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It can be shown that clifford gates do not preserve distance. My question is what if you restrict to local clifford gates, is distance preserved by these? (by local I mean that they act on each qubit …

The generators for qudit clifford group are give here https://arxiv.org/abs/1911.08162 This is more concise than the paper in the comment and takes care of subtleties better. Here is a short GAP progr …

Here's an example for the real Pauli and Clifford groups : $$P_1=<X_1,Z_1>; |P_1|=8;$$ $$P_2=<X_1,Z_1,X_2,Z_2>; |P_2|=32;$$ $$C_1=<X_1,Z_1,H_1>; |C_1|=16;$$ $$C_1^{\otimes 2}=<X_1,Z_1,H_1,X_2,Z_2,H_2> …

I know that Clifford gates can be efficiently simulated on classical computers using tableaux. How are non-clifford gates handled? Can simulators handle 100 qubit non-clifford gates?

Given a stabilizer code on $n$ qubits defined by a set of stabilizers $S_1,\cdots S_m$; The encoder $E$ is a matrix in $U(2^n)$ (unitary group) such that $S_i E v = E v$. I'm pretty sure that $E$ is a …