This is not criticism, I would rather ask some questions to get clarity on the whole concept.
1. What stops other people to use your QR Code? { Or is this randomly created everytime you login? }
2. Do you retrieve a single QR Code from a central online server to enable you to login. {External site?}
3. Is this for login into web sites on the internet, or for a alternative authentication for your notebook etc...
4. How is this protected? {Malware / Trojan Horse} The QR code send, could be intercepted by a hacker. {spoofed}
It's a viable option for lazy people, if it can be secured, but I would not trust a external 3rd party to have access to all my QR codes for every site I access.
Or is this a App running on each site, that generate a QR code as a alternative to the conventional username and password?
1. QR codes are random for every login. QR code contains "challenge". There is an private key in your device (a smartphone) stored. The private key is generated (randomly) at the first time you use the QR Login for particular site. Every site has different key.
2. The QR code (challenge) is generated by javascript using secure random number generator
3. It is for login into the web sites, similar service as OpenID, Facebook login, Google login, etc.
4. There is a private key and the corresponding public key. The private key is stored in your device and should never leave it (unless you explicitly want). The application (downloaded from the qrlogin site as html+js) uses the private key to sign challenge. Then the signature is transfered to the "auth" site an then through the redirect to the service provider. The service provider can calculate the public key from the signature or it can use standard OAuth 2.0 token exchange to retrieve the public key (Public key is then transformed to the bitcoin address, which can be used as an unique user's ID). The service provider can use both ways to receive the public key to ensure, that signer posses the correct private key.
You can object, that qrlogin site is in my possession, so I can modify it to track and store all private keys for evil purposes. But you still have the option to run own site, because source code of qrlogin is open source under the MIT licence hosted on the GitHub. See the link above (in OP).