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Journal of Applied Logics -- IfCoLog Journal of Logics and their Applications

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Quantum logic, Quantum computers -- Testing, Logic circuits -- Design and construction


Previous work has provided methods for decomposing unitary matrices to series of quantum multiplexers, but the multiplexer circuits created in this way may be highly non-minimal. This paper presents a new approach for optimizing quantum multiplexers with arbitrary single-qubit quantum target functions and ternary controls. For multivalued quantum multiplexers, we define standard forms and two types of new forms: Fixed Polarity Quantum Forms (FPQFs) and Kronecker Quantum Forms (KQFs). Drawing inspiration from the usage of butterfly diagrams, we devise a method to exhaustively construct new forms. In contrast to previous butterfly-based methods, which are used with classical Boolean functions, these new forms are used to optimize quantum circuits with arbitrary target unitary matrices. Experimental results on the new forms applied to various target gates such as NOT, V, V+, Hadamard, and Pauli rotations, demonstrate that these new forms greatly reduce the gate costs of ternary quantum multiplexers.


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Special Issue: Multiple Valued Logic. 978-1-84890-323-4.

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