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Zero-knowledge proof systems are now deployed widely in production cryptographic protocols, yet many rely on assumptions (discrete logarithms, pairings, or structured reference strings) that a fault-tolerant quantum computer would break via Shor's algorithm. This systematization of knowledge (SoK) presents a four-layer decomposition (L1 to L4) that separates where quantum risk enters a proof system: arithmetization, polynomial commitment, protocol logic, and non-interactive compilation. Using a two-axis taxonomy that crosses cryptographic impact (structural break, modularly replaceable break, or quantitative degradation) with deployment migration feasibility, we classify the major proof-system families, derive a modularity test for evaluating upgrade paths, and introduce collect now, forge later (CNFL) as the proof-system analogue of harvest-now-decrypt-later. Case studies of Zcash, zkSync Era, and StarkNet show that practical post-quantum outcomes depend on deployment governance and upgrade architecture as much as on cryptographic primitives. The scope covers IOP/PCS-based and algebraic proof families; MPC-in-the-Head constructions are excluded.
