Exact quantum splitting and the structure of finite algebras
The construction provides an exact quantum implementation for splitting Berlekamp’s algorithm, ensuring it factors squarefree polynomials over finite fields with certainty. It replaces a randomized step with an unconditional counting argument, allowing exact amplitude amplification to convert a probabilistic test into a deterministic one. This achieves exact factorization and structure decomposition for finite algebras in large odd characteristic without relying on unproven hypotheses.