How Does Counterfactual Computation Work?

[Careful]

** And the nonperturbative regime in SED seems to be just as frustratingly hard as that in quantum field theories. Hence the simulation approach in the latest paper.**

Right, but the computations involved are still much less intensive as a full QED treatment would demand (ask that to Patrick ).

**
Note that topologically, a torus is the only 2-manifold which can support a vector field that is non-zero everywhere. This doesn't matter in a quantum theory, but in your classical theory it should.**

Sure, but that is precisely what one would like no? That the dust can freely rotate ``at the same speed´´, without clumping up at some poles.

Cheers,

Careful

 

[selfAdjoint]

**
Note that topologically, a torus is the only 2-manifold which can support a vector field that is non-zero everywhere. This doesn't matter in a quantum theory, but in your classical theory it should.**

Sure, but that is precisely what one would like no? That the dust can freely rotate ``at the same speed´´, without clumping up at some poles.

Indeed, I wasn't criticising the idea, just pointing out a nice property it has. Are you looking at a finite torus or the limit, a circle or "closed string" if you will?

 

[Careful]

Indeed, I wasn't criticising the idea, just pointing out a nice property it has. Are you looking at a finite torus or the limit, a circle or "closed string" if you will?

Ah, by dougnut I mean ``filled up´´ torus I just don't like distributional matter configurations - seems very unphysical to me (I could give better reasons here if you want to - but these are somewhat more speculative). But don't misunderstand me: I think that classical string theory - spiced up with SED - could be a very nice thing to look at - in a sense, it would be easier to start with.

Cheers,

Careful

 

[selfAdjoint]

Ah, by dougnut I mean ``filled up´´ torus I just don't like distributional matter configurations - seems very unphysical to me (I could give better reasons here if you want to - but these are somewhat more speculative). But don't misunderstand me: I think that classical string theory - spiced up with SED - could be a very nice thing to look at - in a sense, it would be easier to start with.

Cheers,

Careful

Uh-huh. My limited experience with bosonic string theory suggests it's very hard to derive it from an action principle without allowing closed strings and open strings to interact and change their topology. Recent work has shown ways to get fermions out of this simple bosonic model without going to supersymmetry and superstrings. You might also want to look at string field theory which has had some good news recently, noted over at Lubos Motl's blog.

 

[Careful]

**Uh-huh. My limited experience with bosonic string theory suggests it's very hard to derive it from an action principle without allowing closed strings and open strings to interact and change their topology. **

Where did I mention collisions between different *particles* (I was talking here about interaction between one particle and a classical EM field) ? Obviously, you would expect topology change to occur IF one could find such a configuration in the first place.

** Recent work has shown ways to get fermions out of this simple bosonic model without going to supersymmetry and superstrings. **

Ah, that's interesting, similar work being done ``recently´´ in Einstein-Maxwell theory, I think by Bonnor (that is how the spin-spin interaction behaves for rotating rods - at least I think it was that).

** You might also want to look at string field theory which has had some good news recently, noted over at Lubos Motl's blog. **

You are speaking here about classical string field theory I presume ? That is fine (I would believe interesting results to emerge from that), but as I mentioned before, I have reasons *not* to start from an a priori assumption that matter is given by a string.

Cheers,

Careful

 

[Hurkyl]

There's an arXiv paper on counterfactual computation:

http://arxiv.org/abs/quant-ph/9907007

(which can be found by searching wikipedia, and running into the possible copyright violation notice. )

A quantum computer is modeled as having an input consisting of three components:

(1) A switch that controls whether the computer is to be run or not.
(2) The output register to which the result of computation is added.
(3) Additional registers that are the inputs to the algorithm. (And are left unchanged by the computer)

For the analysis, only the switch and output registers really matter. The computer enacts the transformation:

|0> |j> --> |0> |j>
|1> |j> --> |1> |j+r>

j is the initial value in the output register, and r is the result of the computation. (Both are either 0 or 1. And, of course, 1+1=0)

Let t² = 1/2, to make things pretty.

A rotation is the (unnormalized) transformation that sends:
|0> --> t|0> + t|1>
|1> --> -t|0> + t|1>


Our protocol is this:

(1) We start with |00>.
(2) We rotate the switch bit, putting us in the state t|00> + t|10>
(3) We feed this state into the computer, and wait. (Give it enough time to run, if it were to actually run)
(4) Measure the result. (If we get a 1, we know r=1 and quit)
(5) Rotate the switch bit again.
(6) Feed the state into the computer, and wait.
(7) Measure both the switch and the result.

For an example of what might happen, consider a basis possibility when r = 0
(1) We start in |00>
(2) We rotate to t|00> + t|10>
(3) The computer doesn't run, leaving us in |00,f>
(4) We observe a 0, leaving us in |00,f0>
(5) We rotate to t|00,f0> + t|10,f0>
(6) The computer does run, leaving us in |10,f0n>
(7) We observe a 10, leaving us in |10,f0n10>

As you can see, I've appended additional labels denoting what has actually happened or was measured. "f" for "off", and "n" for on.

In the case of r = 0, the full state evolves as:

(1) |00>
(2) t|00> + t|10>
(3) t|00,f> + t|10,n>
(4) t|00,f0> + t|10,n0>
(5) t²|00,f0> + t²|10,f0> - t²|00,n0> + t²|10,n0>
(6) t²|00,f0f> + t²|10,f0n> - t²|00,n0f> + t²|10,n0n>
(7) t²|00,f0f00> + t²|10,f0n10> - t²|00,n0f00> + t²|10,n0n10>

But it is important to note that the "f" and "n" are not actually measured, and are not actual components of the physical state -- the final state is actually

t²|00,000> + t²|10,010> - t²|00,000> + t²|10,010> = |10,010>

due to interference! However, the observation "010" is known to arise only from histories in which the computer has run. So, when r=0, we can be absolutely certain the computer runs, and that we will observe "010".

When r=1, it evolves as:

(1) |00>
(2) t|00> + t|10>
(3) t|00,f> + t|11,n>
(4) t|00,f0> + t|11,n1>
(5) t²|00,f0> + t²|10,f0> + t|11,n1>
(6) t²|00,f0f> + t²|11,f0n> + t|11,n1>
(7) t²|00,f0f00> + t²|11,f0n11> + t|11,n1>

Of course, as before, the final state is
t²|00,000> + t²|10,010> + t|11,1>

So we can list all the possible results of our experiment:

"010" -- we know that r=0 and that the computer ran.
"000" -- we know that r=1 and the computer did not run.
"011" -- we know that r=1 and the computer did run.
"1" -- we know that r=1 and the computer did run.

The important thing to how this works is that the "000" cases when r=0 destructively interferred, so that it was an impossible outcome.

 

[KAckermann]

There should be fines for publishing drivel like that article.

The first clue that it was B.S. was the fact that they never really said what they succeeded in doing. What does 'successfully search a database' mean?

Ultimately, I'm certain it means nothing, because if they had truly extracted information without using energy, then Ted Koppel would come out of retirement to report it, and Obama would rearrange his inauguration to rejoice in the gift of infinite wealth for all the world.

This is the kind of useless stuff that comes from publish or perish.

 

[Hurkyl]

You did notice the article in the OP was in a newspaper, not a scientific journal, right?