In the United States, degree-granting university programs must generally be approved by an accrediting authority authorized by the Council for Higher Education Accreditation, which sets standards that include access to owned libraries, a minimum number of faculty with terminal degrees, and so forth. As such, it is essentially impossible for a home school to be accredited to grant a university degree. In other words, homeschooling does not exist in higher education.
Homeschooling and education in an Ivy League institution are not, generally, comparable. They represent different phases of the educational experience.
Homeschooling occurs, almost exclusively, at the K–12 level, or kindergarten through 12th grade. It terminates with the awarding of a high school diploma or its equivalent. This is called primary (K–8) and secondary (9–12) education.
The eight Ivy League institutions in the United States are universities, meaning their course of study is geared toward the awarding of a bachelor's degree or higher. Admission requires a high school diploma or its equivalent. This is called tertiary education.
A homeschool student, upon completing a course of study leading to a high school diploma or its equivalent, could advance to enrollment in a university program, potentially including one at an Ivy League University (Harvard, Yale, Columbia, Cornell, Pennsylvania, Dartmouth, Princeton, or Brown).