Class groups of number fields have been studied since the time of Gauss, and in modern times have been used in applications such as integer factorization and public-key cryptography. Computing class groups and a system of fundamental units is a challenging problem for classical computers, but can be solved by a quantum computer in polynomial time. One shortcoming of both the fastest known algorithm for computing these invariants classically and the quantum algorithms is that the output is only correct under the assumption of the generalized Riemann hypothesis. This is fine for some cryptographic applications, but in computational number theory applications such as tabulating class groups for testing unproved conjectures and solving Diophantine equations require unconditional results. In this talk, I will discuss some of these applications where unconditional results are required, as well as the methods used to compute class groups and fundamental units unconditionally.