Lightwave communication systems, optical random memories, and photonic encryption/decryption are important applications that rely on all-optical latches. For the first time, the carrier reservoir semiconductor optical amplifiers (CR-SOAs) are employed to simulate two basic optical latches, Set-Reset (SR) latch, and D Flip-Flop, at a data rate of 120 Gb/s. All-optical NAND and NOT logic operations are used to build these latches, which are implemented using Mach-Zehnder interferometers (MZIs) with CR-SOAs. In the presence of the amplified spontaneous emission noise, the variation of the output quality factor (Q-factor) against the CR-SOA key operating parameters is studied. This is achieved by exploiting and numerically solving a set of coupled partial differential equations that describe the CR-SOAs gain and phase dynamics when operated as nonlinear elements and embedded in MZIs. The results demonstrate that CR-SOAs-based MZIs can achieve a high Q-factor while implementing the logical SR latch and D Flip-Flop at a high speed of 120 Gb/s.