Are zero-knowledge proofs quantum-resistant?
There is no generic answer to this question. Zero-knowledge proof (ZKP) systems can be post-quantum secure, but they need not be. It all depends on the cryptography on which the security of the ZKP rests.
There exist ZKPs that only use collision-resistant hash functions and hence are plausibly post-quantum secure. The most well-known examples are those using the FRI protocol: Aurora, Fractal, and zk-Starks [*].
Other notable ZKPs like Bulletproofs or Groth16 rely on cryptographic assumptions (e.g. hardness of discrete log in elliptic curve groups) for which it is known they would be vulnerable to quantum attacks, if such attacks became practical.
[*] "zk-STARK" refers both to a security definition and to a particular family of FRI-based proof systems that satisfies it. The security definition does not mention post-quantum security, so it is the latter that is meant here.