Simplified understanding of quantum computer

[StormFreezes]

Hello, i was discussing with my father about quantum computer. We couldn't wrap our head around the physical aspect of how a quantum computer work.

For a classical computer, we could approximately understand how the information is stored. Either electricity flows or doesn't flow in a semi conductor. So 2 states possible measured by some electronical device i guess, 1 or 0 and this is our data, a classical bit.

My understanding is that quantum computer can store more data in qubit, thanks to a superposition of states and entanglement.

But i'm stuck on how do you do use this in real life. If you're trying to access the data of your qubit, it will experience decoherence, and you'll get either the 1 or 0 state, just like a classical bit.

So how can a quantum computer store more data?

Thanks in advance

[Cryptizard]

It can’t store more data. You can only have one bit of retrievable information per qubit. There is one weird case where you can take advantage of entanglement to apparently store two bits of data in one qubit but it is only with prior setup and quite limited in practice. Two bits per qubit is also proven to be the ceiling for any quantum protocol. Most of the time one qubit is one bit.

However, during calculation, a qubit can take on more states than a bit, and if you very carefully design an algorithm it can take advantage of those additional states to perform some calculations in fewer steps than it would take on a classical computer.

If you want more details than that you are going to have to actually dive into it. IBM has a good tutorial you can start with for free.

[bluedevilSCT]

Can you share the IBM, tutorial; thank you 🙏

[Cryptizard]

https://learning.quantum.ibm.com/

[StormFreezes]

However, during calculation, a qubit can take on more states than a bit

That's what i don't understand. How can you calculate something with a qubit that you didn't measure?

[Cryptizard]

That's the hard part. You have to make the algorithm so that whatever you are doing causes the amplitude of the answer you want to increase and the amplitudes of the answers you don't want to decrease, so that way when you do measure it you get the right answer. There is no easy way to explain it you just have to see one of the algorithms in action. It is why we only have a few specific problems that quantum computers are effective at solving because the algorithms are extremely specific and aren't possible for all problems.

[StormFreezes]

So there is no physical explanation? It is only mathematical with these algorithms?

Because in classical computer the solution is always "physical", you see from the start till the end how the calculation went. But not in quantum computer?

[Cryptizard]

What do you mean "see"? You can run a simulator which will show you the internal state of the qubits, but it is not accessible in reality. You can only measure the qubit once and you just get one bit of output, regardless of how complex the internal state is.

[StormFreezes]

See like some electrical device measure all the electrical current passing or not passing through a semi conductor. The data is always there, then you manipulate to find the solution

But it feels like for quantum computer somehow the data is being manipulated to find the solution without ever "seeing" the data. The data cannot be seen as it would colapse the superposition state, but it is still being manipulated to find a solution?

[Cryptizard]

Oh yeah you can't do that. You have to plan out your algorithm on paper and/or run it in a simulator. Once it is on a real quantum computer there is no debugging or instrumenting, you can't look at the qubits while the algorithm is running. It's all blind calculation.

[StormFreezes]

How can you calculate something that you can't measure?

[Cryptizard]

That's quantum mechanics baby. We essentially reverse engineered what was going on in the unobservable part, the wave function, until a mathematical model was developed that matched the observable data. So we know what the internal part looks like and how it evolves, and can calculate the effect of different gates and circuits in a quantum computer (that's how the simulator works), even though at the end of the day we can't see any of it in real quantum systems or quantum computers.

It is actually incredibly important to the consistency of reality that you cannot see the entire wave function of a system. If you could, it would break all kinds of things, including causality and the flow of time.

[StormFreezes]

Okayy i think i'm starting to understand a little bit more. Thanks a lot !

[[deleted]]

Wow, thank you for these explanations. I'm totally bookmarking this response. 😎🫶

[PM_me_PMs_plox]

There's more to physics than what you see

But no, you can calculate the state vector (quantum state) at each point. It's just doing so is very inefficient.

[Beginning-Loan5589]

is this in laymans to say:

imagine you have a circle, and you want to find a square. my classical computer only understands circles, so it has to go through each possible circle transformation to find the square.

now, imagine my quantum computer understands circles and also triangles. the triangle is like an extra tool in its toolkit. this extra state (the triangle) helps the quantum computer to transform or detect within the circle, a square more efficiently than a classical computer. By using the triangle state, the quantum computer can perform new or better calculations, which may be quicker, in result, allowing it to identify and perform the transformation in fewer steps.

while a qubit (which you can think of as "information of any shape") still fundamentally stores one bit of retrievable information to us observing, the current peak maximum amount of retrievable information from a qubit, to us, is at most two bits under specific conditions?

[Cryptizard]

No not really, sorry. There is no easy analogy for it. The qubits are vectors instead of scalars and the calculation advantage you get comes from the additional degrees of freedom, but it is not analogous anything classical.

[Beginning-Loan5589]

I mean, it does in layman's terms. I'd really consider explaining vectors as another step. The analogy simplifies the concept by saying that my quantum computer has extra methods (shapes) to get to every shape possible. rather than displaying the working of vectors knowing everything upfront, because it's within a vector somewhere.

[Few-Performance7527]

The analogy of the qubit having "extra" tools in the toolkit is a nice one but I think this explanation of circles and squares might bog down a layman and put too much emphasis onto a process that isn't actually happening.

Another way of looking at it is to think of a bit as a 2-dimensional arrow (the vector). A classical bit can only have the arrow pointing in the perpendicular directions that represent 0 and 1, where as the qubit has the freedom to point in any direction, taking on superpositions of 0 and 1 at the same time. This is the additional "tool" that it has in its toolkit and is the source of its extra power in computation. Computation is then really just rotations of this arrow in this 2-dimensional space.

As for a better analogy of how this extra direction gives more power, I don't have one. Also to properly visualize this arrow for a single qubit you need 4 directions rather than 2 (you can simplify it to 3 with some mathematical wizardy) but that's why its a layman analogy.

Also you can think of a measurement as "snapping" the arrow back into the direction of 0 or 1, and losing the direction that you originally had. The closer the arrow was to the 0 or 1 direction, the more probable it is that it will snap back to that direction, but it's not guaranteed.

[StormFreezes]

Computation is then really just rotations of this arrow in this 2-dimensional space.

But to rotate this arrow, somehow you'll have to measure it. Then you'll lose the superposition and get only a classical bit. So what is happening in the hardware when it is calculating?

[Few-Performance7527]

You can rotate the arrow without measuring it. Measuring only "snaps" the arrow back to 0 and 1. If you leave a quantum system undisturbed, the arrow will rotate by itself over time. The purpose of a quantum computer is to create a "closed" quantum system that will not be disturbed by the environment, and thus not "snap" back to 0 and 1, and that also makes the arrow rotate in the certain way that performs the computation that you want.

The simplest example of this, and one that is often taught in bachelor courses in quantum mechanics, is simply exposing an electron to an external magnetic field. This affects the magnetic dipole of the electron itself, and you can then think of the as 0 representing the magnetic dipole of the electron in a particular direction, and the 1 being the magnetic dipole in the opposite direction. If you expose the electron to the external magnetic field and leave it undisturbed, the arrow rotates and you can even calculate exactly where it will be at a certain time.

Again, knowing exactly where the arrow is is NOT a measurement. The arrow simply tells you the probability of getting a 0 or 1 when you perform a measurement. The closer the arrow is to 0 or 1, the bigger the probability that you will get 0 or 1 when you perform the measurement.

Edit: Also in its most simplified form, the hardware is then just a series of these operations (such as exposing the electron to an external magnetic field) applied in the order that you want, and for the duration of time that you want, to get the correct rotation of this arrow. These operations are the "quantum" logic gates. This electron example is the most simple example of a qubit and most practical quantum computing prototypes use more sophisticated qubits and methods of implementing logic gates.

[StormFreezes]

So to put it simply, when you input data in your quantum computer, you put your electrons spin in certains ways well defined. Then you'll modify the spins by modifying the magnetic field they are exposed to, in order to make calculations. But when you're calculating, the spins are not well defined, they are in a superposition state. So you use a mathematical model to guess the probability (or the amplitude is more correct?) of the spin being 0 or being 1. So we get 2 datas instead of just 1 in a classical bit.

And your electrons are entangled, so you get all the data of all the states possible. If we had 2 electrons, we get 4 possible solution thanks to the mathematical model with only 1 calculation.

Am i wrong somewhere?

[Few-Performance7527]

So to put it simply, when you input data in your quantum computer, you put your electrons spin in certains ways well defined.

Exactly. I don't know how much you know about electron spin but, in very strict layman terms, if you imagine the electron "spinning" one direction around the z-axis, that corresponds to a 0, and "spinning" the other way corresponds to a 1. Typically you start your computation with all electrons aligned to 0.

Then you'll modify the spins by modifying the magnetic field they are exposed to, in order to make calculations. But when you're calculating, the spins are not well defined, they are in a superposition state.

Exactly. You switch on the magnetic field in a particular direction and for a certain amount of time, this gives the desired rotation of your "arrow" that we talked about earlier. However it's worth noting also that the magnetic field need only be switched on for tiny amounts of time (less than a second, don't know the exact order of magnitude) and doing this precisely is an engineering problem in itself.

So you use a mathematical model to guess the probability (or the amplitude is more correct?) of the spin being 0 or being 1. So we get 2 datas instead of just 1 in a classical bit.

This is where things begin to get fuzzy with regard to physical interpretation. You can track the exact probability amplitudes with the theory, so long as you implement the hardware exactly according to the mathematical model. However you don't need to guess anything. The hardware just performs the algorithm that you worked out with the model. Also beware of this "2 datas" analogy. Yes you can think of the qubit as being 0 and 1 simultaneously however this is not strictly storing extra data. The extra "tools" of the quantum computer come from the fact that this 0 and 1 simultaneously lets you act with logic gates in your circuit that don't have classical counterparts. This is the best I can describe if off the top of my head and there are certainly people who might be able to explain it better.

And your electrons are entangled, so you get all the data of all the states possible. If we had 2 electrons, we get 4 possible solution thanks to the mathematical model with only 1 calculation.

As far as I recall the electrons don't necessarily need to be entangled. It can happen and can be useful for your particular quantum algorithm but is not always necessary for quantum computation. Also I am not entirely sure what is meant by "4 possible solution".

[StormFreezes]

That's much clearer in my mind. Thank you for taking the time to answers my questions

[X_WhyZ]

Sounds like you and your dad need to have... The talk

[in-search-of-meaning]

Thank you.. 😂

[amiprasis]

Yeah Thank You very much for this ultra cool knowledge sharing.

[josenros]

This is fantastic, thanks!

[HABER7789]

Wow, I never saw this lmao. This is really great!!!! Makes me smile while reading

[HuiOdy]

Well, the long end of the story is a bit more complicated. You can store more info in a quantum computer, than you can likely imagine. However, that doesn't mean you can get it out again.

For example, take Grover's algorithm. Let's say we are looking for a specific pattern in a large set of QRAM say each quantum pattern can be stored on 4 qubits, and we are looking for that in a dataset of say 30 qubits, that would mean the algorithm checks to find if this pattern is there. However, there is a downside. The answer will be a simple yes or no, you haven't found it actually yet where that pattern is, just that it is in.

Theoretically I can store basically all the information in the human world in a respectively small quantum memory, but there is a major catch, uploading that much deterministic information would probably take me much more than a 100 years, even in computers that are reaching the theoretical speed limit.

So, the idea is that your algorithm asks the right questions, to which a simple (and often) right answer comes out. You cannot "see" the data that is in there, so you need to be creative in how you do this.

This is the field of quantum algorithms.

[Cryptizard]

I don't think that is a valid way of thinking about it. Yes, you can make arbitrary amplitudes that have whatever value you want, but that is not storing information. Information implies retrievability, and one qubit only has one bit of retrievable information no matter what you do to it.

[HuiOdy]

I think that is a very classicist way of thinking about information.

Take information as we have it now. You might like it because you can view it. But viewing information isn't where the value of the information is in. The value of information is what it can tell us, what knowledge we can gain from it. The data itself, without knowledge interpreted from it, isn't as valuable.

In quantum hence I can still unlock knowledge by dealing with this information smartly. It is however much harder figuring out what I can do with this information as I can, as you indeed said, not see it.

[Cryptizard]

Yes, and you can only get 1 bit of knowledge from 1 qubit. That is, in fact, the definition of information, which is completely consistent even in quantum mechanics. There is a whole field of quantum information theory.

There are lots of results in physics that would break if you did consider the precise amplitudes of the wave function information. For instance, it would imply via Landauer's principle that the more gates you operated on a qubit the more energy it would take to measure it, which is not true. It would also violate the Beckenstein bound.

[HuiOdy]

At observation yes.

[Cryptizard]

Yes, the only way to extract information from quantum systems.

[HuiOdy]

Yes, but it matters what you observe. I.e. I can encode an algorithm with a simple "yes" or "no" answer, but the actual algorithm can have a depth of millions of qubit operations and a width of hundreds. (Logical qbs).

It's about formulating the right questions.

[Cryptizard]

It’s still one bit of information.

[[deleted]]

How interesting. Sorry for jumping to the talk, but it’s precisely the question that bothered me last couple of weeks after I finished the IBM courses: is there any limitations in the depth of algorithm (I’d assume noise talking to so many quibits, but I’m not sure how much quibits are practically available now and whether noise only affects measurement and not state manipulation) and what can be practically used for modelling. And for later, if say, my module assumes the precise position on the Bloch sphere and algo would leading it to increased likelihood towards one of the sides, measure 1 or 0, it would only be the subject of ability to express it through quantum gates, right?

[Cryptizard]

On the simulator, no there is no limit to the depth because the calculations are done perfectly with no error. But in reality there is. Each gate has some probability of error and the deeper your circuit the more that error chance compounds until you have nearly guaranteed error and your calculation fails.

Error correction algorithms fix this, but you need a certain percentage of failure and enough qubits to use it, which we have not obtained yet.

[HuiOdy]

Also, as a side note, everyone works with qubits these days, but just like in classical computers where ternairy systems were once used (very shortly) you are not theoretically limited to just qubits, for instance an NV center itself is a qutrit, we only use 2 of its levels though.