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Journal of the Franklin Institute

One port impedance quantization for a class of annihilation operator linear quantum systems

Aline I. Maalouf, Ian R. Petersen

Published Nov 17, 2022• 0 citations
Publisher
DOI
10.1016/j.jfranklin.2022.11.007

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This paper provides a procedure for building a one port 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 one-port circuits may be useful for the implementation of superconducting microwave circuits used in quantum filters found in the field of quantum computing.
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.
Theoretical developments in the field of quantum optics and quantum superconducting electrical circuits involving continuous measurement based feedback control as well as coherent control are an important prerequisites for advances in the domain of quantum technology. Within these perspectives, this paper considers positive real properties for a class of quantum systems whose quantum stochastic differential equation model involves annihilation operators only and then relates them to corresponding bounded real properties and consequently to physical realizability conditions developed earlier by the authors. Based on the positive real properties of these quantum systems, it is anticipated 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, in the case of one-port circuits, may be useful for the implementation of microwave circuits related to quantum filters found in the field of quantum computing.