Gate-based Quantum Computing: An Overview

Marie Ericsson

This is a brief overview of quantum holonomies in the context of quantum computation. We choose an adequate set of quantum logic gates, namely, a phase gate, the Hadamard gate, and a conditional-phase gate and show how they can be implemented by purely geometric means. Such gates may be more resilient to certain types of errors.

Dennis Willsch

JR Basil

An independent study self-introducing the subject of quantum computing by defining a logical basis of terms and concepts; then, exploring states, gates, and related computations; and lastly, concluding with an overview of real world implications.

Dennis Willsch

Sumit Sijher

This thesis serves to give a mathematical overview of topological quantum computation and to apply the theory to characterize desirable fault-tolerant operations called protected gates. Topological quantum computation is a novel paradigm for quantum computation which seeks to harness certain exotic quantum systems known as topological phases of matter that exhibit unique physical phenomena such as the manifestation of quasiparticle excitations called anyons. The low energy effective field theories of these systems can be expressed by certain topological quantum field theories, which in turn are described in terms of unitary modular tensor categories that capture the essential properties of a topological phase of matter and its corresponding anyon model. An overview of the relevant category theoretic concepts is given, and the axioms of a unitary modular tensor category are made explicit. A topological quantum field theory is then defined and used to describe topological quantum computation. Having developed the necessary theoretical background, the theory is then applied to characterize protected gates. The main result is a no-go theorem which states that, for any model, the set of protected gates is finite, and hence, cannot be used to do universal quantum computation using protected gates alone.

Alexander von Consbruch