We introduce Quantum Register Algebra (QRA) as an efficient tool for quantum computing. We show the direct link between QRA and Dirac formalism. We present GAALOP (Geometric Algebra Algorithms Optimizer) implementation of our approach. Using the QRA basis vectors definitions given in Section 4 and the framework based on the de Witt basis presented in Section 5, we are able to fully describe and compute with QRA in GAALOP using the geometric product. We illustrate the intuitiveness of this computation by presenting the QRA form for the well known SWAP operation on a two qubit register.
This paper introduces an application of complex Clifford algebra in a representation of the quantum prisoner's dilemma. The authors propose a novel modification of the Eisert–Lewenstein–Wilkens protocol to represent a repeated version of the quantum game. This repeated modification allows to embed entanglement into players' strategy sets and to see how players will operate with it. The apparatus of complex Clifford algebra enables an intuitive representation of the suggested protocol and efficient computation of the resulting payoff functions. The presented findings provide a new point of view on the interpretation of entanglement as a measure of information transition between rounds of the game.
This paper deals with the task of waste energy recovery and effective price setting of waste-to-energy plants. Its main contribution is the invention of a new approach to pricing of waste disposal in a particular waste management network. This novel method, which is based on a problem of finding the Nash equilibrium, takes into account the amounts of waste production of cities, capacities of waste-to-energy plants and their locations. The best response dynamics algorithm enables the computation of Nash equilibrium for a game of waste-to-energy plants in a normal form with numerous players and multiple strategies in comparison with other standard algorithms. The algorithm is able to find the Nash equilibrium for a sufficiently big step size between possible gate fees. The results of this work are applicable in the forecasting of prices of waste-to-energy plants’ services for real waste management networks.
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