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As a cornerstone for many quantum linear algebraic and quantum machine learning algorithms, controlled quantum state preparation (CQSP) aims to provide the transformation of $|i\rangle |0^n\rangle \to |i\rangle |\psi_i\rangle $ for all $i\in \{0,1\}^k$ for the given $n$-qubit states $|\psi_i\rangle$.
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