The Quran Says that People of Other Religions
are to be Violently Punished in This World

Allah himself fights against the unbelievers (9:30), so why should Muslims not fight in his cause rather than in the cause of evil (4:76)?  About 19% of the Quran is devoted to the violent conquest and subjugation of non-Muslims:

Against them make ready your strength to the utmost of your power, including steeds of war, to strike terror into (the hearts of) the enemies of Allah and your enemies and others besides, whom ye may not know (8:60)

Strive hard (Jihad) against the Unbelievers and the Hypocrites, and be firm against them. Their abode is Hell,- an evil refuge indeed.  (66:9, See also 9:73)

Muslims are to expect a reward in this life as well as the next (4:134), so it makes sense that unbelievers should be punished in this life as well:

…He whom Allah sendeth astray, for him there is no guide. For them is a penalty in the life of this world, but harder, truly, is the penalty of the Hereafter… (13:33-34)

There are at least two places in the Quran where the violent death of non-Muslims is referred to as Allah's reward for unbelief (2:191, 9:26), as in "such is the reward for unbelievers."  Verse 3:56,  bluntly states that "those who reject faith" will be "punished with terrible agony in this world" (a vow that Muhammad and his companions personally took it upon themselves to fulfill).

The Quran tells Muslims that Allah uses them to violently punish others:

Fight them, Allah will punish them by your hands and bring them to disgrace... (9:14)

In the end, All beings on heaven and earth will be forced to bow down to Allah, either willingly or by force:

And unto Allah falleth prostrate whosoever is in the heavens and the earth, willingly or unwillingly (13:15)

Muslims are told that Allah "loves those who fight in his way" to make Islam "victorious over all other religions, even though the disbelievers resist" (61:4-11). Those who do resist Islam will be humiliated:

Those who resist Allah and His Messenger will be among those most humiliated.(58:20 - The context for this verse is the eviction of the Jewish tribes of Medina and the confiscation of their wealth, land, and children by Muhammad).

Non-Muslims are to be fought until religion is only for Allah:

And fight them until there is no more ftna (unbelief, worshipping others beside Allah), and religion is all for Allah… (8:39 – Some translate the word "fitna" as “persecution”, but in this context it means resistance to Islam – defined in the prior verse as an unwillingness to believe (see verse 38).  This passage was “revealed” following a battle that Muhammad deliberately provoked.  Verse 2:193 essentially says the same thing and was also “revealed” at a time when the Muslims were notunder physical attack).

Those with "diseased hearts" - which include Christians and Jews according to 5:52 - are to be"seized wherever found and slain with a (fierce) slaughter" (33:60-62) along with "hypocrites" (Muslims who are judged not to be true believers by their associations with unbelievers or their unwillingness to engage in Jihad).

Non-Muslims are to be encroached on, pressured and punished by the Muslims:

See they not that We gradually reduce the land (in their control) from its outlying borders? (13:41 - See also 21:44)
We shall punish them gradually from directions they perceive not. (68:44)
And He made you heirs to their land and their dwellings and their property, and (to) a land which you have not yet trodden, and Allah has power over all things. (33:27, See also Bukhari 53:392)

Allah will grant Muslims authority and power over all other people:

Allah has promised, to those among you who believe and work righteous deeds, that He will, of a surety, grant them in the land, inheritance (of power), as He granted it to those before them; that He will establish in authority their religion... (24:55)

(Muhammad's companions continued to self-fulfill this prophecy with an aggressive and senseless military expansion that left a trail of bodies from Spain to India).

Allah provides instructions to Muslims for dealing with unbelievers who are unwilling to accept Islamic rule:

Remember thy Lord inspired the angels (with the message): "I am with you: give firmness to the Believers: I will instill terror into the hearts of the Unbelievers: smite ye above their necks and smite all their finger-tips off them." This because they contended against Allah and His Messenger: If any contend against Allah and His Messenger, Allah is strict in punishment. (8:12-13)

Defeating non-Muslims should be easy for true believers because they are superior in intelligence and understanding:

O Prophet! Exhort the believers to fight. If there be of you twenty steadfast they shall overcome two hundred, and if there be of you a hundred (steadfast) they shall overcome a thousand of those who disbelieve, because they (the disbelievers) are a folk without intelligence (8:65)

Other verses of violence may be found here.

Remember that the Quran says that not all men are equal according to Islam.  This even applies to Muslims with regard to their aggressiveness toward unbelievers.  Those who kill or are killed on behalf of Islam are more pleasing to Allah:

Not equal are those of the believers who sit at home... and those who strive hard and fight in the Cause of Allah with their wealth and lives" (4:95)