Related papers: Bases for spin systems and qudits from angular mom…
It is shown that the momentum density of free electromagnetic field splits into two parts. One has no contribution to the net momentum due to the transversality condition. The other yields all the momentum. The angular momentum that…
The usefulness of solid-state spins in quantum technologies depends on how long they can remain in a coherent superposition of quantum states. This Colloquium discusses how first-principles simulations can predict spin dynamics for…
Simple constructions and protocols are demonstrated to allow the implementation of universal quantum computation on an arbitrarily large quantum system by controlling a fixed number of spins, vastly reducing the engineering requirements in…
A quantum spin-1/2, and its associated su(2) algebra of Pauli spin matrices are familiarly linked to Clifford algebra and quaternions. Somewhat more loosely, we develop connections between the su(4) algebra of two spins and of its…
The article is dedicated to q-deformed versions of spinor calculus. As a kind of review, the most relevant properties of the two-dimensional quantum plane are summarized. Additionally, the relationship between the quantum plane and…
We propose a novel platform for quantum many body simulations of dipolar spin models using current circuit QED technology. Our basic building blocks are 3D Transmon qubits where we use the naturally occurring dipolar interactions to realize…
We attempt to contribute some novel points of view to the "foundations of quantum mechanics", using mathematical tools from "quantum probability theory" (such as the theory of operator algebras). We first introduce an abstract algebraic…
A formulation of quantum mechanics based on replacing the general unitary group by finite groups is considered. To solve problems arising in the context of this formulation, we use computer algebra and computational group theory methods.
We study the representation and visualization of finite-dimensional quantum systems. In a generalized Wigner representation, multi-spin operators can be decomposed into a symmetry-adapted tensor basis and they are mapped to multiple…
Spin-orbital entanglement in the ground state of a one-dimensional SU(2)$\otimes$SU(2) spin-orbital model is analyzed using exact diagonalization of finite chains. For $S=1/2$ spins and $T=1/2$ pseudospins one finds that the quantum…
Generalized uncertainty principles are able to serve as useful descriptions of some of the phenomenology of quantum gravity effects, providing an intuitive grasp on non-trivial space-time structures such as a fundamental discreteness of…
In this paper we use the framework of generalized probabilistic theories to present two sets of basic assumptions, called axioms, for which we show that they lead to the Hilbert space formulation of quantum mechanics. The key results in…
We employ quantum circuit learning to simulate quantum field theories (QFTs). Typically, when simulating QFTs with quantum computers, we encounter significant challenges due to the technical limitations of quantum devices when implementing…
We build two-dimensional quantum field theories on spin surfaces starting from theories on oriented surfaces with networks of topological defect lines and junctions. The construction uses a combinatorial description of the spin structure in…
A general technique is outlined for investigating supersymmetry properties of a charged spin-$\half$ quantum particle in time-varying electromagnetic fields. The case of a time-varying uniform magnetic induction is examined and shown to…
We describe an explicit basis for the $\operatorname{SU}(2)$-invariant space of the exterior power $\wedge_{2k} \mathbb{C}^{2m}$ via the combinatorics of plane partitions. In quantum chemistry, this is the space of spin adapted quantum…
By means of the Helmholtz theorem on the decomposition of vector fields, the angular momentum of the classical electromagnetic field is decomposed, in a general and manifestly gauge invariant manner, into a spin component and an orbital…
For certain non-magnetic solids with low symmetry the occurrence of spin-polarized longitudinal currents is predicted. These arise due to an interplay of spin-orbit interaction and the particular crystal symmetry. This result is derived…
Quantum spin liquids may be considered "quantum disordered" ground states of spin systems, in which zero point fluctuations are so strong that they prevent conventional magnetic long range order. More interestingly, quantum spin liquids are…
In this paper a formalism for studying the dynamics of quantum systems coupled to classical spin environments is reviewed. The theory is based on generalized antisymmetric brackets and naturally predicts open-path off-diagonal geometric…