I realize this is a minority opinion, and goes against all theories of how quantum computing works, but I just cannot believe that nature will allow us to reliably compute with amplitudes as small as 2^-256. I still suspect something will break down as we approach and move below the planck scale.
Fun fact: the Planck mass is about 22 micrograms, about the amount of Vitamin D in a typical multivitamin supplement, and the corresponding derived Planck momentum is 6.5 kg m/s, which is around how hard a child kicks a soccer ball. Nothing inherently special or limiting about these.