Unruh-DeWitt Quantum Computing: Realizing Quantum Shannon Theory With Quantum Fields

Qubit-field quantum transduction provides numerous advantages to quantum computing, such as device-specific error-correcting codes, efficient scalability, and effective entanglement generation. An all-to-all connected bus of qubits implanted around the outside of a topological insulator, allowed to interact with the edge state, is a promising arena for transduction with flying fermionic qubits. Unruh--DeWitt detectors have allowed quantum information scientists to model entanglement properties of qubit-field interactions in many settings in a field known as Relativistic Quantum Information (RQI). Unruh--DeWitt detectors are useful tools to realize quantum Shannon theory, a subset of the theory of quantum communication, in condensed matter systems, aptly named Unruh--DeWitt quantum computers. These systems will provide quantitative measurements of communication in quantum materials that utilize coherent states for bosonic and fermionic fields. In this thesis, emphasis is placed on the well-studied theory of Tomonaga-Luttinger liquids, as the bosonization of a helical Luttinger liquid provides a pedagogical arena to construct RQI channels of fermionic systems. Multiple experimentally realizable systems are proposed, and design constraints are constructed to ensure maximum channel capacity. Furthermore, we elucidate the strength of these quantum channels using measurements from quantum Shannon theory such as coherent information, dephasing formalism, diamond distance and universality of Unruh--DeWitt quantum logic gates.