Fuzzy local linear approximation-based sequential design

When approximating complex high-fidelity black box simulators with surrogate models, the experimental design is often created sequentially. LOLA-Voronoi, a powerful state of the art method for sequential design combines an Exploitation and Exploration algorithm and adapts the sampling distribution to provide extra samples in non-linear regions. The LOLA algorithm estimates gradients to identify interesting regions, but has a bad complexity which results in long computation time when simulators are high-dimensional. In this paper, a new gradient estimation approach for the LOLA algorithm is proposed based on Fuzzy Logic. Experiments show the new method is a lot faster and results in experimental designs of comparable quality

Sequential Quantum Cloning

Not all unitary operations upon a set of qubits can be implemented by sequential interactions between each qubit and an ancillary system. We analyze the specific case of sequential quantum cloning 1->M and prove that the minimal dimension D of the ancilla grows linearly with the number of clones M. In particular, we obtain D = 2M for symmetric universal quantum cloning and D = M+1 for symmetric phase-covariant cloning. Furthermore, we provide a recipe for the required ancilla-qubit interactions in each step of the sequential procedure for both cases.Comment: 4 pages, no figures. New version with changes. Accepted in Physical Review Letter