Synthesis of quantum reversible logic circuits means to automatically construct desired quantum reversible logic circuit with minimal quantum cost.We present a novel and efficient algorithm which can construct almost all optimal 4-qubit reversible logic circuits with various types of gates and minimum length cost based on constructing the shortest coding and the specific topological compression

whose lossless compression ratios of the space of n-qubit circuits is near

2×n

!.We firstly have created all 3120218828 optimal 4-qubit circuits whose length is less than 9 for the Controlled-Not gate

NOT gate and Toffoli gate library

and our method can achieve 16 steps through cascading created circuits.Our algorithm can not only synthesizes all the 4-qubit benchmark circuits

but also runs extremely fast.