Using a single particle as quantum computer

[danielhaish]

TL;DR

The idea is to achieve manipulation of state Vector of one particle that have 2^n qunatom states instead of using n qubits each 2 state

It's very hard to entangle many particles and keep them entangled, especially at room temperature. So I had an idea: instead of using many particles, what if we use just one — like a photon — and split its path many times?


Each time the photon hits a splitter, its path is divided. We make sure that both possible paths from each splitter go to the next splitter. This way, the photon’s wave function ends up being spread across many paths — all possible combinations of the split routes.


If we set the lengths of each path so that every possible combination gives a unique total travel time, then when we measure the time the photon arrives, we can figure out exactly which path it took. Since there are 2^n paths (n being the number of splitters), we can create 2^n unique arrival times to represent each possible path. Then we can manipulate the state of the photon to make calculations

 

[PeterDonis]

Each time the photon hits a splitter, its path is divided.

Only if you don't do this---

We make sure that both possible paths from each splitter go to the next splitter.

Doing this just recombines the two paths, getting rid of the split from the first splitter. All you're doing here is reinventing a Mach-Zehnder interferometer. Varying the two path lengths can get you the equivalent of one qubit (by changing the relative probability of a photon coming out of each arm of the second beam splitter), but that's all. There is no way to get more than one qubit's worth of information out of a single photon, no matter how you manipulate it.

 

[danielhaish]

Only if you don't do this---


Doing this just recombines the two paths, getting rid of the split from the first splitter. All you're doing here is reinventing a Mach-Zehnder interferometer. Varying the two path lengths can get you the equivalent of one qubit (by changing the relative probability of a photon coming out of each arm of the second beam splitter), but that's all. There is no way to get more than one qubit's worth of information out of a single photon, no matter how you manipulate it.

Thecnhcilly you can achieve that then without connecting the splitter but that will require amount 2^n of splitters which is not practical . But if one path is longer then then the other how can the the longer path interfere with the shorter path , if the photon hit the second splitter in different time in each path it takes. So there is still distinguishable results since each path will cause to the photon to arrive the end in different time.
I also find this thread about interference in different path length

 

[PeterDonis]

if one path is longer then then the other how can the the longer path interfere with the shorter path

Because the time of emission of the photon is not measured, and is therefore uncertain.

If the path lengths are different enough that the uncertainty in the photon emission time is shorter than the path length difference converted to light travel time, then you get no interference at any of the beam splitters and you're not doing any quantum computing at all, you're just doing the equivalent of sending around classical light beams.

 

[PeterDonis]

you can achieve that then without connecting the splitter but that will require amount 2^n of splitters

This won't get you more than one qubit's worth of information either; on each run of the experiment, only one of the 2^n detectors at the outputs of the last set of splitters will fire.

 

[danielhaish]

This won't get you more than one qubit's worth of information either; on each run of the experiment, only one of the 2^n detectors at the outputs of the last set of splitters will fire.

Yes but this is the same in quantom computer when you measure you get one result the calculation is done by manipulating the statcitics

 

[danielhaish]

Because the time of emission of the photon is not measured, and is therefore uncertain.

If the path lengths are different enough that the uncertainty in the photon emission time is shorter than the path length difference converted to light travel time, then you get no interference at any of the beam splitters and you're not doing any quantum computing at all, you're just doing the equivalent of sending around classical light beams.

The idea is not to get interference in the beams splitter. But to have particle with superposition of 2^n states . The manipulation for the calculation can happened in the end the finel.position. For instance You may put in the end of the path some sort of a mirror that will send all paths to the same point at the same time (I haven't made the calculation to see if this is geamotrycilly possible with number of mirrors which is smaller then 2^n)

 

[PeterDonis]

this is the same in quantom computer when you measure you get one result

But it's one result that involves interference and entangled states of multiple qubits. You can't conjure all that up with just one photon. You can only get one qubit's worth of information out of one photon, no matter what you do to it.

particle with superposition of 2^n states .

It's still just one qubit's worth of information. When you measure one photon, you get one qubit's worth of information. It doesn't matter how many beam splitters you put the photon through.

You may put in the end of the path some sort of a mirror that will send all paths to the same point at the same time

It's still just one qubit's worth of information. You have one photon, and that's all the information one photon can give you, no matter how you manipulate it.

 

[PeterDonis]

the calculation is done by manipulating the statcitics

...of multiple qubits if you want multiple qubits' worth of information.

At this point, if you still don't accept what I've been saying, you're going to need to provide a reference that supports your claim that you can get more than one qubit's worth of information out of one photon. If you can find such a reference, PM me and I'll take a look at it, and reopen this thread if appropriate. In the meantime, this thread is closed.