Maßgeschneiderte Spin-Spin-Kopplung und Quanten-Fouriertransformation mit gespeicherten Yb+-Ionen in einem Magnetfeldgradienten

A quantum computer that combines the concepts of digital information processing and quantum physics holds the promise to efficiently solve certain computational problems that are intractable by a classical computer.
Furthermore, the so called quantum simulators allow new insights into scientific issues from different research fields that go beyond physics.
Currently, one of the most advanced possibility of realizing a quantum computer is based on ions trapped in a Paul trap and using the internal atomic states to store information.
By use of electromagnetic radiation the states can be manipulated and information is processed.
The presence of a static magnetic field gradient or an oscillating magnetic field allows the use of long wavelength microwave radition and both approaches have been tested successfully in the past.

This work follows up the first proof of principle experiments employing a static magnetc field gradient. Using three trapped ions a Quantum Fourier transform was performed as an exemplary algorithm.
The construction of the algorithm was based on a novel approach that takes into account all present spin-spin couplings in the quantum system and yields a speed-up of a factor of three compared to the conventional construction.
In addition, quantum systems with tailored spin-spin couplings intended for quantum simulations have been realized and investigated.
In order to achieve this, novel experimental methods have been developed and tested.
These include a method to detect qubit states based on time series analysis of fluorescence.
Furthermore it was studied, how a static magnetic gradient allows for the addressability of up to eight ions (a quantum byte) by the use of microwave pulses. It was demonstrated that the resulting crosstalk error is of the order of 10-5, which is well below the conventionally accepted threshold for fault-tolerant quantum error correction.
In addition, it was demonstrated how the crosstalk error can be suppressed by suitable experimental parameters.
Also sequences of dynamical decoupling pulses have been used to protect coherent multi-qubit dynamics from dephasing.
The perfomance and susceptability to errors of different pulse sequences were compared and a novel and robust pulse sequence was deduced.
Stabilizing the quantum dynamics during a period that is almost two orders of magnitude longer than the coherence time of the system allows for the creation of entanglement with a fidelity of 0,64(4).