Classic logic relationship can be represented by logic functions. Quantum logic function can be defined similarly. However, quantum logic gates are unitary transformations, which are reversible. So it can not realize irreversible transformation directly. By introducing auxiliary qubits and adding the output signal of quantum bits, the irreversible logic operations can be achieved. The sample irreversible logic gates of OR, NOR, and NAND were studied. Their corresponding reversible realization was proposed. At the cost of losing part of quantum information, the optimized circuits were finally obtained.