using Post-quantum asymmetric ciphers instead of RSA We can't trust RSA to encrypt our Emails so what is best post-quantum cryptography system as alternative for RSA which provide good security and don't be breakable? because McEliece cryptosystem looks break with 2^60.55 bit operations..
My impression is that there is no production ready post quantum scheme ATM.

NTRU seems to be decent (complete spec,  reasonable parameter-sizes and performance), but I think it's patented. No idea about the licensing terms.

But whatever scheme you choose, don't use it instead of a conventional scheme(RSA, DH, ECDH) but in addition to a conventional scheme. If you use a good construction, your protocol will be as secure as the stronger of the schemes.