In this thesis, we introduce the basics of blockchain systems, cryptosystems, and post-quantum cryptography. We discuss how to upgrade and make digital signatures in the cryptocurrency Bitcoin more robust against quantum attacks. In addition, we propose the hash-based post-quantum digital signature Wintersnitz OTS, and SPHINCS+, and describe their application in post-quantum blockchains. We came up with two proposals to upgrade the cryptocurrency Bitcoin. The first proposal is to add a post-quantum signature to the Bitcoin ECDSA public key. The second proposal is to iterate the Bitcoin ECDSA public key 256 times, where each of these keys can be used to make a Bitcoin address. In addition, we also discuss the potential vulnerabilities of our two proposals.