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Quantum Cluster Algebras and Quantum Nilpotent Algebras [PDF]
Proceedings of the National Academy of Sciences of the United States of America, 2014 Significance Cluster algebras are used to study in a unified fashion phenomena from many areas of mathematics. In this paper, we present a new approach to cluster algebras based on noncommutative ring theory. It deals with large, axiomatically defined classes of algebras and does not require initial combinatorial data. Because of this,
Milen Tchernev Yakimov
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Algebraic structure of path-independent quantum control
Physical Review Research, 2022 Path-independent (PI) quantum control has recently been proposed to integrate quantum error correction and quantum control [W.-L. Ma, M. Zhang, Y. Wong, K. Noh, S. Rosenblum, P. Reinhold, R. J. Schoelkopf, and L. Jiang, Phys. Rev. Lett. 125, 110503 (2020)
Wen-Long Ma, Shu-Shen Li, Liang Jiang
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Bicovariant quantum algebras and quantum Lie algebras [PDF]
Communications in Mathematical Physics, 1993 38 ...
Schupp, Peter +2 more
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An algebra of quantum processes [PDF]
ACM Transactions on Computational Logic, 2009 We introduce an algebra qCCS of pure quantum processes in which communications by moving quantum states physically are allowed and computations are modeled by super-operators, but no classical data is explicitly involved. An operational semantics of qCCS is presented in terms of (nonprobabilistic) labeled transition systems. Strong bisimulation between
Mingsheng Ying +3 more
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Quantum -algebras and elliptic algebras [PDF]
Communications in Mathematical Physics, 1996 26 pages ...
Feigin, Boris, Frenkel, Edward
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Perturbatively exact w 1+∞ asymptotic symmetry of quantum self-dual gravity
Journal of High Energy Physics, 2022 The infinite tower of positive-helicity soft gravitons in any minimally coupled, tree-level, asymptotically flat four-dimensional (4D) gravity was recently shown to generate a w 1+∞ asymptotic symmetry algebra. It is natural to ask whether this classical
Adam Ball +3 more
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From quantum universal enveloping algebras to quantum algebras [PDF]
Journal of Physics A: Mathematical and Theoretical, 2008 The ``local'' structure of a quantum group G_q is currently considered to be an infinite-dimensional object: the corresponding quantum universal enveloping algebra U_q(g), which is a Hopf algebra deformation of the universal enveloping algebra of a n-dimensional Lie algebra g=Lie(G).
Celeghini, E. +2 more
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Journal of High Energy Physics, 2020 We study a correspondence between 3d N $$ \mathcal{N} $$ = 2 topologically twisted Chern-Simons-matter theories on S 1 × Σg and quantum K -theory of Grassmannians.
Kazushi Ueda, Yutaka Yoshida
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The Quantum Symmetry in Nonbalanced Hopf Spin Models Determined by a Normal Coideal Subalgebra
Journal of Mathematics, 2021 For a finite-dimensional cocommutative semisimple Hopf C∗-algebra H and a normal coideal ∗-subalgebra H1, we define the nonbalanced quantum double DH1;H as the crossed product of H with H1op^, with respect to the left coadjoint representation of the ...
Xin Qiaoling, Cao Tianqing
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Universal Framework for Quantum Error-Correcting Codes
Entropy, 2021 We present a universal framework for quantum error-correcting codes, i.e., a framework that applies to the most general quantum error-correcting codes. This framework is based on the group algebra, an algebraic notation associated with nice error bases ...
Zhuo Li, Lijuan Xing
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