Owing to the exponential nature of the memory or run-time complexity

many existing methods can only synthesize 3-qubit logic circuits using quantum logic gate library

however

a few can optimally synthesize 3-qubit logic circuits for quantum NOT

CNOT

Controlled-V and Controlled-V+(NCV)gates

the key approach reduces the NCV quantum circuit synthesis problem to four-valued logic synthesis.This paper proposes using NCV gates to create a new quantum logic gate library

which is exactly the same as NCV gate library in the synthesis of all optimal 3-qubit circuits

thus it also reduces the four-valued logic synthesis to easily solved two-valued logic synthesis.We present a 3-qubit efficient synthesis algorithms based on perfect hash function

which can quickly construct all optimal 3-qubit circuits--the average speed that synthesizes circuits with minimum cost is nearly 127 times faster than that of the best result of Maslov 2007.