What is a brief history on the idea that the Pope is the Antichrist?

The papacy is an office, not a person. Antichrist (capital "A") is a single person, though there can be many antichrists (lowercase "a"), those who are against Christ. So, the papacy cannot be Antichrist; however, a pope (really, an anti-pope) could.

Commentary on 2 Thessalonians 2:4 (that Antichrist "sitteth in the temple of God") of the Original Rheims Bible:

St. Augustine therefore li. 20 de civit. c. 19 and St. Jerome q. 11 ad Algasiam. do think, that this sitting of Antichrist in the temple, doth signify his sitting in the Church of Christ, rather than in Solomon's temple. Not as though he should be a chief member of the Church of Christ, or a special part of his body mystical, and be Antichrist and yet withal continuing within the Church of Christ, as the Heretics feign, to make the Pope Antichrist (whereby they plainly confess and agnise [recognize] that the Pope is a member of the Church, & in ipso sinu Ecclesia, and in the very bosom of the Church, say they:) for that is ridiculous, that all Heretics whom St. John calleth antichrists as his precursors, should go out of the Church, and the great Antichrist himself should be of the Church, and in the Church, and continue in the same. And yet to them that make the whole Church in revolt from God, this is no absurdity. But the truth is, that this antichristian revolt here spoken of, is from the Catholic Church: and Antichrist, if he ever were of or in the Church, shall be an apostate and a renegade out of the Church, and he shall usurp upon it by tyranny, and by challenging worship, religion, and government thereof, so that himself shall be adored in all the Churches of the world which he list to leave standing for his honor. And this is to sit in the temple or against the Temple of God, as some interpret. If any Pope did ever this, or shall do, then let the adversaries call him Antichrist.

This passage, summarizing Church Fathers' views, makes it clear that a true pope cannot be Antichrist, but Antichrist could be an anti-pope; anti-popes are not members of the Church.

^{taken from this answer to the question "What is the Catholic interpretation of 2 Thessalonians 2:3 [that Antichrist 'sitteth in the temple of God')]?"}

A brief history on the idea that the Papacy is the AntiChrist.

What follows below is taken from Antichrist | new Advent.

The article says that when the Antichrist is understood as an individual person, a signal enemy of Christ, it excludes the contention of those who explain Antichrist as the papacy.

The article then goes on to say that

The Waldensian and Albigensian heretics, as well as Wyclif and Hus, called the Pope by the name of Antichrist; but the expression was only a metaphor in their case. It was only after the time of the Reformation that the name was applied to the Pope in its proper sense. It then passed practically into the creed of the Lutherans, and has been seriously defended by them as late as 1861 in the "Zeitschrift für lutherische Theologie".

Who are the Waldensians?

The Waldensians (also known variously as Waldenses are a Christian movement and religious cultural group which started in Lyon and spread soon to the Cottian Alps in the late 1170s. - Source: Waldensians | Wikipedia.

And who were the Albigenses?

A neo-Manichæan sect that flourished in southern France in the twelfth and thirteenth centuries. The name Albigenses, given them by the Council of Tours (1163) prevailed towards the end of the twelfth century and was for a long time applied to all the heretics of the south of France. They were also called Catharists (katharos, pure), though in reality they were only a branch of the Catharistic movement. The rise and spread of the new doctrine in southern France was favoured by various circumstances, among which may be mentioned: the fascination exercised by the readily-grasped dualistic principle; the remnant of Jewish and Mohammedan doctrinal elements; the wealth, leisure, and imaginative mind of the inhabitants of Languedoc; their contempt for the Catholic clergy, caused by the ignorance and the worldly, too frequently scandalous, lives of the latter; the protection of an overwhelming majority of the nobility, and the intimate local blending of national aspirations and religious sentiment. - Source: Albigenses | New Advent.

I have not found exactly when The Waldensian and Albigensian heretics called the Pope by the name of Antichrist.

According to the article, during some time in their life, John Wycliffe, an Englishman (c. 1330-1384) and Jan Hus (c. 1370-1415 and born in Bohemia), called the Pope by the name of Antichrist.

Within the Catholic Church, the way I understand it, the future wicked Pope is more identified with the false prophet than with the Antichrist.

Below are a couple of prophecies regarding the papacy:

1. I saw a great power rise up against the Church. It plundered, devastated, and threw into confusion and disorder the vine of the Lord, having it trampled underfoot by the people and holding it up to ridicule by all nations. Having vilified celibacy and oppressed the priesthood, it had the effrontery to confiscate the Church's property and to arrogate to itself the powers of the Holy Father, whose person and whose laws it held in contempt. - Jeanne le Royer (Sister of the Nativity, b. 1731 and became a nun in 1755).
2. [...] an arrogant Pope will divide the Church. His orders will be obeyed and what is precious will be thrown out. A great spiritual confusion is on the way… the one who could have been Peter will become Judas. He will open the doors for the enemy and will make men and women of faith suffer… The church will be without Peter… a war will explode on Rome and there will be few survivors. - Pedro Regis.

The roots of the doctrine in its primative form actually reaches back to the views of very early church fathers. I add this history to show the period prior to people like Joachim described in the other post. The idea stems from a very early belief by church fathers that the antichrist would be a new form of government in the Roman Empire. A powerful papacy was not existent at the time so the connection was impossible to foresee but all the seeds of the belief were sewn by them, later appropriated by those witnessing papal abuses that fit the church father expectation.

The principal idea of the church fathers is rooted in the connection of the anti-Christ with the little horn that ‘has eyes’ and ‘speaks blasphemous things’ in Daniel Chapter 7. This expected soon-to-come antichrist from some sort of mysterious sinister change within the Roman Empire (this evil horn) was considered by the Fathers to include a dreadful 'apostasy of believers' which would start a terrible history of persecution against true believers who opposed the risen new Roman power. Therefore, the prayers of the fathers was that Rome would be kept safe from any such political changes. The hope was that the dreaded horn of antichrist and massive church apostasy would be kept at bay as long as possible as it was greatly feared.

One author has already collected this history of the church fathers on this subject providing to us a convenient collection of these origins to the view adopted by nearly all early protestant reformers:

All quotes from Horae Apocalypticae; or, A commentary on the Apocalypse, critical and historical; including also an examination of the chief prophecies of Daniel (1846). page 365

Cyril, ordained Bishop of Jerusalem A.D. 350 had this view.

He, like the fathers before him, explained the four wild Beasts of Dan. 7. to be the Babylonian, Persian, Macedonian, and Roman empires, and identified the fourth Beast’s little horn with St. Paul’s Man of Sin and St. John’s Antichrist. Further he judged that the time of his coming was to be when the times of the then Roman empire were fulfilled, (ὁταν πληρωθωσιν οἱ καιροι της των Ῥωμαιων βασιλειας,) and it was dissolved into ten kingdoms, kingdoms rising up contemporaneously, but in different places:—that then Antichrist, (“some great man raised up by the devil,”) falsely calling himself the Christ, and so seducing the Jews, would by magical arts and false miracles seize on, and usurp, the power of the Roman empire, eradicate three of the ten kings, and subjugate the other seven:—that at first mild in semblance, and prudent, and the abolisher of idols, (all with a view to self-exaltation,) he would afterwards show himself as God, sitting in the Jewish temple; (“for God forbid it should be that in which we are;”) and for three years and a half persecute the Church:—finally that the apostasy, of which St. Paul spoke as Antichrist’s precursor, meant a religious apostasy, “from the right faith, from truth, and from right words.” (So Catech. Lect. xv.)

Ambrose, ordained Bishop of Milan A.D. 374 contributed this view:

The only prophetical notices on the point proposed in the genuine writings of this father, are those in his Comment on Luke 21:20; Book x. § 15–18. He there (like Cyril) explains the apostasy of St. Paul to mean an apostasy from true religion: (“à verâ religione plerique lapsi errore deseiscent:”)—that it would be the Jewish inner or mental temple in which Antichrist would sit: and that then, seizing on the kingdom, (I presume the Roman kingdom or supremacy,) he would claim for himself a throne of divine authority; “sibi divinæ vindicet solium potestatis.”

In the Comment on 2 Thess. 2. of the Pseudo-Ambrose, the hindrance to Antichrist’s manifestation is explained to be the Roman empire; its defection (αποστασια), or abolition, being the occasion of his appearance; and that he would then restore freedom to the Romans, “sub suo nomine:”—that the mystery of iniquity spoken of by St. Paul was Nero’s persecuting spirit against Christians, which still afterwards had continued to actuate succeeding Pagan emperors down to Diocletian and Julian; finally that he would, “in domo Domini, in sede sedeat Christi, et ipsum Deum se asserat.”

Chrysostom, ordained Presbyter A.D. 386 expresses the same gist:

He too (on Daniel) expounded Nebuchadnezzar’s quadripartite Image, and Daniel’s four Beasts, as the other fathers. “The days of those kings,” said of the time of the stone being cut out, he explains as the days of the Romans: and that, in smiting and destroying the Roman kingdom, it would destroy the others too, as included.—Also in his” Hom. iv. on 2 Thess. 2 he made the Roman empire to be the let or hindrance to Antichrist’s manifestation meant by St. Paul: τουτʼ εστιν ἡ αρχη ἡ Ῥωμαικη· ὁταν αρθῃ εκ μεσου τοτε εκεινος ηξει· and again: ὁταν αὑτη καταλυθῃ επιθησεται (ὁ Αντιχριστος) τῃ αναρχιᾳ, και την των ανθρωπων και την του Θεου επιχειρησει ἁρπασαι αρχην· and he explained the temple in which Antichrist would sit to be rather “the Christian Churches everywhere,” than the Jewish temple.—The mystery of iniquity he thought might be Nero, as in spirit a type of Antichrist: Νερωνα ὡσανει τυπον οντα του Αντιχριστου· και γαρ οὑτος εβουλετο νομιζεσθαι Θεος· and that Antichrist was to be αντιθεος τις; overthrowing indeed the worship of idols and other gods, but only so as to enforce the worship of himself in the place of them and of God.—The apostasy Chrysostom identifies pretty much with Antichrist himself; ὡς πολλους μελλοντα απολλυναι και αφιστᾶν. He adds that, as Rome succeeded Greece, so Rome would be succeeded by Antichrist, and Antichrist by Christ.

Jerome, ordained Presbyter A.D. 378, has again the same:

On Dan. 2. he expounds the gold, silver, brass, and iron of the symbolic Image to be the same four kingdoms as the other fathers: the stone cut out of the mountain without hands being Christ born of a virgin; whose kingdom, upon the destruction of all the other kingdoms, was finally to fill the whole earth. The breaking of the iron legs into ten toes,—part iron, part clay,—he explained of the weakness of the Roman empire at the time he wrote,—about A.D. 407....—On Dan. 7. he explains the four Beasts of the same four empires; the four heads of the third or Macedonian Beast indicating its subdivisions, on Alexander’s death, into the kingdoms of Ptolemy, Seleucus, Philip, Antigonus. On the divisions of the fourth, or Roman...—adding that this eleventh king is to be a man, with Satan’s spirit indwelling, the same as St. Paul’s man of sin: also that the Roman empire is to be finally destroyed on account of this Antichrist’s blasphemies, and with it all earthly kingdoms

Augustine notices and agrees in Jerome’s view of Daniel’s, four Beasts

As to the identity of the fourth Beast’s little horn with St. Paul’s man of sin and St. John’s Antichrist.’ He explains the apostasy in 2 Thess. 2 of a religious apostasy; indeed, (expounding the abstract of the concrete,) as the apostate Antichrist himself; “Nisi venerit refuga primùm, utique a Domino Deo:”—also as to the temple he would sit in, that it seemed to him dubious whether it might mean. Solomon’s ruined temple, or the Christian Church: that at any rate it could not be an idol’s or dæmon’s temple; because that would not be called God’s temple:—further that the let, or hindrance, in Antichrist’s way might not absurdly be taken to mean the Roman empire.

So we see that the church fathers while experiencing persecutions in Rome observed these prophecies with serious expectation that some new Roman power would rise within the churches themselves, claiming to be in some sense equal to Christ in authority over all the churches, ushering in a widespread apostasy and persecution if true believers. It is from this ancient belief that later generations came to consider that the papacy in its previous military and religious power was that 'horn' with religious oversight represented as 'eyes' and speaking 'blasphemous things' such as the Pope's claim as being Christ's vice-regent on earth and insinuating fake authority over all believers.

It is rare a major biblical doctrine is to be entirely absent in the first few hundred years of Christianity and it should be of no surprise that this also has it roots there.