= Solution
Here $H^2=I$. Both remaining gates fix the all-zero computational <vector>: the <T gate> fixes $|0\rangle$, and the <controlled-NOT gate> fixes $|00\rangle$. Therefore every finite circuit, on any number of initially zero wires, leaves $|0\cdots0\rangle$ unchanged.
It cannot even approximate $|+\rangle\otimes|0\cdots0\rangle$, whose squared overlap with that unchanged <vector> is $1/2$. Thus \b[the gate set is not universal]. The needed <quantum superposition> cannot be created from this input by <basis> permutations and diagonal phases alone.
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