Quantum state preparation

Quantum state preparation constructs a circuit $B$ that maps a simple reference state to a desired state, $B|0^n⟩=|\psi ⟩$. Efficient amplitude encoding requires structure or suitable oracle access to avoid reading exponentially many arbitrary amplitudes.

Hierarchical probability-distribution state preparation recursively bisects a classical probability distribution. At each level, a controlled rotation splits every parent interval's amplitude between its two children according to their conditional probabilities.