This isn’t specific to Harvard but I figured this thread has lots of traffic, so…
It would be as a sophomore. Nobody I’ve met has done it at my school but I want to because I’ve heard of students doing it elsewhere? Who should I speak to if I’m interested?
My son took several grad level courses at Yale during his junior and senior years in conjunction with his thesis. He had to jump through a bunch of hoops to do so, including obtaining the permission of his advisor, the instructor and the registrar. I would speak with your advisor at your current college. In all likelihood though, you probably won’t be allowed to do it as a sophomore, unless there are extenuating circumstances, such you’ve maxed out of the undergrad level courses.
Speak to an advisor, or possibly a professor who knows your work, or the professor of the class you want to take. Colleges vary a great deal on access to grad level classes so you need to check it out at your particular school. There are schools that would allow this for a sophomore, yes.
Check prerequisites listed as well, though they can sometimes be waived.
@compmon speaks truth. When my son wanted to take graduate level physics classes as a junior and senior at his college, he simply went through the departmental protocols. Good luck!
This will vary from institution to institution. At my kids’ college, graduate courses were very open to undergraduates with the instructor’s permission. The undergrads just had to show that they were prepared to take the class. My daughter took a graduate class in English Lit as a first-year student. It was a mixed experience: she learned that she disliked taking classes with grad students, because they were so focused on whatever they were doing and so little interested in anyone else’s work. But she became friends with one of the students in the class who became an informal mentor and wound up as her BA thesis preceptor a few years later.
Many years ago, I took a grad class as a sophomore, without remotely having maxed out on undergraduate classes in that field. Instead of registering for the course itself, I was registered for independent study with the professor teaching it, and my independent study consisted of taking the course. The teacher was my advisor, so that made things easier.
If you are interested more in visiting the cutting edge of your field than in having a course with a graduate-level number on your transcript, it’s usually easy to get on your department’s listserve and start going to the events where people present their PhD theses and other research or people being considered for faculty appointments give talks. You can often learn a lot there, make friends with graduate students and faculty, and get free food. And establish your bona fides if you decide you do want to ask permission to register for a graduate course.