The quantum resistance of zk-SNARKs, a zero-knowledge proof protocol, is a critical concern in post-quantum cryptography. zk-SNARKs rely on elliptic curve cryptography (ECC) and pairing-based cryptography, which are vulnerable to quantum attacks, particularly Shor's algorithm, capable of breaking ECC in polynomial time. To achieve quantum resistance, zk-SNARKs could adopt post-quantum cryptographic primitives, such as lattice-based schemes or hash-based signatures, which are believed to withstand quantum computing threats. However, integrating these primitives increases computational overhead, impacting efficiency. Current research explores quantum-resistant zk-SNARK constructions, like STARKs, which use hash functions and are inherently quantum-safe. While promising, these alternatives require further optimization to match zk-SNARKs' efficiency, ensuring scalability for blockchain and privacy applications in a quantum future.