  The present article primarily focuses on the design of an ultra-low-noise
amplifier specifically tailored for quantum applications. The circuit design
places a significant emphasis on improving the noise figure, as
quantum-associated applications require the circuit's noise temperature to be
around 0.4 K. This requirement aims to achieve performance comparable to the
Josephson Junction amplifier. Although this task presents considerable
challenges, the work concentrates on engineering the circuit to minimize
mismatch and reflection coefficients, while simultaneously enhancing circuit
transconductance. These efforts aim to improve the noise figure as efficiently
as possible. The results of this study indicate the possibility of achieving a
noise figure of approximately 0.009 dB for a unique circuit design operating at
10 K. In a departure from traditional approaches, this study employs quantum
mechanical theory to analyze the circuit comprehensively. By employing quantum
theory, the researchers derive relationships that highlight the crucial
quantities upon which the circuit design should focus to optimize the noise
figure. For example, the circuit's gain power, which depends on the circuit's
photonic modes, is theoretically derived and found to affect the noise figure
directly. Ultimately, by merging quantum theory with engineering approaches,
this study successfully designs a highly efficient circuit that significantly
minimizes the noise figure in a quantum application setting.
