As an important strategic resource for safeguarding national information security and the healthy development of digital economy, cryptography is the cornerstone of protecting the security of critical infrastructure, government affairs data, financial transactions, and other fields. Currently, the rapid development of quantum computing poses a disruptive challenge to the existing public-key cryptosystems and a fatal threat to the global information security landscape, making research on post-quantum public-key cryptography (PQC) both necessary and urgent. This study expounds on the current development status of five mainstream technical routes in PQC: lattice-based, code-based, hash-based signature, multivariate, and isogeny-based cryptography, and finds that each of these five routes has its own focus yet is in a stage of continuous iteration and verification. The study identifies the existing issues of the development of PQC including performance bottlenecks, insufficient ecological compatibility, and difficulties in security evaluation. Meanwhile, the development of PQC in China is confronted with challenges such as a weak foundation in theoretical research, lagging standards formulation, an imperfect industrial ecosystem, and a shortage of professional talents. To safeguard China's information security in the quantum computing era, we propose the following suggestions: strengthening basic research to enhance the independent innovation capability of the industry; accelerating standards formulation to boost international discourse power; improving the industrial ecosystem to promote the phased migration to PQC; intensifying talent cultivation to build a professional talent team. These measures are expected to help China construct a multi-dimensional and highly resilient digital security ecosystem, and drive the leap-forward development of China's cyberspace security capability from classical to quantum security.