Noob alert! Can we run quantum safe algorithms on commercial devices (like phones, laptops, etc)? I've seen some messaging apps and vpn providers marketing themselves as quantum-proof. How likely is that all these claims are bogus for marketing (imo, very)?
Post-quantum cryptography addresses the problem of developing public-schemes whose underlying assumptions are (believed to be) quantum resilient, i.e., the assumptions hold even in the presence of quantum computers.
There are many proposals for the underlying assumption and this leads to several branches like lattice-based cryptography, multivariate cryptography, code-based cryptography, hash-based cryptography or isogeny-based cryptography, among others. The cool thing about these assumptions and techniques is that they can be implemented in classical computers. In fact, many of these are already implemented and there is a competition driven by NIST to standardize some of these.
So, yes, these primitives are usable nowadays. Maybe these companies use a scheme of this nature, that may be the case.
Yes you can.
Post-quantum algorithms do not require a quantum computer to run. In fact, symmetric ciphers are quantum-proof, i.e. remains secure even quantum computers exsit. Many lattice-based cryptographic schemes (including, for example, some Fully homomorphic encryption schemes) have been implemented. They can be run on a normal PC or laptop.