The Talk

[tjackson2112]

Would anyone like to walk with me down the yellow brick road of 'The Talk', as I try to understand quantum computing myself?

http://www.smbc-comics.com/comic/the-talk-3

I arrive at the frame that begins "In Quantum Computing, the whole idea..."

So you don't need a jillion photons to paint an entire interference pattern to do useful quantum computing?  You just wait for a single photon paint stroke to arrive representing a single 'right answer' to have a useful computation for whatever supra-double-slit geometry you're investigating?  And, if necessary you wait for a sufficiently long time to satisfy yourself that no right answer is findable if the 'projection screen remains dark'?  Or you wait for a jillion photons to find the multiple possible solutions (the distribution - if any) corresponding to your geometry?  But don't you just confirm what you already knew, that the constructively reinforced paths are right answers and the destructive ones wrong?  Don't you just verify that your geometry is as you constructed it?  How is that useful for computation?  What am I missing?  How is that useful for, say, solving the traveling salesman problem?  Or two plus two equals four for that matter.

Unfortunately that comic strip ends just before the moment of mathematical orgasm and just crawls back into the (admittedly hilarious) sex talk metaphor and doesn't seem to answer how useful quantum computation is actually done.  The end, though, is classic.  "Quantum computing and consciousness are both weird and therefore equivalent."  That smells so much like my little sister's shelves full of new age spiritualism pornos.  Where can I get a copy of 'Futurologism' or 'X-Treme Tek'?  Those sound hot.  Are they still in print?

 

Edited July 9, 2019 by tjackson2112

[Strange]

16 minutes ago, tjackson2112 said:

So you don't need a jillion photons to paint an entire interference pattern to do useful quantum computing?

I'm guessing you are comparing this with the double slit experiment? Where we need a gazillion photons before we can begin to see that the experiment reproduces the classical interference pattern. But that is a different level of interference than we are concerned with when considering the behaviour of a single photon.

In this case, we can consider a single photon and look at all the ways it could behave (at the simplest level, it could go through one slit or, with the same probability, through the other sit). We can calculate every path the photon could take (whether through a slit or not) and then combine them. Some of those will cancel out completely (the photon will never be observed on the back wall of the lab) and some will partially cancel (the photon is unlikely to fall in the dark areas in the interference pattern), and some will interfere constructively and be very probable (the photon is very likely to hit in the bright areas of the interference pattern). 

It just so happens (not at all by coincidence) that the resulting probabilities of where the photon could end up correspond to where would expect to see light in the classical interference pattern.

When you change the probabilities associated with all possible paths (eg. by measuring which slit) then this changes the resulting probabilities. And hence the patten disappears.

I think that comic is a great precursor to the Feynman lectures on QED. These are online somewhere as videos. He is talking to a non-scientific audience and he explains really well how this while process sum-over-every-path process works. 

[swansont]

52 minutes ago, tjackson2112 said:

 How is that useful for computation?  What am I missing?  How is that useful for, say, solving the traveling salesman problem?  Or two plus two equals four for that matter.

Did you miss the panel that says "We only know how to do that for a few special problems"?

[tjackson2112]

Quote

I'm guessing you are comparing this with the double slit experiment? 

I'm trying to use an understanding of why an interference pattern is produced in that experiment to extend that understanding to how other geometries can solve other computational problems.  Can you state in words what computation the double slit is effectively computing with its familiar interference pattern?  At least as I understand it, it verifies that there are a bunch of answers to 1+1=2, which in that case is a vector relationship, i.e. the magnitude of a unit vector aX+bY is always 1?  As I understand it, the single photon verifies the theoretical question that a photon can interfere with itself when traveling through two closely spaced slits for any given photon or electron passing through.  The jillion is a response in a stochiastic domain and the single in a quantum domain?

I understand your second paragraph.  Your third, I think I understand, in that classical physics could be considered a subset of quantum physics.   Your forth begins to lose me and becomes a matter of the observer being intimately involved with the observed.  At that point, Einstein keeps running and I trip over my shoe laces. 

Swansont, could you illustrate one of those other few special problems in terms of geometries other than the double slit and explain what rudimentary computation is performed thereby?  I submitted the traveling salesman problem, only because that was offered up in a recent NOVA (I think) as a problem which quantum computing might someday be able to compute more effectively than traditional means.

Edited July 9, 2019 by tjackson2112

[Strange]

23 minutes ago, tjackson2112 said:

Can you state in words what computation the double slit is effectively computing with its familiar interference pattern? 

I'm not sure it is computing anything. (Unless you think that a stone falling from the Leaning Tower of Pisa is calculating Newton's laws of motion! If so, I suppose you could say it is computing the classical wave interference pattern.)

Quote

As I understand it, the single photon verifies the theoretical question that a photon can interfere with itself when traveling through two closely spaced slits for any given photon or electron passing through. 

You can interpret it as the photon going through both slits and then interfering with itself.

But the mathematics describes the wave function that describes the evolution of the photon. You can then calculate all possible outcomes and determine the probability of the photon being in a particular place.

Is either of those what "really" happens? Mu. Don't know.

23 minutes ago, tjackson2112 said:

Your third, I think I understand, in that classical physics could be considered a subset of quantum physics.

Not really. It is just that, overall, classical and quantum theories give the same results. They have to: they are both describing the world. I don't think we know why they do, though.

23 minutes ago, tjackson2112 said:

Your forth begins to lose me and becomes a matter of the observer being intimately involved with the observed.

Yes. Because of non-locality, you have to take everything into account (I think Feynman says something about having to consider the path where the photon shoots of to Jupiter, goes round it three times and then comes back. If you want to get a really accurate result.)

And, because it is non-local, even measuring an entangled photon (which is how the which-slit measurement is done) also affects the result. Even if you do it (or erase it) after it could affect the result, classically.

 

Here is an example of a problem that can be solved (only) by a quantum computer: https://www.quantamagazine.org/finally-a-problem-that-only-quantum-computers-will-ever-be-able-to-solve-20180621/

[swansont]

1 hour ago, tjackson2112 said:

 Swansont, could you illustrate one of those other few special problems in terms of geometries other than the double slit and explain what rudimentary computation is performed thereby?  I submitted the traveling salesman problem, only because that was offered up in a recent NOVA (I think) as a problem which quantum computing might someday be able to compute more effectively than traditional means.

You offered up 2 + 2 = 4 as well.

1 hour ago, tjackson2112 said:

I'm trying to use an understanding of why an interference pattern is produced in that experiment to extend that understanding to how other geometries can solve other computational problems.  Can you state in words what computation the double slit is effectively computing with its familiar interference pattern?   

As the double-slit has a classical solution, I am not sure that it solves any quantum computation problem.

[tjackson2112]

Strange,

Quote

I'm not sure it is computing anything. (Unless you think that a stone falling from the Leaning Tower of Pisa is calculating Newton's laws of motion! If so, I suppose you could say it is computing the classical wave interference pattern.)

Yes, that's precisely what it's calculating.  But I think the geometry can be cast into another domain of reasoning (i.e. a computational challenge).  And of course a stone falling from the Leaning Tower is indeed calculating Newton's laws of motion.  I'd say - good example.  And the Earth's gravitational influence upon the moon with its known mass and distance and current velocity and direction of motion is doing a calculation of both Newton's laws and offering a proof of Kepler's and nature is can give us a precise mass measurement of the Earth if the motion of the moon can observed with precision for a little while.  And it's effectively doing the calculation in nature's way - instantaneously, innately, precisely, without error.  Rather like the way the photon takes every possible path.

But in terms of the interference pattern and its distributed optima of photon intensity, I think quantum scientists are considering those as being the possible right answers of varying degrees of rightness in the solution to a computational problem with multiple solutions, rather like the vector relationship I mentioned.  A question of how you look at it.  And the geometry a computational program of sorts.  I'm still seeking clarity myself.

Quote

 

Here is an example of a problem

No, that is a proof (as I read it) that quantum computing can be considered able to tackle a superset of what traditional computing can.  Not an example of a problem that can be tackled by a quantum computer.

Swansont,

Quote

Did you miss the panel that says "We only know how to do that for a few special problems"?

I was hoping that if you (or Strange) know something of the subject that you could illustrate one of those few special problems and show how rudimentary quantum computing can compute it.

The double slit has a classical solution that as I understand it is a subset of the quantum superset.  There are those possibilities among all possible paths that include but one photon passing through but one slit without interference from the other are there not?  That's a classical subset of the quantum superset.

Edited July 9, 2019 by tjackson2112

[swansont]

11 hours ago, tjackson2112 said:

I was hoping that if you (or Strange) know something of the subject that you could illustrate one of those few special problems and show how rudimentary quantum computing can compute it.

No, not my area of expertise.

11 hours ago, tjackson2112 said:

The double slit has a classical solution that as I understand it is a subset of the quantum superset.  There are those possibilities among all possible paths that include but one photon passing through but one slit without interference from the other are there not?  That's a classical subset of the quantum superset.

AFAIK quantum computing is leveraging purely quantum behavior that has no classical analogue. There is no quantum state superposition involved in the interference in the double-slit.

11 hours ago, tjackson2112 said:

Yes, that's precisely what it's calculating.  But I think the geometry can be cast into another domain of reasoning (i.e. a computational challenge).  And of course a stone falling from the Leaning Tower is indeed calculating Newton's laws of motion.  I'd say - good example.  And the Earth's gravitational influence upon the moon with its known mass and distance and current velocity and direction of motion is doing a calculation of both Newton's laws and offering a proof of Kepler's and nature is can give us a precise mass measurement of the Earth if the motion of the moon can observed with precision for a little while.  And it's effectively doing the calculation in nature's way - instantaneously, innately, precisely, without error.  Rather like the way the photon takes every possible path.

I disagree. These are not calculations.

[Strange]

11 hours ago, tjackson2112 said:

I was hoping that if you (or Strange) know something of the subject that you could illustrate one of those few special problems and show how rudimentary quantum computing can compute it.

Not me.

Try here: https://en.wikipedia.org/wiki/Quantum_algorithm