  This study unveils a groundbreaking exploration of using semiconductor
technology in quantum circuitry. Leveraging the unique operability of 45 nm
CMOS technology at deep cryogenic temperatures (~ 300 mK), a novel quantum
electronic circuit is meticulously designed. Through the intricate coupling of
two matching circuits via a 45 nm nMOS transistor, operating as an open quantum
system, the circuit quantum Hamiltonian and the related Heisenberg-Langevin
equation are derived, setting the stage for a comprehensive quantum analysis.
Central to this investigation are three pivotal coefficients derived, which are
the coupling between the coupled oscillator charge and flux operators through
the internal circuit of the transistor. These coefficients emerge as critical
determinants, shaping both the circuit potential as a parametric amplifier and
its impact on quantum properties. The study unfolds a delicate interplay
between these coefficients, showcasing their profound influence on quantum
discord and the gain of the parametric amplifier. Consequently, the
assimilation of 45 nm CMOS technology with quantum circuitry makes it possible
to potentially bridge the technological gap in quantum computing applications,
where the parametric amplifier is a necessary and critical device. The designed
novel quantum device serves not only as a quantum parametric amplifier to
amplify quantum signals but also enhances the inherent quantum properties of
the signals such as non-classicality. Therefore, one can create an effective
parametric amplifier that simultaneously improves the quantum characteristics
of the signals. The more interesting result is that if such a theory becomes
applicable, the circuit implemented in the deep-cryogenic temperature can be
easily compatible with the next step of circuitry while keeping the same
electronic features compatibility with the quantum processor.
