No post-quantum roadmap, proposal or research programme for TON was found at the time of writing. source
1 Signature scheme 0/10, weighted 30%
Band 0: Classical signatures only on mainnet, with nothing post-quantum protecting live funds. Short-lived devnets and one-off benchmarks sit here: they demonstrate research rather than something a user can hold keys on.
TON wallets verify Ed25519 signatures, which are broken by Shor's algorithm. Nothing post-quantum protects TON on mainnet today. source