New techniques for bounding stabilizer rank

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Standard

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

Harvard

Lovitz, B & Steffan, V 2022, 'New techniques for bounding stabilizer rank', Quantum, bind 6, 692, s. 1-22. https://doi.org/10.22331/q-2022-04-20-692

APA

Lovitz, B., & Steffan, V. (2022). New techniques for bounding stabilizer rank. Quantum, 6, 1-22. [692]. https://doi.org/10.22331/q-2022-04-20-692

Vancouver

Lovitz B, Steffan V. New techniques for bounding stabilizer rank. Quantum. 2022;6:1-22. 692. https://doi.org/10.22331/q-2022-04-20-692

Author

Lovitz, Benjamin ; Steffan, Vincent. / New techniques for bounding stabilizer rank. I: Quantum. 2022 ; Bind 6. s. 1-22.

Bibtex

@article{2a2f920179f4402a81090ab76bb51305,
title = "New techniques for bounding stabilizer rank",
abstract = "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.",
author = "Benjamin Lovitz and Vincent Steffan",
year = "2022",
doi = "10.22331/q-2022-04-20-692",
language = "English",
volume = "6",
pages = "1--22",
journal = "Quantum",
issn = "2521-327X",
publisher = "Verein zur F{\"o}rderung des Open Access Publizierens in den Quantenwissenschaften",

}

RIS

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