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Generalized clifford groups and simulation of associated quantum circuits

- Sean Clark, R. Jozsa, N. Linden
- Physics, Mathematics
- Quantum Inf. Comput.
- 15 January 2007

TLDR

23 3- PDF

Valence bond solid formalism for d-level one-way quantum computation

- Sean Clark
- Mathematics, Physics
- 19 December 2005

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 deriving… Expand

27 3- PDF

Quantum Shuffles and Quantum Supergroups of Basic Type

- Sean Clark, D. Hill, W. Wang
- Mathematics
- 28 October 2013

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 inside… Expand

11 1- PDF

Canonical Basis for Quantum $${\mathfrak{osp}(1|2)}$$

- Sean Clark, W. Wang
- Mathematics, Physics
- 17 April 2012

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 compute… Expand

19 1- PDF

Quantum Supergroups V. Braid Group Action

- Sean Clark, D. Hill
- Mathematics, Physics
- 1 September 2014

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 inner… Expand

4- PDF

Super tableaux and a branching rule for the general linear Lie superalgebra

- Sean Clark, Yung-Ning Peng, Sittipong Thamrongpairoj
- Mathematics
- 2 January 2013

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. A… Expand

4- PDF

Linear preservers of higher rank numerical ranges and radii

- Sean Clark, C. Li, Jennifer Mahle, L. Rodman
- Mathematics
- 22 June 2009

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 bounded… Expand

3- PDF

Quantum supergroups II. Canonical basis

- Sean Clark, D. Hill, W. Wang
- Mathematics
- 30 April 2013

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.

18- PDF

Quantum Supergroups III. Twistors

- Sean Clark, Zhaobing Fan, Y. Li, W. Wang
- Mathematics, Physics
- 26 July 2013

AbstractWe establish direct connections at several levels between quantum groups and supergroups associated to bar-consistent anisotropic super Cartan datum by constructing an automorphism (called… Expand

25- PDF

SCHUR MULTIPLICATIVE MAPS ON MATRICES

- Sean Clark, C. Li, Ashwin Rastogi
- Mathematics
- Bulletin of the Australian Mathematical Society
- 1 February 2008

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 $f(S) \subseteq S$ for… Expand

7- PDF

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