We need to prevent non-citizens from voting

Only citizens should vote in national elections. Since that's already the law, the question becomes how to prevent non-citizens from voting.

The answer, according to the Brennan Center for Justice has been easy detection and harsh penalties.

Voter lists are regularly maintained to detect non-citizens. So any non-citizen trying to stay "beneath the radar", or hoping to become a citizen, would give up any chance by registering to vote or actually voting. All for the highest possible payoff of adding a single vote to the tally.

Do they do it anyway?

That argument, of course, does not guarantee that a non-citizen wouldn't vote. What matters is - do they actually do it? The simple answer is "No."

In Utah, an audit of the state's 2 million registered voters verified that every single registered voter was a U.S. citizen - except for 1 non-citizen. Though registered, the non-citizen had never voted.

Searches for noncitizen voters by other states have yielded similar results, according to the Cato Institute.

For more, read the New York Times article and this Brennan Center for Justice report.