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. We also mention how could this be extended to any qunit gate.

中文翻译：

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三值量子位 (qutrit) 门组的通用性

如何找到通用集量子门（其组成可以在给定范围内形成任何其他门的门）是过去成功探索的量子计算科学发展的重要组成部分。然而，在将这个完全相同的理论扩展到称为 quregisters 或我们在此处称它们为 qunits（类似于量子位的信息的量子单位，使用任何自然数 n 基态而不是 2 作为量子位做）。在本文中，我们将首先回顾一下量子位门的量子门普遍性的一些基本证明背后的理论。之后，我们将展示一种以类似方式将这些语句扩展到任意 qutrit 门的新方法。我们还提到了如何将其扩展到任何 qunit 门。