Questions tagged [clifford-hierarchy]

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what is the equivalent of Clifford group if you add T gate to Pauli's

Let's take the 1 qubit case first; the Pauli group $G_p=<X_1,Z_1>$ has order $16$. Now add $T_1$ (T gate) to the two generators then $G_t=<X_1,Z_1,T_1>$ is finite and has order $128$. The ...
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Is there a closure property for the entire Clifford hierarchy?

TL;DR Is the entire Clifford hierarchy (as opposed to any one level), a group? Background. The Clifford hierarchy (on $n$ qubits), is a collection of nested subsets $\mathcal C^{(1)} \subset \mathcal ...
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