The United States Constitution sets forth the qualifications necessary for the legislative branch of the federal government, but any qualifications for state legislatures would be a matter of each state's own constitution. As it stands, for the House, one must be 25 years of age, a citizen of at least seven years, and a resident of the state one seeks to represent. For the Senate, one must be 30 years of age, a citizen for 9 years, and inhabit the state one seeks to represent. I assume that most states have similar requirements. This leads to the second inquiry, as to whether there should be some additional qualifications required.
There is certainly bound to be a difference of opinion on this matter, but I do not think any additional qualifications would lead to good governance and democracy. Let's look at a few reasons for this. The kinds of qualifications we would require would have to be objective ones and very general ones, for example, a college degree, a minimum IQ, or a license to practice law. A college degree does not automatically confer wisdom or intelligence upon a person, any more than the Wizard of Oz could provide the Scarecrow with a brain. If we required a college degree, I cannot see that there would be any meaningful improvement in the makeup of any legislature. There are plenty of non-degreed people who are hardworking, intelligent, and have common sense, people who could do the work ably. The IQ test, most people agree, is culturally biased and is able to test just a few forms of intelligence, those valued by schools, but by no means able to identify qualities such as creativity or perseverance. I am acquainted with many people with IQs lower than my own whom I consider to be wonderfully intelligent, just in ways I am not. We would not want to eliminate such people from the pool. In a democracy, we do not want to make a certain sum of assets to be a requirement, since that would tip the scales even more toward the wealthy than they are right now. If someone were to find some sort of litmus test, an objective means of assessing what makes for a good legislator, I would be for it, but as it stands right now, I can see no such means of judging.