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Study of two-photon absorption (TPA) has been carried out for all-optical logic operation based on quantum-dot semiconductor optical amplifier (QD-SOA). XOR gate, AND gate and pseudo-random bit sequence (PRBS) were all modeled with the TPA effect on the existing rate equation. Inclusion of TPA induced pumping has increased the output Q-factor (quality). The output result demonstrates that the quality of the output is dependent on the input pulse width and the operation speed. The PRBS system modeled with TPA shows that it can operate at 250 Gb/s and 320 Gb/s and increase in pulse width decrease the Q-factor.