Related papers: QuAlg -- A symbolic algebra package for quantum in…
We show how the basic operations of quantum computing can be expressed and manipulated in a clear and concise fashion using a multiparticle version of geometric (aka Clifford) algebra. This algebra encompasses the product operator formalism…
A geometrical approach to quantum computation is presented, where a non-abelian connection is introduced in order to rewrite the evolution operator of an energy degenerate system as a holonomic unitary. For a simple geometrical model we…
The coherent state method has proved to be useful in quantum physics and mathematics. This method, more precisely, the vector coherent state method, has been used by some authors to construct representations of superalgebras but almost, to…
Based on the {\it nonlinear coherent states} method, a general and simple algebraic formalism for the construction of \textit{`$f$-deformed intelligent states'} has been introduced. The structure has the potentiality to apply to systems…
We present an introduction to the Quantum Toolbox in Python (QuTiP) in the context of an undergraduate quantum mechanics class and potential senior research projects. QuTiP provides ready-to-use definitions of standard quantum states and…
The gauge invariant observables of the closed bosonic string are quantized without anomalies in four space-time dimensions by constructing their quantum algebra in a manifestly covariant approach. The quantum algebra is the kernel of a…
Quantum computation is inherently hybrid, and fast classical manipulation of qubit operators is necessary to ensure scalability in quantum software. We introduce PauliEngine, a high-performance C++ framework that provides efficient…
We introduce QuESTlink, pronounced "quest link", an open-source Mathematica package which efficiently emulates quantum computers. By integrating with the Quantum Exact Simulation Toolkit (QuEST), QuESTlink offers a high-level, expressive…
This survey article is concerned with the modeling of the kinematical structure of quantum systems in an algebraic framework which eliminates certain conceptual and computational difficulties of the conventional approaches. Relying on the…
In this paper we discuss a model of quantum computer in which a state is an operator of density matrix and gates are general quantum operations, not necessarily unitary. A mixed state (operator of density matrix) of n two-level quantum…
We review a geometric approach to classification and examination of quantum correlations in composite systems. Since quantum information tasks are usually achieved by manipulating spin and alike systems or, in general, systems with a finite…
We propose a categorical and algebraic study of quantale modules. The results and constructions presented are also applied to abstract algebraic logic and to image processing tasks.
Modern approaches to semanic analysis if reformulated as Hilbert-space problems reveal formal structures known from quantum mechanics. Similar situation is found in distributed representations of cognitive structures developed for the…
States of a quantum mechanical system are represented by rays in a complex Hilbert space. The space of rays has, naturally, the structure of a K\"ahler manifold. This leads to a geometrical formulation of the postulates of quantum mechanics…
We present an algebraic algorithm for quantum state tomography that leverages measurements of certain observables to estimate structured entries of the underlying density matrix. Under low-rank assumptions, the remaining entries can be…
Qudits with a large Hilbert space to host quantum information are widely utilized in various applications, such as quantum simulation and quantum computation, but the manipulation and scalability of qudits still face challenges. Here, we…
This is the manual of the first version of QEDtool, an object-oriented Python package that performs numerical quantum electrodynamics calculations, with focus on full state reconstruction in the internal degrees of freedom, correlations and…
Quantum algebras are a mathematical tool which provides us with a class of symmetries wider than that of Lie algebras, which are contained in the former as a special case. After a self-contained introduction to the necessary mathematical…
A full quantum mechanical treatment of open quantum systems via a Master equation is often limited by the size of the underlying Hilbert space. As an alternative, the dynamics can also be formulated in terms of systems of coupled…
Let $\mathfrak{g}$ be a semi-simple Lie algebra with fixed root system, and $U_q(\mathfrak{g})$ the quantization of its universal enveloping algebra. Let $\mathcal{S}$ be a subset of the simple roots of $\mathfrak{g}$. We show that the…