kaz29Вестник Казахстанско-Британского технического университетаHerald of the Kazakh-British Technical University1998-66882959-8109Казахстанско-Британский Технический Университет10.55452/1998-6688-2024-21-3-128-136kaz29-1374Research ArticleКОМПЬЮТЕРНЫЕ НАУКИCOMPUTER SCIENCEВЫЧИСЛЕНИЕ БАЗИСА ИНВАРИАНТНЫХ МНОГОЧЛЕНОВ СТЕПЕНИ 4 ДЛЯ 7 КУБИТОВCOMPUTING THE DEGREE-4 INVARIANT POLYNOMIAL BASIS FOR 7 QUBITShttps://orcid.org/0000-0002-7669-0656АмановА.AmanovA.

докторант 

050000, г. Алматы

PhD student 

050000, Almaty

alimzhan.amanov@gmail.comКазахстанско-Британский технический университетКазахстанKazakh-British Technical UniversityKazakhstan202401102024213128136Copyright © Аманов А., 20242024Аманов А.Amanov A.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://vestnik.kbtu.edu.kz/jour/article/view/1374

Понимание сложности запутанных состояний в контексте SLOCC (стохастические локальные операции и классическая коммуникация), включающих несколько кубитов, важно для продвижения нашего знания о квантовых системах. Эта сложность часто анализируется путем классификации состояний через локальные группы симметрии. На практике полученные классы можно различать с помощью инвариантных многочленов, но размер этих многочленов быстро растет. Поэтому важно получить инварианты наименьшей возможной степени. В этой короткой заметке мы вычисляем базис инвариантных многочленов для 7 кубитов степени 4, которые являются инвариантами наименьшей степени. Мы получаем эти многочлены, используя теорию представлений и алгебраическую комбинаторику

Understanding the complexity of entangled states within the context of SLOCC (stochastic local operations and classical communications) involving several number qubits is essential for advancing our knowledge of quantum systems. This complexity is often analyzed by classifying the states via local symmetry groups. Practically, tthe resulting classes can be distinguished using invariant polynomials, but the size of these polynomials grows rapidly. Hence, it is crucial to obtain the smallest possible invariants. In this short note, we compute the basis of invariant polynomials of 7 qubits of degree 4, which are the smallest degree invariants. We obtain these polynomials using the representation theory and algebraic combinatorics. 

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The authors declare that there are no conflicts of interest present.