Related papers: Generalized spin bases for quantum chemistry and q…
Quantum spaces with $\frak{su}(2)$ noncommutativity can be modelled by using a family of $SO(3)$-equivariant differential $^*$-representations. The quantization maps are determined from the combination of the Wigner theorem for $SU(2)$ with…
This thesis presents an efficient quantum algorithm and explicit circuits for generating eigenstates of arbitrary SU(2) and SU(3) representations. These include a wide variety of highly entangled states. The algorithm uses Schur transform…
A new functional calculus, developed recently for a fully non-perturbative treatment of quantum gravity, is used to begin a systematic construction of a quantum theory of geometry. Regulated operators corresponding to areas of 2-surfaces…
Using the natural extension of the notion of the generalized coherent states the scalar and spinor ones for the de Sitter group SO(4,1) are constructed. These systems of coherent states obey the de Sitter--invariant Klein-Gordon and Dirac…
Matrices of the irreducible representations of double crystallographic point groups O, Td, Ox{1,I} and Tdx{1,I} are derived. The characteristic polynomials (spinor bases) up to the sixth power are obtained. The method for the derivation of…
Quantum groups were invented largely to provide solutions of the Yang-Baxter equation and hence solvable models in 2-dimensional statistical mechanics and one-dimensional quantum mechanics. They have been hugely successful. But not all…
The universal quantum computation is obtained when there exists asymmetric anisotropic exchange between electron spins in coupled semiconductor quantum dots. The asymmetric Heisenberg model can be transformed into the isotropic model…
Let ${\mathbf U}_q^-$ be the negative half of a quantum group of finite type. Let $P$ be the transition matrix between the canonical basis and a PBW basis of ${\mathbf U}_q^-$. In the case ${\mathbf U}_q^-$ is symmetric, Antor gave a simple…
Generalizing the quantum sine-Gordon and sausage models, we construct exact S-matrices for higher spin representations with quantum U_q(su(2)) symmetry, which satisfy unitarity, crossing-symmetry, and the Yang-Baxter equations with…
A concrete representation of the Clifford algebra (for any hyperbolic quadratic space) is given using what are called Suslin matrices. This explicit construction is used to analyze the corresponding Spin groups and the involution and might…
We prove that universal quantum computation is possible using only (i) the physically natural measurement on two qubits which distinguishes the singlet from the triplet subspace, and (ii) qubits prepared in almost any three different…
Molecular platforms are regarded as promising candidates in the generation of units of information for quantum computing. Herein, a strategy combining spin-crossover metal ions and radical ligands is proposed from a model Hamiltonian first…
The symmetric subspace of multi-qubit systems, that is, the space of states invariant under permutations, is commonly encountered in applications in the context of quantum information and communication theory. It is known that the symmetric…
Although intrinsic spin is usually viewed as a purely quantum property with no classical analog, we present evidence here that fermion spin has a classical origin rooted in the geometry of three-dimensional physical space. Our approach to…
We recently derived a spin-mapping approach for treating the nonadiabatic dynamics of a two-level system in a classical environment [J. Chem. Phys. 151, 044119 (2019)] based on the well-known quantum equivalence between a two-level system…
A proposal for a magnetic quantum processor that consists of individual molecular spins coupled to superconducting coplanar resonators and transmission lines is carefully examined. We derive a simple magnetic quantum electrodynamics…
We present an operational reconstruction of the well-known two-to-one homomorphism between the groups $SU(2)$ and $SO(3)$, grounded in the physical description of quantum state preparation and evolution. Starting from the connection between…
We discuss the symmetry aspects of quantum field theory in global four-dimensional de Sitter spacetime linked to $SO(1,4)$ isometries. For the unitary irreducible representations relevant to elementary particles, we obtain explicit…
The universal covering of SO(3) is modelled as a reflection group G_R in a representation independent fashion. For relativistic quantum fields, the Unruh effect of vacuum states is known to imply an intrinsic form of reflection symmetry,…
Previously a new scheme of quantum information processing based on spin coherent states of two component Bose-Einstein condensates was proposed (Byrnes {\it et al.} Phys. Rev. A 85, 40306(R)). In this paper we give a more detailed…