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

Optimal conversion of non--local unitary operations

We study when a non--local unitary operation acting on two $d$--level systems can probabilistically simulate another one when arbitrary local operations and classical communication are allowed. We provide necessary and sufficient conditions for the simulation to be possible. Probabilistic interconvertability is used to define an equivalence relation between gates. We show that this relation induces a finite number of classes, that we identify. In the case of two qubits, two classes of non--local operations exist. We choose the CNOT and SWAP as representatives of these classes. We show how the CNOT [SWAP] can be deterministically converted into any operation of its class. We also calculate the optimal probability of obtaining the CNOT [SWAP] from any operation of the corresponding class and provide a protocol to achieve this task.Comment: 4 pages, no figure

Entanglement generation via a completely mixed nuclear spin bath

We show that qubits coupled sequentially to a mesoscopic static completely mixed spin bath via the Heisenberg interaction can become highly entangled. Straightforward protocols for the generation of multipartite entangled (Greenberger-Horne-Zeilinger-)states are presented. We show the feasibility of an experimental realization in a quantum dot by the hyperfine interaction of an electron with the nuclear spins.Comment: 4+pages, 3 figure

Storing quantum dynamics in quantum states: stochastic programmable gate for U(1) operations

We show how quantum dynamics can be captured in the state of a quantum system, in such a way that the system can be used to stochastically perform, at a later time, the stored transformation perfectly on some other quantum system. Thus programmable quantum gates for quantum information processing are feasible if some probability of failure -that we show to decrease exponentially with the size of the storing resources- is allowed.Comment: RevTex, 4 pages, 3 figures. Extension of quant-ph/0012067, including several results concerning optimality of the scheme for storage of operation

Delocalized Entanglement of Atoms in optical Lattices

We show how to detect and quantify entanglement of atoms in optical lattices in terms of correlations functions of the momentum distribution. These distributions can be measured directly in the experiments. We introduce two kinds of entanglement measures related to the position and the spin of the atoms

An Error Model for the Cirac-Zoller CNOT gate

In the framework of ion-trap quantum computing, we develop a characterization of experimentally realistic imperfections which may affect the Cirac-Zoller implementation of the CNOT gate. The CNOT operation is performed by applying a protocol of five laser pulses of appropriate frequency and polarization. The laser-pulse protocol exploits auxiliary levels, and its imperfect implementation leads to unitary as well as non-unitary errors affecting the CNOT operation. We provide a characterization of such imperfections, which are physically realistic and have never been considered before to the best of our knowledge. Our characterization shows that imperfect laser pulses unavoidably cause a leak of information from the states which alone should be transformed by the ideal gate, into the ancillary states exploited by the experimental implementation.Comment: 10 pages, 1 figure. Accepted as a contributed oral communication in the QuantumComm 2009 International Conference on Quantum Communication and Quantum Networking, Vico Equense, Italy, October 26-30, 200

Quantum simulators, continuous-time automata, and translationally invariant systems

The general problem of finding the ground state energy of lattice Hamiltonians is known to be very hard, even for a quantum computer. We show here that this is the case even for translationally invariant systems. We also show that a quantum computer can be built in a 1D chain with a fixed, translationally invariant Hamitonian consisting of nearest--neighbor interactions only. The result of the computation is obtained after a prescribed time with high probability.Comment: partily rewritten and important references include