This is a common misconception. The Romans themselves were aware of vast lands to the east which had been conquered by Alexander the Great. These lands extended from the eastern boundary of the Roman Empire to India. It's also likely that Romans were vaguely aware of the Han Empire in China whose influence extended to the eastern shore of the Caspian Sea.
Also, the US is a republic with popular elections, a written constitution including a Bill of Rights, a free press and democratic institutions. The Roman Empire had none of these. Unfortunately, the US does have a lot of public and private debt.