Related papers: Revisiting Boole Equation in the Quantum Context
This work has the purpose of applying the concept of Geometric Calculus (Clifford Algebras) to the Fibre Bundle description of Quantum Mechanics. Thus, it is intended to generalize that formulation to curved spacetimes [the base space of…
Our primary purpose is to isolate the abstract, mathematical properties of circuits -- both classical Boolean circuits and quantum circuits -- that are essential for their computational interpretation. A secondary purpose is to clarify the…
The relation that exists in quantum mechanics among action variables, angle variables and the phases of quantum states is clarified, by referring to the system of a generalized oscillator. As a by-product, quantum-mechanical meaning of the…
A key notion bridging the gap between {\it quantum operator algebras} \cite{LZ10} and {\it vertex operator algebras} \cite{Bor}\cite{FLM} is the definition of the commutativity of a pair of quantum operators (see section 2 below). This is…
Using tangent bundle geometry we construct an equivalent reformulation of classical field theory on flat spacetimes which simultaneously encodes the perspectives of multiple observers. Its generalization to curved spacetimes realizes a new…
We develop an unified algebraic approach to the description of gauge interactions within the framework of a new concept of quantum mechanics. The next step in generalizing the space-time and the action vector space is made. The gauge field…
Generally, the measurement process consists in coupling a system to a detector that can give a continuous output. However, it may be interesting to use as a detector a system with a discrete spectrum, especially in view of applications to…
A noncommutative-geometric generalization of the classical formalism of frame bundles is developed, incorporating into the theory of quantum principal bundles the concept of the Levi-Civita connection. The construction of a natural…
General Relativity describes gravity in geometrical terms. This suggests that quantizing such theory is the same as quantizing geometry. The subject can therefore be called quantum geometry and one may think that mathematicians are…
The geometrical description of Quantum Mechanics is reviewed and proposed as an alternative picture to the standard ones. The basic notions of observables, states, evolution and composition of systems are analised from this perspective, the…
Quantum programs today are written at a low level of abstraction - quantum circuits akin to assembly languages - and the unitary parts of even advanced quantum programming languages essentially function as circuit description languages.…
Quantum particles in a potential are described by classical statistical probabilities. We formulate a basic time evolution law for the probability distribution of classical position and momentum such that all known quantum phenomena follow,…
In this paper we present a survey of the use of differential geometric formalisms to describe Quantum Mechanics. We analyze Schr\"odinger framework from this perspective and provide a description of the Weyl-Wigner construction. Finally,…
We show a systematic construction for implementing general measurements on a single qubit, including both strong (or projection) and weak measurements. We mainly focus on linear optical qubits. The present approach is composed of simple and…
A geometric framework for describing quantum particles on a possibly curved background is proposed. Natural constructions on certain distributional bundles (`quantum bundles') over the spacetime manifold yield a quantum ``formalism'' along…
Implementing a qubit quantum computer in continuous-variable systems conventionally requires the engineering of specific interactions according to the encoding basis states. In this work, we present a unified formalism to conduct universal…
By encoding a qudit in a harmonic oscillator and investigating the d --> infinity limit, we give an entirely new realization of continuous-variable quantum computation. The generalized Pauli group is generated by number and phase operators…
A generalized algebra of quantum observables, depending on extra dimensional constants, is considered. Some limiting forms of the algebra are investigated and their possible applications to the descriptions of interactions of fundamental…
Qubits are neither fermions nor bosons. A Fock space description of qubits leads to a mapping from qubits to parafermions: particles with a hybrid boson-fermion quantum statistics. We study this mapping in detail, and use it to provide a…
Quantum computation has suggested new forms of quantum logic, called quantum computational logics. The basic semantic idea is the following: the meaning of a sentence is identified with a quregister, a system of qubits, representing a…