Quarton structure) is utilized as a parametric amplifier. We begin by theoretical deriving the system’s Lagrangian, quantum Hamiltonian, and then analyze the dynamics using the quantum Langevin equation. By transforming these equations into the Fourier domain and employing the input-output formalism, leading metric indicators of the parametric amplifier become calculated. The new proposed design offers significant advantages over traditional designs due to its ability to manipulate nonlinearity. This premier feature enhances the compression point (P1dB) of the amplifier dramatically, and also provides its tunability across a broad band. The enhanced linearity, essential for quantum applications, is achieved through effective nonlinearity management, which is theoretically derived. Also, the ability to sweep the C-band without significant spectral overlap is crucial for frequency multiplexing in scalable quantum systems. Simulation results show that Blochnium parametric amplifiers can reach to a signal gain around 25 dB with a compression point better than of -92 dBm. Therefore, our proposed parametric amplifier, with its superior degree of freedom, surpasses traditional designs like arrays of Josephson junctions, making it a highly promising candidate for advanced quantum computing applications.