the noise figure and its improvement to be used in quantum applications at which the noise added due to the circuit designed should be strongly limited. If the designed low noise amplifier could have quantum-associated applications, its noise temperature should be around 0.4 K, in which the designed circuit is comparable with the Josephson Junction amplifier. Although this task seems to be highly challenging, this work focuses on engineering the circuit, minimizing the mismatch and reflection coefficients in the circuit, and enhancing the circuit transconductance to improve the noise figure in the circuit as efficiently as possible. The results indicated the possibility of reaching the noise figure around 0.008 dB in the circuit operating at 10 K. Additionally, the circuit is analyzed via quantum mechanical analysis, through which some important quantities, such as noise figure, is theoretically derived. In fact, the derived relationship using quantum theory reveals that on which quantities the design should focus in order to optimize the noise figure. Thus, merging quantum theory and engineering the approach contributed to designing a highly efficient circuit for strongly minimizing the noise figure.