Revisiting fixed-point quantum search

We review the fixed-point quantum search (Yoder, Low, and Chuang, 2014) that overcomes the souffle problem while maintaining quadratic speedups. We give a rigorous proof of the lemma regarding the explicit formula of recursive quasi-Chebyshev polynomials. This lemma is crucial to the correctness of the fixed-point quantum search, or more precisely the closed-form angle parameters therein, but its proof is missing in the original paper.