I'm thinking that if the computation is actually the time evolution of a suitably structured time crystal, one which by definition is traversing/existing in its

I'm thinking that if the computation is actually the time evolution of a suitably structured time crystal, one which by definition is traversing/existing in its own ground state. Then either no computation can be done, or it must not require any energy. Reading out the answer must AFAIU (which is very superficial) however take energy, not unlikely to be exactly proportional to any part of the answer not read / erased, and thus closing the apparent loophole, and making you still being right :)