Public-key cryptosystems without poly-time quantum attacks It's well-known that Shor's algorithm can solve integer factorization, discrete logarithm and discrete log over elliptic curves in cubic time.  This implies that cryptosystems like RSA, ElGamal, and Elliptic Curve Diffie-Hellman (ECDH) are vulnerable to quantum computers.

Are there any existing public-key cryptosystem that are NOT known to have a polynomial-time quantum attack?

This question was inspired by this blog post.
McEliece

NTRU

Multivariate

If you mean "syntactically public key" instead of "implies the existence of secure key agreement",

then there is also hash-based signatures.