The answer
No. Some STARK systems rely on hash-based assumptions while many SNARK constructions rely on pairing-based cryptography.
What to do next
Check the particular proof system rather than assuming all zero-knowledge means quantum-safe.
NIST post-quantum standards
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Trezor hardware wallet
A current-generation hardware wallet for managing keys; it does not make Bitcoin or Ethereum quantum-resistant or resolve a future protocol migration.
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