= Solution
{c}
A <universal quantum gate set> can approximate any finite-register <unitary operator> to arbitrary accuracy, disregarding a common <global phase>. A finite example is the <Hadamard gate>, <T gate> and <CNOT gate>. In the ordered one-<qubit> <basis> $(|g\rangle,|e\rangle)$,
$$
H=\frac1{\sqrt2}\begin{pmatrix}1&1\\1&-1\end{pmatrix},\qquad
T=\begin{pmatrix}1&0\\0&e^{i\pi/4}\end{pmatrix}.
$$
In the ordered two-<qubit> <basis> $(|gg\rangle,|ge\rangle,|eg\rangle,|ee\rangle)$, with the first <qubit> the control,
$$
\boxed{C_X=\begin{pmatrix}1&0&0&0\\0&1&0&0\\0&0&0&1\\0&0&1&0\end{pmatrix}.}
$$
The one-<qubit> gates generate a dense set of one-<qubit> <unitary operators>, and <CNOT gates> supply entangling operations. Approximate universality is the appropriate qualification for a finite discrete set: its finite circuits cannot exactly equal every member of a continuous uncountable <unitary group>.
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