  A set of universal quantum gates is a vital part of the theory of quantum
computing, but is absent in the developing theory of Relativistic Quantum
Information (RQI). Yet, the Unruh--DeWitt (UDW) detector formalism can be
elevated to unitary gates between qubits and quantum fields and has allowed RQI
applications in quantum Shannon theory, such as mutual information, coherent
information, and quantum capacity in field-mediated quantum channels. Recently,
experimental realizations of UDW-style qubits have been proposed in
two-dimensional quantum materials, but their value as a quantum technology,
including quantum communication and computation, is not yet clear, especially
since fields introduce many avenues for decoherence. We introduce
controlled-unitary UDW logic gates between qubit and field that are comparable
to the two-qubit CNOT gate. We then extend this formalism to demonstrate
Quantum State Transfer (QST) (two CNOT gates) and SWAP (three CNOT gates)
channels. We illustrate the performance of these quantum operation gates with
the diamond distance, a measure of distinguishability between quantum channels.
Distinguishability measures like diamond distance allow for a rigorous
comparison between field-mediated transduction through UDW detectors and local
quantum mechanical operations and so quantify the performance of UDW detectors
in quantum technological applications. Using the controlled-unitary qubit-field
interactions we define an exact form of the CNOT gate. With this technique we
also define quantum field-mediated single qubit operations associated with the
Hadamard $H$, the $S$, and $T$ gates. Thus, UDW detectors in simple settings
enable a collection of gates known to provide universal quantum computing.
