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Regarding point 1: I should say that I'm not an expert in Quantum Computing, but reading the referenced paper leaves me unconvinced that such an algorithm exists in general. In the paper they show that they can simulate phi^4 efficiently and with arbitrary small discretisation error. My point regarding the graph isomorphism in this case is as follows: In order to carry out the discretisation, they employ a d-dimensional lattice and additionally introduce a discrete number of Q-bits per lattice site. Then they require to be able to evolve the state according to some time dependent hamiltonian (with interactions adiabatically switched on and off). All proposed realistic quantum computers only allow for a limited operator set of primitive operations, dictated by the physical geometry of the implementation (1d lattice of atoms in a trap etc.). My point was that more likely than not you will always be able to come up with theories for which a mapping respecting these physical constraints is hard (you won't easily be able to simulate a 3d lattice with multiple q-bits per lattice site on a 2-d lattice of q-bits). Also the article has to restrict itself to the case of massive particles and as you know lattice simulation of fermions is also a problem.

Point 2 & 3: You are right of course, ultimately this is a question of what techniques are useful. My comment was mostly aimed at the situation where people start to discuss the philosophy of QM. There I find that QFT clarifies the situation more than any philosophical elaboration on "measurement" and things like that do.




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