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This study unveils a groundbreaking exploration of using semiconductortechnology in quantum circuitry. Leveraging the unique operability of 45 nmCMOS technology at deep cryogenic temperatures (~ 300 mK), a novel quantumelectronic circuit is meticulously designed. Through the intricate coupling oftwo matching circuits via a 45 nm nMOS transistor, operating as an open quantumsystem, the circuit quantum Hamiltonian and the related Heisenberg-Langevinequation are derived, setting the stage for a comprehensive quantum analysis.Central to this investigation are three pivotal coefficients derived, which arethe coupling between the coupled oscillator charge and flux operators throughthe internal circuit of the transistor. These coefficients emerge as criticaldeterminants, shaping both the circuit potential as a parametric amplifier andits impact on quantum properties. The study unfolds a delicate interplaybetween these coefficients, showcasing their profound influence on quantumdiscord and the gain of the parametric amplifier. Consequently, theassimilation of 45 nm CMOS technology with quantum circuitry makes it possibleto potentially bridge the technological gap in quantum computing applications,where the parametric amplifier is a necessary and critical device. The designednovel quantum device serves not only as a quantum parametric amplifier toamplify quantum signals but also enhances the inherent quantum properties ofthe signals such as non-classicality. Therefore, one can create an effectiveparametric amplifier that simultaneously improves the quantum characteristicsof the signals. The more interesting result is that if such a theory becomesapplicable, the circuit implemented in the deep-cryogenic temperature can beeasily compatible with the next step of circuitry while keeping the sameelectronic features compatibility with the quantum processor.

Quantum Parametric Amplification and NonClassical Correlations due to 45 nm nMOS Circuitry Effect