New techniques for bounding stabilizer rank
Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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New techniques for bounding stabilizer rank. / Lovitz, Benjamin; Steffan, Vincent.
I: Quantum, Bind 6, 692, 2022, s. 1-22.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - New techniques for bounding stabilizer rank
AU - Lovitz, Benjamin
AU - Steffan, Vincent
PY - 2022
Y1 - 2022
N2 - 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.
AB - 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.
U2 - 10.22331/q-2022-04-20-692
DO - 10.22331/q-2022-04-20-692
M3 - Journal article
VL - 6
SP - 1
EP - 22
JO - Quantum
JF - Quantum
SN - 2521-327X
M1 - 692
ER -
ID: 303590813