There is no concrete post-quantum signature scheme for Bitcoin today.
But over the last year Blockstream Research has been working on exactly this. Director Jonas Nick lays out the proposal: OP_CHECKSHRINCS, a hash-based signature opcode for post-quantum Bitcoin.
SHRINCS reaches up to 3 TPS on the compact path. 580-byte signatures from a dedicated signing device. A stateless fallback always available.
Already demonstrated on the @Liquid Network . The C++ implementation, Simplicity verifier, and draft spec are all on GitHub.

SHRINCS reaches up to 3 TPS on the compact path. 580-byte signatures from a dedicated signing device. A stateless fallback always available.
Already demonstrated on the @Liquid Network . The C++ implementation, Simplicity verifier, and draft spec are all on GitHub.

Blockstream
OP_CHECKSHRINCS: A Hash-Based Signature Opcode for Post-Quantum Bitcoin
OP_CHECKSHRINCS is a proposed Bitcoin opcode for post-quantum signatures whose security rests on SHA-256, the hash function Bitcoin already uses.