Blockchain technology finds widespread application across various fields due to its key features such as immutability, reduced costs, decentralization, and transparency. The security of blockchain relies on elements like hashing, digital signatures, and cryptography. However, the emergence of quantum computers and supporting algorithms poses a threat to blockchain security. These quantum algorithms pose a significant threat to both public-key cryptography and hash functions, compelling the redesign of blockchain architectures. This paper investigates the status quo of the post-quantum, quantum-safe, or quantum-resistant cryptosystems within the framework of blockchain. This study starts with a fundamental overview of both blockchain and quantum computing, examining their reciprocal influence and evolution. Subsequently, a comprehensive literature review is conducted focusing on Post-Quantum Distributed Ledger Technology (PQDLT). This research emphasizes the practical implementation of these protocols and algorithms providing extensive comparisons of characteristics and performance. This work will help to foster further research at the intersection of post-quantum cryptography and blockchain systems and give prospective directions for future PQDLT researchers and developers.
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