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Tracing the orbitals of the quantum permutation group
Using a suitably noncommutative flat matrix model, it is shown that the quantum permutation group has free orbitals: that is, a monomial in the...
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Discrete quantum walks on the symmetric group
Both the transient and limiting dynamical behavior of classical random walks on non-abelian groups have a well-developed theory utilizing...
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Almost Periodic Type Group Actions on Compact Quantum Metric Spaces
A compact quantum metric space is a complete order unit space A endowed with a Lipnorm L . We give some characterizations of almost periodic type...
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On evolution of the classical heat and the quantum wave generated by the Laplacian on the Heisenberg group
The Laplacian on the Heisenberg group as a sum of squares of the standard vector fields on the Heisenberg group is first made explicit to be a...
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Explicit Generators of the Centre of the Quantum Group
A finite generating set of the centre of any quantum group is obtained, where the generators are given by an explicit formulae. For the slightly...
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Convex PBW-type Lyndon Bases and Restricted Two-parameter Quantum Group of Type F4
The convex PBW-type Lyndon basis for two-parameter quantum group U r,s ( F 4 )is given. Assume that rs −1 is a primitive ℓ-th root of unity with ℓ odd,...
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The de Sitter (dS) Group and Its Representations An Introduction to Elementary Systems and Modeling the Dark Energy Universe
This Second Edition is a comprehensive update, integrating the latest research and theoretical advancements in the field of de Sitter (dS) group...
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The Quantum-Mechanical Context
In this chapter, we study the construction of (projective) unitary irreducible representations (UIR’s) of the...
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Quantum Permutation Matrices
Quantum permutations arise in many aspects of modern “quantum mathematics”. However, the aim of this article is to detach these objects from their...
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Permutation Group and the Determinant
Let us design a new group: the group of permutations. It will help define the determinant in a new way. This will give us a few attractive...
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The Quantum Double
The quantum double construction originally has been introduced by Drinfel’d (Quantum groups. In: Proceedings of the International Congress of...
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Quantum Operads
The most standard description of symmetries of a mathematical structure produces a group. However, when the definition of this structure is motivated...
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Method of Hydrodynamic Images and Quantum Calculus in Fock-Bargmann Representation of Quantum States
We propose a new approach to quantum states in Fock space in terms of classical hydrodynamics. By conformal map** of complex analytic function,...
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Quantum Hall Effect
The date of discovery of the quantum Hall effect (QHE) is known pretty accurately.
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Quantum Gates and Circuits
A quantum circuit, like the classical case, represents qubits by lines and gates by various symbols. At the hardware level, a quantum circuit, like a...
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Machine Learning for Quantum Control
This chapter presents results on learning controlLearning control of quantum systems. In Sect. 5.2, two differential evolutionDifferential...