相关论文: Quantum SL(3,C)'s: the missing case
A new method is introduced to study three-body clusters. Triangular configurations with ${\cal D}_{3h}$ point-group symmetry are analyzed. The spectrum, transition form factors and $B(E\lambda)$ values of $^{12}$C are investigated. It is…
An overview of quantum computing and in particular the Hidden Subgroup Problem are presented from a mathematical viewpoint. Detailed proofs are supplied for many important results from the literature, and notation is unified, making it…
In [5] the author conjectures and partially shows that the Cuntz semigroup classifies unitary elements of unital AF-algebras. We provide a complete proof by addressing the existence part of the conjecture, under a mild adjustment of both…
We classify semisimple module categories over the tensor category of representations of quantum SL(2) extending previous results to the roots of unity and positive characteristic cases.
This is a set of lecture notes suitable for a Master's course on quantum computation and information from the perspective of theoretical computer science. The first version was written in 2011, with many extensions and improvements in…
In this paper, we review some features of quantum annealing and related topics from viewpoints of statistical physics, condensed matter physics, and computational physics. We can obtain a better solution of optimization problems in many…
We show that the algebra of the recently proposed Triply Special Relativity can be brought to a linear (ie, Lie) form by a correct identification of its generators. The resulting Lie algebra is the stable form proposed by Vilela Mendes a…
We present a classification of three-qubit states based in their three-qubit and reduced two-qubit entanglements. For pure states these criteria can be easily implemented, and the different types can be related with sets of equivalence…
We combine the study of resources in measurement-based quantum computation (MBQC) with that of quantum solutions to linear constraint systems (LCS). Contextuality of the input state in MBQC has been identified as a key resource for quantum…
In this paper we explore graded algebras of quotients of Lie algebras with special emphasis on the 3-graded case and answer some natural questions concerning its relation to maximal Jordan systems of quotients.
This work presents a classification of $U_q(\mathfrak{sl}_2)$-symmetries on the quantum disc. The principal invariant of such classification, the grading jump, is introduced. It turns out that, under the present subjects, the grading jump…
Differential calculus on the quantum quaternionic group GL(1,H$_q$) is introduced.
We comment on the paper ``Numerical study of the SWKB condition of novel classes of exactly solvable systems'' [Y. Nasuda and N. Sawado, Mod. Phys. Lett. A 36, 2150025 (2021)]. We show that it misrepresents our prior work [J. Bougie, A.…
In this paper, we have considered the problem of general conclusive quantum state classification; the necessary and sufficient conditions for the existence of conclusive classification strategies have also been presented. Moreover, we have…
This paper consists of two (still only vaguely) related parts: in the first, we briefly review work done in the past three years on the ``planar equivalence" between a class of non-supersymmetric theories (including limiting cases of QCD)…
In this paper, we study the nature of entanglement in quantum Grover's and Shor's algorithms. So far, the authors who have been interested in this problem have approached the question quantitatively by introducing entanglement measures…
One of the fundamental conditions for one-way quantum computation (1WQC) is the ability to make sequential measurements on isolated qubits that comprise the highly entangled resource for 1WQC, the cluster state. This has been a significant…
Quantum machine learning (QML) is a promising early use case for quantum computing. There has been progress in the last five years from theoretical studies and numerical simulations to proof of concepts. Use cases demonstrated on…
Using the fact that the algebra M(3,C) of 3 x 3 complex matrices can be taken as a reduced quantum plane, we build a differential calculus Omega(S) on the quantum space S defined by the algebra C^\infty(M) \otimes M(3,C), where M is a…
We give a description of the construction of Chevalley supergroups, providing some explanatory examples. We avoid the discussion of the $A(1,1)$, $P(3)$ and $Q(n)$ cases, for which our construction holds, but the exposition becomes more…