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Multiport Impedance Quantization For a Class of Annihilation Operator Linear Quantum Systems

This paper provides a procedure for building a multiport impedance quantization involving annihilation operators only for a class of linear quantum systems having a positive real impedance transfer function matrix. Based on the positive real properties of these quantum systems, it is shown that it is possible to use the Brune algorithm in order to find an electrical circuit that can physically implement these quantum systems. This theory, illustrated for multiport circuits may be useful for the implementation of superconducting microwave circuits used in quantum filters found in the field of quantum computing.