So, quantum computers will break (discover) the secret relationship between public/private key-pair for public encryption algorithm, and not brute force solve the private key bits?

Depending on the key management scheme that is true, but symmetric encryption does not stipulate that it is a single use. While the public key of a key-pair may be persistent, in many cases, it is used for exchanging the symmetric key. So, doesn’t the adversary have to break both the private key and the symmetric key…

Why only Public Encryptions (RSA, ECC, etc.)? Why are Symmetric Key Encryption Algorithms (AES, Simon, etc.) not being warned? I don’t understand how Quantum Computer is only a threat to breaking Public key. Or is NSA saying that any key that is publicly sent in plain text will be broken, and other private-symmetric…