Quantum-safe security platforms must operate at cloud scale to protect modern distributed systems, yet existing quantum cryptography tools are designed as standalone utilities with no consideration for horizontal scaling, multi-tenancy, or container orchestration. We present the architecture of QCrypton, a stateless cloud-native quantum security platform that combines AI threat detection, post-quantum cryptography, and cryptographic code auditing in a fully database-backed, horizontally-scalable design. Key contributions include: (1) a stateless authentication architecture combining JWT sessions with API key fallback and distributed token revocation via hash-based blocklists; (2) domain-verified multi-tenant provisioning with wildcard email matching and per-user permission overrides computed at request time using set algebra; (3) idempotent bootstrap enabling safe replica restart without coordination or distributed locks; and (4) Kubernetes-native deployment with defense-in-depth security across application and infrastructure layers. The platform supports three deployment modes (CLI, SDK, Server) from a single codebase with consistent security guarantees. We evaluate the architecture under horizontal scaling scenarios, demonstrating linear throughput scaling to 10 replicas with 96% efficiency, sub-4ms authentication latency, and 99.97% availability over a 30-day production evaluation with zero dropped requests during rolling updates.