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  Can quantum computing be simulated by an optical network?

+ 5 like - 0 dislike

On page 43 of http://arnold-neumaier.at/ms/optslides.pdf, we read

8. Simulating quantum mechanics

The simulation of quantum computing by classical fields is essentially achieved by using an optical network in which each quantum level is modelled by a corresponding mode of the electromagnetic field.

The linearity of the Maxwell equations then directly translates into the superposition principle for pure quantum states.

Thus it is possible to simulate arbitrary quantum systems which have a finite number of levels by the Maxwell equations, and hence by a classical model.

Therefore we shall look a little more closely into the reasons for this ability to simulate quantum systems.

...some explanations about second order coherence theory of the Maxwell equations...

As a consequence, it is possible (at least in principle) to simulate with classical electromagnetic waves and suitable classical linear optical networks any quantum system that can be embedded into the single photon quantum system.

Since all Hilbert spaces arising in applications of quantum physics are separable, they have a countable basis, and can be embedded into the single photon quantum system, at least in principle.

Thus it appears that, all quantum systems can be simulated by classical electromagnetic waves!

Of course, a practical realization may be difficult.


How is this optical network supposed to work? Does it really work? I don't see how the fact that all separable Hilbert spaces are isomorphic to each other would allow me to conclude that the time evolution of a single photon by the Schrödinger equation will be able to simulate the time evolution of an arbirary quantum system by the Schrödinger equation. But "optical network" sounds very concrete to me, so maybe some simple examples of how to simulate the time evolution of a two photon quantum systems by them could be help me?

asked Dec 16, 2014 in Theoretical Physics by Thomas Klimpel (280 points) [ no revision ]
I suppose @ArnoldNeumaier (who wrote the lecture notes) could answer this question?

In http://arnold-neumaier.at/ms/hidden.pdf @ArnoldNeumaier writes: "With more beam splitters, through which several narrowly spaced beams are passed, one can produce a cascade of more complex tensor product states. Indeed, Reck et al. [23] showed that (i) any quantum system with only finitely many degrees of freedom can be simulated by a collection of spatially entangled beams; (ii) in the simulated system, there is for any Hermitian operator H an experiment measuring H; (iii) for every unitary operator S, there is an optical arrangement in the simulated system realizing this transformation, assuming lossless beam splitters."

Neither that article, nor its reference [23] can be found in the reference section of the presentation which is quoted in the question. So the answer to the question seems to be "yes!", but one would have to read (and understand) "some" references proving this to be sure.

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