This paper explores the implications of quantum computing on the security of payment systems and examines the development and application of post-quantum cryptographic (PQC) methods to counter these emerging threats. We start by outlining the fundamentals of quantum computing, including quantum key distribution (QKD) and notable quantum algorithms like Shor's and Grover's, which pose challenges to conventional cryptographic techniques. We then analyze the vulnerabilities of current payment systems—mobile payments, e-payments, and blockchain—to quantum attacks. We then explore various post-quantum cryptographic (PQC) techniques, including hash-based, code-based, lattice-based, and multivariate quadratic equation cryptography. Each approach is thoroughly analyzed, highlighting its strengths, implementation challenges, and the trade-offs required to protect against quantum attacks. Finally, we present the application of these PQC methods in securing mobile payments and blockchain systems, demonstrating significant advancements and ongoing efforts to future-proof these technologies.