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On the one hand, the use of graphical language in quantum computing for the representation of algorithms, although intuitive, is not very useful for different tasks such as the description of quantum circuits in text environments, the calculation of quantum states or the optimization of quantum circuits. An algebraic language has been developed to represent quantum circuits in a convenient and concise manner, similar to the way Boolean expressions are used in classical circuits. The proposed notation, QAlgebra, allows the consistent and parameterized description of quantum algorithms, as well as the easy handling of the elements that compose it to achieve powerful optimizations in the number of gates of the circuits. On the other hand, the QuantumSolver (QS) python library has been implemented as a link between different quantum disciplines and applications. It is composed of several submodules: QS Basic, where simple algorithms are included; QS Subroutine, a collection of algorithms in which the quantum part forms only a part of the procedure; QS Crypto, which includes numerous implementations of Quantum Key Distribution algorithms; QS Composer, a transpiler from traditional classical gates to quantum gates; QS AI, which allows solving the classification problem by supervised learning with Variational Quantum Circuits. This library is in a process of constant evolution, as it is an open source project, which tries to maintain an accessible and easily extendable structure. Several open questions will be raised for discussion, such as the possible undecidability in the application of overwriting rules in the minimisation of a circuit using algebraic notation, the evaluation of the expressiveness and practicality of QAlgebra, or the formulation of new QKD protocols based on those already implemented in QS Crypto (such as BBM92, SARG04).

https://combalgo.labri.fr/pmwiki.php/Groupe/Info-Quantique

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