Quantum Error Correction for Physically Inspired Error Models

In this dissertation we will discuss methods for creating error-robust logical qubits which have been optimized for trapped ion quantum computers. We will cover the basic building blocks of quantum information and develop an understanding of the standard techniques for building fault-tolerant quantum computers through the use of quantum error correcting codes. We will then focus on trapped ion systems, although many of the errors we consider also occur in other hardware implementations.

The majority of this dissertation is concerned with taking advantage of the structure found in experimental errors to maximize system performance. Using numerical simulation, we study the interplay of structured error models and quantum error correction. We then cover optimizations to the standard quantum error correction framework, both through gate compilation and code design, to correct coherent gate overrotation and dephasing errors. The latter section will also include experiments run on a quantum computer at the University of Maryland which verify the effectiveness of our ideas. We will end with a discussion of a method for quantum error detection in near-term systems by extending the flag gadget framework often used in quantum error correction.

Through this body of work we hope to provide evidence for the value, within the context of quantum error correction, of detailed understanding of our physical systems. Oftentimes, codes and protocols are designed without actual implementation in mind. While these studied often produce useful results, more effective methods can sometimes be found when the physics is kept in mind. Our hope is that this dissertation motivates further study of the physical error processes present in quantum computing architectures, as well as development of novel methods to correct them.