Universality for Sets of Three-Valued Qubit Gates

Abstract: How to find universal sets quantum gates (gates whose composition can form any othergate within a given range) is an important part of the development of quantum computation science that has been explored in the past with success. However, there has not been much development in extending this very same theory to a generalization of qubits known as quregisters or as we call them here qunits (quantum units of information analogous to qubits that use any natural number n of basis states instead of 2 as qubits do). In this paper we will first do a review of the theory behind some essential proofs of quantum gate universality for qubit gates. After that we will show a new way of extending those statements to arbitrary qutrit gates in an analogous manner.