We demonstrate theoretically that a topological insulator quantum dot can be formed via double topological insulator constrictions (TICs). The TICs are created by appropriate split-gate electrode patterns on the top of a HgTe/CdTe quantum well (QW) with inverted band structures. In sharp contrast to conventional semiconductor quantum dots, the presence or absence of topological insulator edge states in the proposed quantum Hall bar system leads to distinct propagating behaviors. This topological insulator quantum dot can be used as a charge and/or spin carrier trap memory element with near perfect program/erase efficiency by properly adjusting the voltages applied to the split-gates. For completeness, we also demonstrate that a small perturbation of the Rashba spin orbit interaction (RSOI) or a magnetic field in the quantum dot does not destroy the topological edge states and has negligible impact on the on-(edge)-state transport behaviors of the quantum Hall bar.