Construction, Optimization, and Applications of a Small Trapped-Ion Quantum Computer
A large-scale quantum computer will have the ability to solve many computational problems beyond the capabilities of today's most powerful computers. Significant efforts to build such a computer are underway, many of which are small prototypes that are believed to be extensible to larger systems. Such systems, like the one in this thesis is built off of 171Yb ions, are enticing scientific endeavors for their potential to inform the production of large-scale systems as well as the interesting experiments they can perform despite their small size. In this work, experimental research is presented on both topics: scalability as well as compelling computations.
The first half of this thesis discusses building and optimizing a quantum computer to have high-fidelity qubit operations. The performance of single- and two-qubit gates using Raman lasers are derived, and methods for optimizing such gate are discussed. We consider coherence-related properties of the system necessary to perform these operations and how they can be experimentally improved. Single-qubit gates are presented alongside sources of error and techniques for increasing their fidelity. The two-qubit gates considered feature amplitude modulation, frequency modulation, and both to effect the sets of constraints necessary for high-fidelity entanglement.
The second half of the thesis features three experimental applications of the quantum computer: quantifying quantum scrambling, quantum error correction, and measuring Rényi entropy. Quantum scrambling is the coherent delocalization of information through a quantum system and is notably difficult to quantify experimentally. We present an efficient scheme to measure it using quantum teleportation. Quantum error correction is a set of techniques for mitigating the unavoidably imperfect operations performed on a quantum computer, and we demonstrate some of these techniques in order to fault-tolerantly prepare a logical qubit. Lastly, Rényi entropy is an information theoretic quantity that can directly quantify the amount of entanglement in a system. We present a method for measuring it efficiently using a quantum gate known as a Fredkin gate.