Religious history also offers another striking parallel between Rome and China. The Buddhist faith began to penetrate the Han empire in the first century A. D., and soon won converts in high places. Its period of official dominance in court circles extended from the third to the ninth centuries A. D. This obviously parallels the successes that came to Christianity in the Roman empire during the same period.
Ch.3 "Confluence of the Disease Pools of Eurasia: 500 B.C. to A.D. 1200". - Plagues and Peoples (1976)