You may have explained this in the paragraph above but there was issues with the tex. I understand your answer, but quickly to clarify:$(\langle x | \otimes \mathbb{1})$ and $(| y \rangle \otimes \...

Welcome to QCSE. Indeed the original overhead for the initial Hamiltonian simulation algorithms that used product formulae grew as $O(1/\epsilon)$ - but through a very clever sequence of ...

The most efficient way I have found is to perform a random walk in the following expression:$$|ψ⟩=|K|^{−1/2}∑_{x∈K}i^{d⋅x}(−1)^{q(x)+b⋅x}|x⟩$$5-qubits stabilizer states are obtained in few hours.