Is the following protocol perfect zero knowledge or computational zero knowledge?
This is Blum's protocol for Hamiltonicity. The answer to your question depends on the commitments. There are two possibilities:


The commitments are perfectly hiding: in this case, the proof is perfect zero knowledge, but is only an argument (meaning that soundness is computational, and so only holds against a polynomial-time cheating prover).
The commitments are perfectly binding: in this case, the proof is only computational zero knowledge, but is a proof (meaning that soundness is unconditional).


Note that no commitment scheme can be both perfectly binding and hiding. In addition, the class of perfect zero knowledge proofs (unconditional soundness) is contained in $AM \cap co-AM$ and so is very unlikely to contain an $NP$-complete problem.