Can an ancient Chinese bow and arrow exceed the speed of sound?

Theoretically, yes, but in practice, no. The weight of the arrow limits the speed, and the strength of the arrow material limits the speed! The weight of the arrow limits the speed, the strength of the arrow material limits the speed. The deflection of the arrow limits the speed, and the tension of the bow and the rebound of the blade pulley limits the speed. An arrow you shoot at supersonic speeds will burst the moment it leaves the string! A modern top speed blazing chariot compound bow will only reach 300+ feet per second . Short crossbow arrows might work. Because the shorter the arrow the lower the deflection, the stronger it is, and the lighter it weighs!