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Quantum simulation qubit models of electronic Hamiltonians rely on specific transformations in order to take into account the fermionic permutation properties of electrons. These transformations (principally the Jordan–Wigner transformation (JWT) and the Bravyi–Kitaev transformation) correspond in a quantum circuit to the introduction of a supplementary circuit level. In order to include the fermionic properties in a more straightforward way in quantum computations, we propose to use methods issued from Geometric Algebra (GA), which, due to its commutation properties, are well adapted for fermionic systems. First, we apply the Witt basis method in GA to reformulate the JWT in this framework and use this formulation to express various quantum gates. We then rewrite the general one and two-electron Hamiltonian and use it for building a quantum simulation circuit for the Hydrogen molecule. Finally, the quantum Ising Hamiltonian, widely used in quantum simulation, is reformulated in this framework. [ABSTRACT FROM AUTHOR]

An analytical model of intermodulation distortion and chirp in cable television (CATV) distributed feedback laser diodes was presented. Longitudinal spatial hole burning was compared to gain compression over the CATV band. Results showed that the effects of longitudinal spatial hole burning on chirp and distortion were significant in actual lasers. In addition, the entire CATV band was affected by the nonhomogenous distribution of the photon along the cavity.

Theoretical studies involving cross- and time-covariance functions of the variables controlling Langevin noise sources help examine the noise in semiconductor lasers. Analytical expressions represent frequency noise, carrier noise spectrum, the AM and FM noise and the phase change modification. Approximations of the phase dynamics require the inclusion of the shot noise factor in addition to carrier contributions.

A novel analytical model, associated with Volterra nonlinear functionals, describes the internal parameters and transmission characteristics of semiconductor lasers. This model generates output expressions of such forms of input as multiple frequency and step function. These lasers are essential for broadband fiber optic communication.

Considering links between logic and physics is important because of the fast development of quantum information technologies in our everyday life. This paper discusses a new method in logic inspired from quantum theory using operators, named Eigenlogic. It expresses logical propositions using linear algebra. Logical functions are represented by operators and logical truth tables correspond to the eigenvalue structure. It extends the possibilities of classical logic by changing the semantics from the Boolean binary alphabet { 0 , 1 } using projection operators to the binary alphabet { + 1 , − 1 } employing reversible involution operators. Also, many-valued logical operators are synthesized, for whatever alphabet, using operator methods based on Lagrange interpolation and on the Cayley–Hamilton theorem. Considering a superposition of logical input states one gets a fuzzy logic representation where the fuzzy membership function is the quantum probability given by the Born rule. Historical parallels from Boole, Post, Poincaré and Combinatory Logic are presented in relation to probability theory, non-commutative quaternion algebra and Turing machines. An extension to first order logic is proposed inspired by Grover's algorithm. Eigenlogic is essentially a logic of operators and its truth-table logical semantics is provided by the eigenvalue structure which is shown to be related to the universality of logical quantum gates, a fundamental role being played by non-commutativity and entanglement. [ABSTRACT FROM AUTHOR]