Theoretical studies for experimental implementation of quantum computing with trapped ions
Creator
Yoshimura, Bryce Tadashi
Advisor
Freericks, James K
Abstract
Certain quantum manybody physics problems, such as the transverse field Ising model are intractable on a classical computer, meaning that as the number of particles grows, or spins, the amount of memory and computational time required to solve the problem exactly increases faster than a polynomial behavior. However, quantum simulators are being developed to efficiently solve quantum problems that are intractable via conventional computing. Some of the most successful quantum simulators are based on ion traps. Their success depends on the ability to achieve long coherence time, precise spin control, and high fidelity in state preparation.
In this work, I present calculations that characterizes the oblate Paul trap that creates twodimensional Coulomb crystals in a triangular lattice and phonon modes. We also calculate the spinspin Isinglike interaction that can be generated in the oblate Paul trap using the same techinques as the linear radiofrequency Paul trap. In addition, I discuss two possible challenges that arise in the Penning trap: the effects of defects ( namely when $Be^+ \rightarrow BeH^+$) and the creation of a more uniform spinspin Isinglike interaction. We show that most properties are not significantly influenced by the appearance of defects, and that by adding two potentials to the Penning trap a more uniform spinspin Isinglike interaction can be achieved.
Next, I discuss techniques tfor preparing the ground state of the Isinglike Hamiltonian. In particular, we explore the use of the bangbang protocol to prepare the ground state and compare optimized results to conventional adiabatic ramps ( the exponential and locally adiabatic ramp ). The bangbang optimization in general outperforms the exponential; however the locally adiabatic ramp consistently is somewhat better. However, compared to the locally adiabatic ramp, the bangbang optimization is simpler to implement, and it has the advantage of providingrovide a simple procedure for estimating the groundstate probability.
Finally, I discuss techniques for exploring the coherent dynamics of the manybody system. Since diabatic excitations occur in experimental implementation of adiabatic state preparation one can ask whether these states resemble thermal distributions. In addition we can use these excitations to calculate the energy spectra of the transverse field Ising model. Finally we investigate a procedure that can be used to study both the shorttime and longtime behavior of the system. The former directly relates to bounds for the transport of manybody correlations, while the latter rlates to the excitation spectra of the Hamiltonian.
Description
Ph.D.
Permanent Link
http://hdl.handle.net/10822/1040763Date Published
2016Subject
Type
Collections
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