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Generalized clifford groups and simulation of associated quantum circuits
TLDR
In this paper we isolate the ingredients of the theorem and provide generalisations of some of them with the aim of identifying new classes of quantum circuits that can be classically efficiently simulated. Expand
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Valence bond solid formalism for d-level one-way quantum computation
The d-level or qudit one-way quantum computer (d1WQC) is described using the valence bond solid formalism and the generalized Pauli group. This formalism provides a transparent means of derivingExpand
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Quantum Shuffles and Quantum Supergroups of Basic Type
We initiate the study of several distinguished bases for the positive half of a quantum supergroup $U_q$ associated to a general super Cartan datum $(\mathrm{I}, (\cdot,\cdot))$ of basic type insideExpand
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Canonical Basis for Quantum $${\mathfrak{osp}(1|2)}$$
We introduce a modified quantum enveloping algebra as well as a (modified) covering quantum algebra for the ortho-symplectic Lie superalgebra $${\mathfrak{osp}(1|2)}$$. Then we formulate and computeExpand
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Quantum Supergroups V. Braid Group Action
We construct a braid group action on quantum covering groups. We further use this action to construct a PBW basis for the positive half in finite type which is pairwise-orthogonal under the innerExpand
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Super tableaux and a branching rule for the general linear Lie superalgebra
In this note, we formulate and prove a branching rule for simple polynomial modules of the Lie superalgebra . Our branching rules depend on the conjugacy class of a Borel subalgebra. AExpand
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Linear preservers of higher rank numerical ranges and radii
Structural theorems regarding linear preservers of the higher rank numerical ranges are proved for the real linear space of bounded self-adjoint operators or the complex linear space of boundedExpand
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Quantum supergroups II. Canonical basis
Following Kashiwara's algebraic approach, we construct crystal bases and canonical bases for quantum supergroups with no isotropic odd roots and for their integrable modules.
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Quantum Supergroups III. Twistors
AbstractWe establish direct connections at several levels between quantum groups and supergroups associated to bar-consistent anisotropic super Cartan datum by constructing an automorphism (calledExpand
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SCHUR MULTIPLICATIVE MAPS ON MATRICES
Abstract The structure of Schur multiplicative maps on matrices over a field is studied. The result is then used to characterize Schur multiplicative maps f satisfying $f(S) \subseteq S$ forExpand
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