New techniques for bounding stabilizer rank

• DOI: 10.22331/q-2022-04-20-692
• Publication Date: 2022-04-20T10:40:25Z
• Authors: Benjamin Lovitz; Vincent Steffan
• Keywords: Rank (graph theory); Stabilizer (aeronautics); Bounding overwatch

In this work, we present number-theoretic and algebraic-geometric techniques for bounding the stabilizer rank of quantum states. First, refine a theorem Moulton to exhibit an explicit sequence product states with exponential but constant approximate rank, provide alternate (and simplified) proofs best-known asymptotic lower bounds on up log factor. Second, find first non-trivial examples multiplicative under tensor product. Third, introduce study generic using techniques.