The post-quantum signature schemes standardized by the National Institute of Standards and Technology (NIST) to date fall into two cryptographic families: lattice-based and hash-based schemes. Both rely on mathematical problems that no known quantum algorithm can efficiently solve.
While both families are also considered safe against classical attacks, hash-based digital signatures are a more conservative choice, as they rely only on the security properties of hash functions, which are already fundamental to Bitcoin design. For this reason, there is rough consensus on preferring hash-based post-quantum cryptography for Bitcoin, at least as a first step. However, the hash-based scheme standardized by NIST (SLH-DSA) produces signatures of approximately 8 kilobytes. A current ECC signature is 64 bytes, making this a roughly 125-fold increase in size.
If you simply replaced Bitcoin's current signatures with SLH-DSA, the network's throughput would drop from roughly six transactions per second to 0.3 — one transaction every three seconds, for the entire world. This is why the migration cannot be treated as a software update. The NIST standards were designed for general-purpose cryptography, not for blockchains with hard constraints on block space.
Still, Bitcoin developers are working on optimizations that reduce this penalty. Blockstream's SHRINCS proposal, for example, achieves a 324-byte signature, which is dramatically smaller than the NIST baseline, but still roughly five times larger than what Bitcoin uses today.
In general, there is no “perfect” replacement for ECC digital signatures: post-quantum digital signatures introduce tradeoffs between size, signing and verification speed, suitability for aggregation, and the strength of the underlying security assumptions.