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- Regarding your first point, I'm pretty sure this is untrue without further qualifications (which I understand that you don't mention because this a forum and

- Regarding your first point, I'm pretty sure this is untrue without further qualifications (which I understand that you don't mention because this a forum and not a scientific setting). In any case any such mapping would most likely be NP hard (assuming your quantum computer has q-bits that can only interact according to some graph, I would expect this to reduce to a graph isomorphism problem). - You would deal with that by writing down a path integral (see for example Feynman's PhD thesis) (btw. particle creation is not possible in non-relativistic QM). The tricky thing is that of course "closing the slit" is a very tricky thing to model in a path integral, but the situations "slit closed" and "slit open" are rather straightforward. In any case even without any computation what is clear from the path integral perspective is that nothing mysterious is going on: You are supposed to sum over all possible histories of the particle passing through the slit and hitting the screen, weighted by e^iS. If there is some temporal variability in the position of the slit, this just results in a huge complication in the integral to be carried out (if you model closing the slit by a time dependent potential let's say). The path integral is fundamentally a very good way of thinking about this, because it generalises to much more complicated settings (gauge theory etc.), whereas there really is nothing fundamental about measuring, you just happen to drastically and in a temporally complicated way change the background your quantum fields are propagating in. - On the contrary, basically QFT is the only way to deal with mixed states in a principled way. For scattering you typically start out with the assumption that things are in pure states at t=-infty and t=+infty, but in between the whole point of introducing quantum fields is to keep track of how things are spatially (plus gauge degrees of freedom etc.) "mixed". To be more specific QM is just a D=1,0 QFT, with 1 time dimension and (zero-dimensional) points as spatial dimensions. A mixed state rho is nothing more than a general quantum field on these discrete points.

krastanov 7y ago
On point 1: I did not get your argument about NP hardness and equivalence to graph isomorphism. On the contrary, algorithms for efficiently simulating non-trivial QFTs on a non-relativistic quantum computers exist: https://arxiv.org/abs/1111.3633 https://arxiv.org/abs/1111.3633 Point 2: If "there is nothing fundamental about measuring" in the QFT case, I do not see what is so special about the QM case (you just take a partial trace over the "environment"). I (admittedly with humility as I am not as well versed in QFT) really do not see how your answer is any different from this (and I do not see how the path integral gives you anything new for this particular problem, albeit being a beautiful formalism). Point 3: QM has developed a lot of tools to deal with Marcovian and Non-marcovian non-unitary dynamics (the whole zoo of master equations available in it). Of course QFT can deal with density matrices if QM already can do that, but the sophistication of the toolkit used for that purpose in QM seems yet unsurpassed to me. And to your last point about creation of particles: Second quantization is already available in non-relativistic QM, so there is nothing weird about an a^dagger*b Hamiltonian in QM (I use it all the time for cavity-qubit interactions) - so, yes, you can not deal with the creation of arbitrary particles in QM, but you can still easily work with some restricted modes of a field, without involving QFT.
- orbifold 7y ago
  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.

krastanov 7y ago

On point 1: I did not get your argument about NP hardness and equivalence to graph isomorphism. On the contrary, algorithms for efficiently simulating non-trivial QFTs on a non-relativistic quantum computers exist: https://arxiv.org/abs/1111.3633 https://arxiv.org/abs/1111.3633 Point 2: If "there is nothing fundamental about measuring" in the QFT case, I do not see what is so special about the QM case (you just take a partial trace over the "environment"). I (admittedly with humility as I am not as well versed in QFT) really do not see how your answer is any different from this (and I do not see how the path integral gives you anything new for this particular problem, albeit being a beautiful formalism). Point 3: QM has developed a lot of tools to deal with Marcovian and Non-marcovian non-unitary dynamics (the whole zoo of master equations available in it). Of course QFT can deal with density matrices if QM already can do that, but the sophistication of the toolkit used for that purpose in QM seems yet unsurpassed to me. And to your last point about creation of particles: Second quantization is already available in non-relativistic QM, so there is nothing weird about an a^dagger*b Hamiltonian in QM (I use it all the time for cavity-qubit interactions) - so, yes, you can not deal with the creation of arbitrary particles in QM, but you can still easily work with some restricted modes of a field, without involving QFT.

orbifold 7y ago
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.