Ensemble Quantum Computation with atoms in periodic potentials

We show how to perform universal quantum computation with atoms confined in optical lattices which works both in the presence of defects and without individual addressing. The method is based on using the defects in the lattice, wherever they are, both to ``mark'' different copies on which ensemble quantum computation is carried out and to define pointer atoms which perform the quantum gates. We also show how to overcome the problem of scalability on this system

Mapping local Hamiltonians of fermions to local Hamiltonians of spins

We show how to map local fermionic problems onto local spin problems on a lattice in any dimension. The main idea is to introduce auxiliary degrees of freedom, represented by Majorana fermions, which allow us to extend the Jordan-Wigner transformation to dimensions higher than one. We also discuss the implications of our results in the numerical investigation of fermionic systems.Comment: Added explicit mappin

Bose-Einstein Condensation and strong-correlation behavior of phonons in ion traps

We show that the dynamics of phonons in a set of trapped ions interacting with lasers is described by a Bose-Hubbard model whose parameters can be externally adjusted. We investigate the possibility of observing several quantum many-body phenomena, including (quasi) Bose-Einstein condensation as well as a superfluid-Mott insulator quantum phase transition.Comment: 5 pages, 3 figure

Quantum emulsion: a glassy phase of bosonic mixtures in optical lattices

We numerically investigate mixtures of two interacting bosonic species with unequal parameters in one-dimensional optical lattices. In large parameter regions full phase segregation is seen to minimize the energy of the system, but the true ground state is masked by an exponentially large number of metastable states characterized by microscopic phase separation. The ensemble of these quantum emulsion states, reminiscent of emulsions of immiscible fluids, has macroscopic properties analogous to those of a Bose glass, namely a finite compressibility in absence of superfluidity. Their metastability is probed by extensive quantum Monte Carlo simulations generating a rich correlated stochastic dynamics. The tuning of the repulsion of one of the two species via a Feshbach resonance drives the system through a quantum phase transition to the superfluid state.Comment: 4 pages, 3 figure

Matrix product states represent ground states faithfully

We quantify how well matrix product states approximate exact ground states of 1-D quantum spin systems as a function of the number of spins and the entropy of blocks of spins. We also investigate the convex set of local reduced density operators of translational invariant systems. The results give a theoretical justification for the high accuracy of renormalization group algorithms, and justifies their use even in the case of critical systems

Equivalence classes of non-local unitary operations

We study when a multipartite non--local unitary operation can deterministically or probabilistically simulate another one when local operations of a certain kind -in some cases including also classical communication- are allowed. In the case of probabilistic simulation and allowing for arbitrary local operations, we provide necessary and sufficient conditions for the simulation to be possible. Deterministic and probabilistic interconversion under certain kinds of local operations are used to define equivalence relations between gates. In the probabilistic, bipartite case this induces a finite number of classes. In multiqubit systems, however, two unitary operations typically cannot simulate each other with non-zero probability of success. We also show which kind of entanglement can be created by a given non--local unitary operation and generalize our results to arbitrary operators.Comment: (1) 9 pages, no figures, submitted to QIC; (2) reference added, minor change

Time-dependent study of disordered models with infinite projected entangled pair states

Infinite projected entangled pair states (iPEPS), the tensor network ansatz for two-dimensional systems in the thermodynamic limit, already provide excellent results on ground-state quantities using either imaginary-time evolution or variational optimisation. Here, we show (i) the feasibility of real-time evolution in iPEPS to simulate the dynamics of an infinite system after a global quench and (ii) the application of disorder-averaging to obtain translationally invariant systems in the presence of disorder. To illustrate the approach, we study the short-time dynamics of the square lattice Heisenberg model in the presence of a bi-valued disorder field

Continuous Tensor Network States for Quantum Fields

We introduce a new class of states for bosonic quantum fields which extend tensor network states to the continuum and generalize continuous matrix product states (cMPS) to spatial dimensions $d\geq 2$. By construction, they are Euclidean invariant, and are genuine continuum limits of discrete tensor network states. Admitting both a functional integral and an operator representation, they share the important properties of their discrete counterparts: expressiveness, invariance under gauge transformations, simple rescaling flow, and compact expressions for the $N$-point functions of local observables. While we discuss mostly the continuous tensor network states extending Projected Entangled Pair States (PEPS), we propose a generalization bearing similarities with the continuum Multi-scale Entanglement Renormalization Ansatz (cMERA).Comment: 16 pages, 5 figures, close to published versio