Focusing on the Bayesian part, if I understand correctly you do this on measurements though, so it’s kind of semiclassical? Basically you measure one quantity, get an outcome p∈[0,1], then normalise and use that as your token plus evolve the system with that operator. This would have to be an ensemble operation on prepared qubits in a real experiment since the measured quantities aren’t orthogonal. I guess I could try and check whether we recover your update formula for the case of discrete measurements, but I’m not sure how to go about it off the top of my head.
Read—thanks! Not digested in detail yet but enough to get the general outline. I didn’t remember your name so was pleasantly surprised to realise this was a “sequel” to Transformers represent belief state geometry in their residual streams.
Focusing on the Bayesian part, if I understand correctly you do this on measurements though, so it’s kind of semiclassical? Basically you measure one quantity, get an outcome p∈[0,1], then normalise and use that as your token plus evolve the system with that operator. This would have to be an ensemble operation on prepared qubits in a real experiment since the measured quantities aren’t orthogonal. I guess I could try and check whether we recover your update formula for the case of discrete measurements, but I’m not sure how to go about it off the top of my head.