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Suppose you have a chain of length $n$. Then the smallest amplitude in that chain is no larger than $2^{-n}$. But this implies the operations you are applying have a maximum error term $\epsilon$ that is smaller than that, since otherwise they would overwhelm that amplitude. And approximating arbitrary rotations to within $\epsilon$ requires $\Omega(\lg(1/\... 2 You can use stim for this, although you do have to write the stabilizer projection procedure for yourself. Write some methods to project a system into the +1 eigenstate of several stabilizers: from typing import List import stim def find_compatible_tableau(stabilizers: List[stim.PauliString]) -> stim.Tableau: num_qubits = max(len(e) for e in ... 8 Let$\mathcal{G}_n$denote the Pauli group on$n$qubits. An$n$-qubit state$|\psi\rangle$is called a stabilizer state if there exists a subgroup$S \subset \mathcal{G}_n$such that$|S|=2^n$and$A|\psi\rangle = |\psi\rangle$for every$A\in S$. For example,$(|00\rangle+|11\rangle)/\sqrt2$is a stabilizer state, because it is a$+1\$ eigenstate of the ...