Quantum Simulation In Trapped Ions

Quantum simulation and quantum computing are the fundamentals of quantum information science.In 1982,R.Feynman proposed the concept of 'quantum simula-tion',which pointed out that those physical or unphysical models that can not be ob-served in natural systems can be realized in other well-controlled quantum platforms.Besides,quantum simulation may be used to develop new theories and discover new ap-plications to quantum information science.Till now,platforms for quantum simulation enjoys interdisciplinarity.Quantum simulators such as trapped ions,superconducting circuits,quantum photonics,optical lattices have been applied to different fields like condensed matter physics,quantum mechanics,quantum chemistry,among others.In this thesis,I would like to give you a glance about quantum simulation with embedding quantum simulator for different models,some of which have been proposed to trapped ions.The works obtained are listed below,?.Study of the nonlinear dynamics of trapped-ion models far away from the Lamb-Dicke regime.This nonlinearity induces a blockade on the propagation of quan-tum information along the Hilbert space of the light-matter interactions which are de-scribed with Jaynes-Cummings and quantum Rabi models.We propose to use this blockade as a resource for the dissipative generation of high-number Fock states.Also,we compare the linear and nonlinear cases of the quantum Rabi model in the ultra-strong and deep strong coupling regimes.Moreover,we propose a scheme to simulate the nonlinear quantum Rabi model in all coupling regimes.This can be done via off-resonant nonlinear red and blue sideband interactions in a single trapped ion,yielding applications as a dynamical quantum filter.?.The research upon the implementations of unphysical operations with embed-ding quantum simulator.(?).Implementation of time and spatial parity transformations,as well as Galilean boosts,in a trapped-ion quantum simulator.By embedding the simulated model into an enlarged simulating Hilbert space,these fundamental symmetry operations can be fully realized and measured with ion traps.Besides,we introduced all the possible decoherences in different trapped-ion platforms to analyze the fidelity of our proposal to show the feasibility.(?).Implementation of a switch of particle statistics with an embedding quantum simulator.By encoding both Bose-Einstein and Fermi-Dirac statistics into an enlarged Hilbert space,the statistics of the simulated quantum particles may be changed in situ during the time evolution,from bosons to fermions and from fermions to bosons,as many times as desired before a measurement is performed.We illustrate our proposal with few-qubit examples and a general N-qubit algorithm.This proposal can be im-plemented on different quantum platforms such as trapped ions,quantum photonics,and superconducting circuits,among others.The possibility to implement permutation symmetrization and antisymmetrization of quantum particles enhances the toolbox of quantum simulations,for unphysical operations as well as for symmetry transforma-tions.