Comment by MrRadar

Only the asymmetric portion of the cryptography (which is only used in the handshake) will need to use PQC algorithms. Symmetric crypto algorithms (AES/ChaCha20/SHA-*), which are used after the handshake, are not as badly affected by quantum computing so they're not being replaced in the immediate term. I'm pretty sure that general purpose CPUs do not have hardware acceleration for the asymmetric crypto anyways.