New techniques for bounding stabilizer rank

Research output: Contribution to journalJournal articleResearchpeer-review


  • Fulltext

    Final published version, 593 KB, PDF document

In this work, we present number-theoretic and algebraic-geometric techniques for bounding the stabilizer rank of quantum states. First, we refine a number-theoretic theorem of Moulton to exhibit an explicit sequence of product states with exponential stabilizer rank but constant approximate stabilizer rank, and to provide alternate (and simplified) proofs of the best-known asymptotic lower bounds on stabilizer rank and approximate stabilizer rank, up to a log factor. Second, we find the first non-trivial examples of quantum states with multiplicative stabilizer rank under the tensor product. Third, we introduce and study the generic stabilizer rank using algebraic-geometric techniques.
Original languageEnglish
Article number692
Pages (from-to)1-22
Publication statusPublished - 2022

Number of downloads are based on statistics from Google Scholar and

No data available

ID: 303590813