What to tell professors to persuade them to let a pre-college student work with them
You might want to try aiming a bit lower, such as those schools that don't have graduate programs.
At these types of places, where it is difficult for professors to even get any students (let alone the top undergraduates) involved in their research program, some professors may actually want to bring on board a high school / junior high student, if for no other reason than to impress some administrative type (dean, department head, etc.) that this particular professor is engaging in some form of outreach (you know, to help spread the word about the program to get students excited about going to school there).
Just send an email to someone involved in the area you are interested in, attach a CV *, and briefly explain your aims. If the school is close by to you, you could also arrange an in-person visit. For the in-person visit route, if you are indeed interested in attending the school for your undergraduate degree, I suggest you indicate this fact when you attempt to setup the meeting.
Good luck.
* In your CV, you can briefly summarize your self-study progress and plans, your research interests, any projects you've undertaken on your own, and the like, if you don't have any formal educational training in the research area of interest, any papers published, etc.
I think the biggest obstacle you face is convincing a professor that you are a good investment of his/her time. Quantum computing is a tough subject even for advanced undergraduates and graduate students, so I think the default response for any professor to an 8th grader would be one of skepticism that you have the basic skills to be an asset to his/her research. In other words, will you be able to contribute enough to a project to justify the time and effort the professor will invest in you?
One slightly unconventional approach would be to try lower on the academic totem pole. Do the professors you identified have any graduate or undergraduate students? Do they work in a department that has an academic coordinator? These people may be more responsive to emails, more willing to talk with you, or better abled to point you to other people (key word is may). If you can impress a professor's graduate student with your initiative, skills, etc., this could be a way to get your foot in the door.
I actually did roughly what you're after back when I was in high school. I ended up working in a chemistry lab at the local university from my sophomore year through the summer after my senior year---and got paid pretty well to boot! While not the same field as what you're after, hopefully you can learn from some of my experiences. As most of the other answers are from a professor's perspective, I'll try to give my recollections from the high school point of view (rather than my thoughts as a current PhD candidate).
- I found this job via networking with a family friend that was working as a post-doc in a different lab (same department). The "hiring process" consisted of meeting with the professor for a 45 minute talk before being welcomed aboard and given a tour of the lab. As with many jobs, networking beats cold-calling almost every time. Even if it's not your "dream research group," see if you can't get your foot in the door by seeing if anyone is hiring for "Research Assistants" or "Laboratory Technicians." Large research groups will sometimes even have listings for such things.
- Try to strike a balance and not oversell your abilities. As you mention, you have a large number of accomplishments, especially compared to your peers. Keep in mind, though, that you are looking to join a research group that will have people with years of formal schooling and research experience. As an analogy, you have probably figured out that (some) of your teachers don't take it kindly when you prove them wrong in front of the class; a similar level of tact is useful here as well. You're asking to join their research group!
- When you reach out to professors and hopefully meet with them, try to sell why you would be beneficial to their group. In my case, the first year or so I spent in the lab was very much laboratory tech / assistant work---cleaning glassware, updating MSDS sheets, organizing the stockroom, updating the website, etc. However, I was proving myself to be a known and helpful quantity and learning everything I could about all of the ongoing research projects. This slowly transitioned into helping perform experiments and eventually designing and running experiments that were helpful for the research that others had going on. In comparison, don't necessarily be expected to be "handed to keys" to whatever multi-million dollar machines are around on the first day.
- Learn everything you can. There's an amazing amount of information you can pick up by attending lab meetings or asking different researchers about what they're working on (and especially where to learn more). Even if you're doing "grunt work," make the most of it!
The professor in charge of the research group ended up writing me an awesome letter of recommendation when I was applying for university as well as writing letters of introduction to several people at the university I chose. This helped me start working in a lab on the first day of my freshman year in a new city on the opposite side of the country, rather than being just another face in a large lecture hall. In addition to keeping on top of my own coursework, the experience of working in a research lab was probably the most productive thing I did with my time in high school.