> They have poor space/bandwidth usage properties, which is one reason
> why Bitcoin doesn't use them today, but as far as I know the same is
> so for all post-QC schemes.
>
I believe post-QC schemes based on Regev's LWE assumption are getting
competitive with more traditional schemes. A paper from 2010 says they were
able to get to around the same as large RSA key sizes (2048 bits), which is
much worse than ECC but not entirely infeasible. Especially given that
barring some breakthrough, by the time QC is a real problem we'll have
gigabit wifi and 32 core devices with a terabyte of storage embedded in our
hands :)
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