How do you implement cryptography for top secret information exchange foreseeing a post quantum scenario soon and what types of algorithms do you use? What about network security, are VPN keys are more secure?

VPNs have many known vulnerabilities, and TunnelVision pretty much rendered most (if not all) VPNs vulnerable.  I'd use a Zero Trust architecture like a Software Defined Perimeter (SDP), especially one that is encrypted end-to-end at Layer 2. At NVIS AI, we do this, and we've also partnered recently with a company on the bleeding edge of cryptology, using a dynamic manifold projection system, ensuring that each cryptographic nonce public key is unique and non-reusable in replay attacks.  Connect with me if you wish to learn more.

Agree with a few of the comments made below.  Move to a Zero Trust framework.  VPNs, because they place the user/device directly on the network, are security challenges.  Better to broker access with modern ZTNA solutions.  You gain multiple factors to determine access policies and most critically, visibility.  

Zero trust architecture can be a good option  

A burning platform, money, and a strong partnership of industry, academia, and government. And to the second questions Zero Trust appears to be the rising model to replace the traditional huge pipe VPN. 

I think we need to be patient and wait for approved NIST algorithms and not rush ahead.