The NAND operation at 250 Gbit/s based on quantum dot-semiconductor optical amplifiers (QD-SOAs) is modeled. By solving the rate equations of SOAs in the form of a Mach-Zehnder interferometer (MZI), the performance of NAND gate is numerically investigated. The model takes the effects of amplified spontaneous emission (ASE) and the input pulse energy on the system’s quality factor into account. Results show that NAND gate in QD-SOA-MZI based structure is feasible at 250 Gbit/s with a proper quality factor. The decrease in quality factor is predicted for high spontaneous emission factor (N_SP). For an ideal amplifier (N_SP = 2), the Q-factor is 17.8 for 30 dB gain.