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This study examines the convergence of rapid Central Bank Digital Currency adoption and the growing threat that quantum computing poses to existing cryptographic systems. As digital sovereign currencies expand globally, with many economies actively exploring or piloting CBDCs, the vulnerability of classical public key cryptography to quantum attacks creates an urgent need for quantum resistant solutions. The research responds to this challenge by developing an evaluation framework focused on secure and interoperable cross border CBDC systems in a post quantum environment. Using desk based computational analysis and simulation methods suitable for remote researchers, the study evaluates lattice based algorithms standardized by the National Institute of Standards and Technology, specifically ML KEM for key encapsulation and ML DSA for digital signatures. The analysis confirms strong quantum resistance against known quantum algorithms, effectively removing harvest now decrypt later risks for future transactions. Interoperability assessments show that ISO 20022 with cryptographic abstraction is well suited for retail CBDC systems, while bridge based architectures such as BIS mBridge are more effective for wholesale settlements. Performance testing on thousands of simulated transactions indicates that post quantum protocols are feasible for wholesale use but introduce significant computational and bandwidth overheads that limit immediate retail scalability without hardware acceleration. Overall, the findings support a phased migration strategy that combines classical and post quantum cryptography in the near term, guided by cryptographic agility. The study provides practical insights for central banks seeking to balance security, efficiency, and cross border compatibility in an evolving quantum threat landscape.