A hurdle in quantum computing I've never been able to figure out

[jaketodd]

So the whole idea with quantum entangled computing, is that particles in superposition can compute more than one thing at the same time, right? But how does a system know which computed result is which? Maybe like a hashtag that separates one from another? But wouldn't that get jumbled, and the problem would persist? Thanks

 

[anuttarasammyak]

Usually we get quantum computing results by multiple "observation" done to well prepared ensembles.
Though good algorithms would enhance the probabity of the solution we require, we should carry out observation, or measurement, many times and get statistical data according to which the solution is deduced.

[EDIT] I find the below mentioned website cartoon informative to express how quantum computer works in factorization of 21 as an example, along the idea of Young's double slit experiment. The green cube symbolize a realized algorithm to enhance the probability to find the solution.
https://gendai-m.ismcdn.jp/mwimgs/c/2/2048m/img_c295b088806b55f1acb606806bf2af37102255.jpg　

 

[Hornbein]

It is a mystery to me how a quantum computer is "programmed." Somehow you set it up so that it decoheres most often into the state you want, lowest energy or something. Do this N times and look at the result that comes up most often.

 

[Demystifier]

But how does a system know which computed result is which?

The point is to combine all these individual results into a single result, so in the end you don't need to know the individual results. The results are combined via the quantum interference.

 

[gentzen]

But how does a system know which computed result is which? Maybe like a hashtag that separates one from another? But wouldn't that get jumbled, and the problem would persist?

Why not have a look at some simple quantum algorithm, for example to one for the Bernstein-Vazirani problem as described in
https://arxiv.org/abs/quant-ph/0305088 Copenhagen Computation: How I Learned to Stop Worrying and Love Bohr by N. David Mermin

 

[f95toli]

It is a mystery to me how a quantum computer is "programmed." Somehow you set it up so that it decoheres most often into the state you want, lowest energy or something. Do this N times and look at the result that comes up most often.

That is not how it works. At the end of each circuit you do a read-out operation which then tells you the state of the qubits ( |0> or |1>). All QC have some way of turning the interaction with the read-out "on" or "off".
I don't think it is helpful to think of a read-out operation in terms of decoherence. Firstly, it is always arranged so that the read-out is much faster than the T1 and T2 or the system (if not your read-out fidelity will suffer). Secondly, when you read-out the system you can obviously find the system in the |1> state which is typically the excited state (if not all results would be 0 which is not very informative).
That said, decoherence is of course important if you want to start doing things like non-demolition read-out etc (where back action is obviously important) or measurement based QC. But for a gate based QC, it can to a first approximation be neglected as long as the circuit run-time is much shorter than the coherence time of the system.

 

[jaketodd]

The point is to combine all these individual results into a single result, so in the end you don't need to know the individual results. The results are combined via the quantum interference.

But if the final qubits are in superposition, then how can you read just one result from them? How could you decohere or make weak measurements that can figure out whether they are 1's and/or 0's, when they embody both? Seems to me that they would be ambiguous as to the final result of the computation.

 

[jaketodd]

Isn't the only way to get two entangled particles to take a definite state is to make one collapse to a single state, and then the other one does too? But how do you know which collapsed state is representative of the computation in the second particle?? And then how would you get them both back into superposition?

 

[jaketodd]

I guess the collapsed state of the second particle could represent computation in the first one.

 

[PeroK]

I guess the collapsed state of the second particle could represent computation in the first one.

I suggest you find a paper on quantum computing and study it!

 

[jaketodd]

I suggest you find a paper on quantum computing and study it!

Ya you're probably right, but I don't think I have the stamina for that. Maybe you guys will just answer my basic questions here. Thanks

 

[gentzen]

Ya you're probably right, but I don't think I have the stamina for that. Maybe you guys will just answer my basic questions here. Thanks

Well, then try to browse at least some papers, to get some feeling what you would understand, where you are missing background, and how you like the writing style of different authors.

But if the final qubits are in superposition, then how can you read just one result from them?

The famous Born rule might help here.

 

[anuttarasammyak]

But if the final qubits are in superposition, then how can you read just one result from them? How could you decohere or make weak measurements that can figure out whether they are 1's and/or 0's, when they embody both? Seems to me that they would be ambiguous as to the final result of the computation.

In Young's slit experiment. we observe dots on the screen and know how |slit A> and |slit B> interfere.
In Feynman's path integral we observe a ball goes along classical deterministic path as a result of interference of all the paths. We may regard them as jobs of natural quantum computer. I am optimistic to get result from artificial quatum computer as well, though I do not have enough expertise to tell how to do it.

 

[Demystifier]

But if the final qubits are in superposition, then how can you read just one result from them? How could you decohere or make weak measurements that can figure out whether they are 1's and/or 0's, when they embody both? Seems to me that they would be ambiguous as to the final result of the computation.

In a classical computer, you want to know whether it is 1 or 0. But in a quantum computer, you have more options. For example, you may want to know whether the state is $|0\rangle+|1\rangle$ or $|0\rangle-|1\rangle$. The quantum computer may be such that it always produces either $|0\rangle+|1\rangle$ or $|0\rangle-|1\rangle$, and your measurement can determine which of those two is the case.

 

[jaketodd]

How are the measurements of the qubits done? Weak measurements, and then the qubits go back into full superposition? Thanks

 

[Demystifier]

How are the measurements of the qubits done? Weak measurements, and then the qubits go back into full superposition? Thanks

No, the measurement is only performed at the end when the computation is finished. After the measurement, the qubit is no longer used. Hence there is no need for weak measurement, the ordinary strong measurement is perfectly fine. The computation itself (namely, the process before the measurement) is a complicated series of unitary operations that do not involve any measurements.

 

[jaketodd]

No, the measurement is only performed at the end when the computation is finished. After the measurement, the qubit is no longer used. Hence there is no need for weak measurement, the ordinary strong measurement is perfectly fine. The computation itself (namely, the process before the measurement) is a complicated series of unitary operations that do not involve any measurements.

Thanks!

If the qubits are no longer used, is it a whole new system of entangled qubits? Or do the computational qubits (not the end ones that are totally collapsed), get used again? If so, how are they then entangled with a new set of final qubits?

 

[f95toli]

Thanks!

If the qubits are no longer used, is it a whole new system of entangled qubits? Or do the computational qubits (not the end ones that are totally collapsed), get used again? If so, how are they then entangled with a new set of final qubits?

You need to be a bit more precise. In solid state quantum computing as well as e.g., ion traps each qubit is a physical "thing" (e.g., an electronic device or an ion) and in this case each qubit in the system is just re-initialized to some known state (e.g., all qubits in the |0> state) before the next computation. Quantum computing based on photons is obviously different, here you typically need to generate a bunch of new photons before each computation. The practical implementation of photonic QC is -in my view- quite a bit more complicated than solid-state or ion trap modalities, so I would focus on the latter if your goal is to understand QC in general.

 

[jaketodd]

You need to be a bit more precise. In solid state quantum computing as well as e.g., ion traps each qubit is a physical "thing" (e.g., an electronic device or an ion) and in this case each qubit in the system is just re-initialized to some known state (e.g., all qubits in the |0> state) before the next computation. Quantum computing based on photons is obviously different, here you typically need to generate a bunch of new photons before each computation. The practical implementation of photonic QC is -in my view- quite a bit more complicated than solid-state or ion trap modalities, so I would focus on the latter if your goal is to understand QC in general.

I love entanglement, so I'm more interested in the photons. Question: How do you stop the photons from getting away since they move so fast?

 

[gentzen]

I love entanglement, so I'm more interested in the photons. Question: How do you stop the photons from getting away since they move so fast?

In Scott Aaronson’s lecture notes Lecture notes! Intro to Quantum Information Science,
Lecture 29: Experimental Realizations of QC (9 pages)
you can find a description of the Dual-Rail-Representation used for encoding qubits by photons.
This representation indeed addresses a problem related to photons being so fast, but in a different sense than in your naive classical picture. (The addressed problem is rather that using quantum states with different energy would be extremely challenging to turn into a working quantum computer for photons, because the energy difference would define a frequency scale on which you would have to operate.)

 

[jaketodd]

In Scott Aaronson’s lecture notes Lecture notes! Intro to Quantum Information Science,
Lecture 29: Experimental Realizations of QC (9 pages)
you can find a description of the Dual-Rail-Representation used for encoding qubits by photons.
This representation indeed addresses a problem related to photons being so fast, but in a different sense than in your naive classical picture. (The addressed problem is rather that using quantum states with different energy would be extremely challenging to turn into a working quantum computer for photons, because the energy difference would define a frequency scale on which you would have to operate.)

How about matter waves. Not photons. I am guessing they have frequencies much lower than photons.

https://en.wikipedia.org/wiki/Matter_wave

 

[PeterDonis]

How about matter waves. Not photons. I am guessing they have frequencies much lower than photons.

The frequency of a "matter wave" depends on its energy, just as with photons.

However, in both cases you appear to be working with a highly oversimplified mental model. "Photons" are not just little balls moving at the speed of light, nor are they just little waves of electromagnetism, and "matter wave" is not a very good description of quantum systems with nonzero rest mass.

 

[gentzen]

How about matter waves. Not photons. I am guessing they have frequencies much lower than photons.

https://en.wikipedia.org/wiki/Matter_wave

I wrote an answer, but then stored it away instead of posting it here, because you would just jump to the next topic anyway, and don't even try to browse or understand my references. At some point you really should start reading papers, or lecture notes, or books, if this topic interests you. And if you think that this approach would not work for you, then I have no idea how we should be able to help you get some basic understanding of how quantum computers and their different physical implementations work.

 

[anuttarasammyak]

If the qubits are no longer used, is it a whole new system of entangled qubits? Or do the computational qubits (not the end ones that are totally collapsed), get used again? If so, how are they then entangled with a new set of final qubits?

Measurement ends quantum procedures. This is what I learned in
https://files.webservices.illinois.edu/9156/keyconceptsforfutureqislearners5-20.pdf at
https://qis-learners.research.illinois.edu/ as below cited:

3. Quantum applications are designed to carefully manipulate fragile quantum systems without observation to increase the probability that the final measurement will provide the intended result.
a. A measurement is an interaction with the quantum system that transforms a state with multiple possible outcomes into a “collapsed” state that now has only one outcome: the measured outcome.
b. A quantum state determines the probability of the outcome of a single quantum measurement, but one outcome rarely reveals complete information about the system.
c. Repeated measurements on identically prepared quantum systems are required to determine more complete information about the state.
d. Because of the limitations of quantum measurement (providing only partial information and disturbing the system), quantum states cannot be copied or duplicated.

 

[jaketodd]

I'm sorry for my shortcomings, you guys. Thanks for putting up with me. Forgive me but it's not like I'm going for the PhD here. I appreciate all your help. Please continue to put up with me.

 

[jaketodd]

I'm only human, Harry!

 

[f95toli]

I love entanglement, so I'm more interested in the photons.

I'm not sure what you mean. All quantum computing uses entanglement, not just photon based ones. Photons are often used in pop-sci to try to explain or demonstrate properties of quantum physics, but the problem with that is that people then tend to end up confusing specific properties of photons (massless bosons) with "general" properties/phenomena (which applies to everything).
Hence, as I mentioned above, if you want to understand QC you are better off starting with some other modality that is easier to understand; most of it will then also be applicable to photon based QM.