In order to reduce the interference among multiple users, a new system (multi-bit, multiple access differential chaos shift keying, MA-DCSK) of chaotic multiple access communication is proposed, and the multi-user detection algorithm is designed. Through simulation, the bit error rate (BER) of multi-bit MA-DCSK system is compared with the variable delay MA-DCSK (VDMA-DCSK), and the result proves that the new system has lower BER. By making use of the parallelism computation characteristic of quantum, the Grover quantum algorithm is used to solve the computational complexity of the multi-user detection algorithm, and it can reduce the computational complexity from N to N. The simulation result shows Grover quantum algorithm can effectively reduce the computational complexity without affecting the system performance at the same time.