Cannon had . . . . . . . . unique qualities . . . . . . . . it was used widely in ancient times.

The phrase such ... that is used to show cause and effect. It highlights the extent or degree of something and its resulting consequence.

In this sentence, such is used to emphasize the unique qualities of the cannon, and that introduces the result of these qualities, which is its widespread use in ancient times.

that, that is incorrect because it does not correctly establish the cause-and-effect relationship.

that, since is incorrect because since indicates time or reason, not the degree of qualities.

such, so is incorrect because so is typically followed by an adjective or adverb, not a clause.

Therefore, the correct answer is such, that.