Automatic and adaptive approximation, optimization, or integration of functions in a cone with guarantee of accuracy is a relatively new paradigm. Our purpose is to create an open-source MATLAB package, Guaranteed Automatic Integration Library (GAIL)
, following the philosophy of reproducible research and sustainable practices of robust scientific software development. For our conviction that true scholarship in computational sciences are characterized by reliable reproducibility, we employ the best practices in mathematical research and software engineering known to us and available in MATLAB. This document describes the key features of functions in GAIL, which includes one-dimensional function approximation and minimization using linear splines, one-dimensional numerical integration using trapezoidal rule, and last but not least, mean estimation and multidimensional integration by Monte Carlo methods or Quasi Monte Carlo methods.
We demonstrate high fidelity entangling quantum gates within a chain of five trapped ion qubits by optimally shaping optical fields that couple to multiple collective modes of motion. We individually address qubits with segmented optical pulses to co
nstruct multipartite entangled states in a programmable way. This approach enables both high fidelity and fast quantum gates that can be scaled to larger qubit registers for quantum computation and simulation.
We stabilize a chosen radiofrequency beat note between two optical fields derived from the same mode-locked laser pulse train, in order to coherently manipulate quantum information. This scheme does not require access or active stabilization of the l
aser repetition rate. We implement and characterize this external lock, in the context of two-photon stimulated Raman transitions between the hyperfine ground states of trapped 171-Yb+ quantum bits.
The coupling between a two-level system and its environment leads to decoherence. Within the context of coherent manipulation of electronic or quasiparticle states in nanostructures, it is crucial to understand the sources of decoherence. Here, we st
udy the effect of electron-phonon coupling in a graphene and an InAs nanowire double quantum dot. Our measurements reveal oscillations of the double quantum dot current periodic in energy detuning between the two levels. These periodic peaks are more pronounced in the nanowire than in graphene, and disappear when the temperature is increased. We attribute the oscillations to an interference effect between two alternative inelastic decay paths involving acoustic phonons present in these materials. This interpretation predicts the oscillations to wash out when temperature is increased, as observed experimentally.
