Quantcast
  • Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.

News

PO is now at the Physics Department of Bielefeld University!

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback

Attributions

(propose a free ad)

Site Statistics

205 submissions , 163 unreviewed
5,082 questions , 2,232 unanswered
5,353 answers , 22,791 comments
1,470 users with positive rep
820 active unimported users
More ...

  Can quantum computing be simulated by an optical network?

+ 5 like - 0 dislike
833 views

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.

Question

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.

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
p$\varnothing$ysicsOverflow
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
Please complete the anti-spam verification




user contributions licensed under cc by-sa 3.0 with attribution required

Your rights
...