. 103 213603). It is demonstrated that with suitable driving, the maximum degree of entanglement can be significantly enhanced, in a way exhibiting a nontrivial dependence on the specifics of the modulation. Such time-dependent driving might help to experimentally achieve entangled mechanical systems also in situations when quantum correlations are otherwise suppressed by thermal noise.},
  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{OhligerEisert2012,
  author    = {Ohliger, M. and Eisert, J.},
  title     = {Efficient measurement-based quantum computing with continuous-variable systems},
  series = {Physical review : A, Atomic, molecular, and optical physics},
  volume    = {85},
  journal   = {Physical review : A, Atomic, molecular, and optical physics},
  number    = {6},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {1050-2947},
  doi       = {10.1103/PhysRevA.85.062318},
  pages     = {12},
  year      = {2012},
  abstract  = {We present strictly efficient schemes for scalable measurement-based quantum computing using continuous-variable systems: These schemes are based on suitable non-Gaussian resource states, ones that can be prepared using interactions of light with matter systems or even purely optically. Merely Gaussian measurements such as optical homodyning as well as photon counting measurements are required, on individual sites. These schemes overcome limitations posed by Gaussian cluster states, which are known not to be universal for quantum computations of unbounded length, unless one is willing to scale the degree of squeezing with the total system size. We establish a framework derived from tensor networks and matrix product states with infinite physical dimension and finite auxiliary dimension general enough to provide a framework for such schemes. Since in the discussed schemes the logical encoding is finite dimensional, tools of error correction are applicable. We also identify some further limitations for any continuous-variable computing scheme from which one can argue that no substantially easier ways of continuous-variable measurement-based computing than the presented one can exist.},
  language  = {en}
}