How can a quantum computer be faster than a classic computer?

[KingGambit]

TL;DR Summary

Qubit vs Bit; super position.

Dear PF Forum,

It's been a while since I logged in. And I hope everybody is in good health.
Here I have a question concerning quantum computer.
First, I'm no unfamiliar with a computer. I'm a computer programmer, but I don't know any physics.
How can a quantum computer be a lot faster then an ordinary computer?
I read about this qubit thing in many articles. And they say that qubit has super position. And I imagine something like this.
While bit has 1 or 0 value, qubit can be anything from 0 to 1. Such as 0.001, 0.002, 0.0003, etc...
So 1 qubit can replace several bits. But that's not the case.
From those articles, to read 1 qubit, we have to colapse its wave function (do I understand it right), and this qubit is fixed to 0 or 1.
But then again, 1 qubit is equal to 1 bit (ordinary computer).
So again, how can quantum computer be much faster?

Or, perhaps to change 1 qubit status it takes much, much faster than ordinary computer clock.
1 clock cycle in x86 family, in Pentium I7 about 2 Ghz,

So instruction such as, say. mov AX, BX takes about 1 or 0.5 nano seconds
Or perhaps a quantum computer can process mov AX, BX (or should I say mov QAX, QBX ) in some pico second??
And I also read that a quantum computer can crack, say RSA private key or SHA256 in matter of minutes. Then again, its speed must be in the order of trillion by trillion of ordinary computer.

Can someone explain it to me in simple language, why a quantum computer can be much faster than ordinary computer?

Thank you very much

 

[fresh_42]

A classical computer can check one solution per program execution which makes it slow for testing whether a certain key is valid for RSA or not. A quantum computer can check exponentially many solutions simultaneously per program execution which makes RSA vulnerable to a brute force attack. The keys had to grow exponentially, too, to achieve the same level of security. It is not the speed, it is the simultaneousness.

 

[gentzen]

A classical computer can check one solution per program execution which makes it slow for testing whether a certain key is valid for RSA or not. A quantum computer can check exponentially many solutions simultaneously per program execution which makes RSA vulnerable to a brute force attack. The keys had to grow exponentially, too, to achieve the same level of security. It is not the speed, it is the simultaneousness.

How familiar are you with quantum computers and quantum information science more generally? Have you ever heard of Scott Aaronson and his blog? Its headline says:

If you take nothing else from this blog: quantum computers won't solve hard problems instantly by just trying all solutions in parallel.

 

[KingGambit]

How familiar are you with quantum computers and quantum information science more generally? Have you ever heard of Scott Aaronson and his blog? Its headline says:

Well, sir, to tell you the truth. I don't even know about quantum mechanic other then the double slit experiment, Schrodinger cat,... much less quantum computer. But thanks for the blog link. I'm reading it now!

 

[fresh_42]

How familiar are you with quantum computers and quantum information science more generally? Have you ever heard of Scott Aaronson and his blog? Its headline says:

No, but this (commercial) source
https://www.kearney.com/documents/291362523/291370149/Why+quantum+computing+is+a+big+deal.pdf
says

So let’s take a closer look at a quantum computing
paradigm. How does it cause algorithms to scale
more slowly? The secret sauce is called quantum
parallelism. Recall that quantum superposition allows
us to make calculations on all possible values of an
input at the same time in a single step. As we do so,
quantum interference allows us to destroy any
outcomes that are not part of the solution.

 

[fresh_42]

Here is a more scientific source:
https://www.sciencedirect.com/science/article/pii/S1877050919316588

This machinery, if demonstrated to be applicable, would utilize quantum properties to execute infinite calculations in parallel. These quantum mainframes would be exceptionally more effective than present supercomputers.

However, I have to correct myself in the sense that they are also faster. But this is only a factor of about 100.

Maybe a bit more interesting is the following article (University of Virginia, Department of Computer Science):
https://www.cs.virginia.edu/~robins/The_Limits_of_Quantum_Computers.pdf

A small number of particles in superposition states can carry an enormous amount of information: a mere 1,000 particles can be in a superposition that represents every number from 1 to ##2^{1,000}## (about ##10^{300}##), and a quantum computer would manipulate all those numbers in parallel, for instance, by hitting the particles with laser pulses.

 

[FactChecker]

Here is a crude, back of the envelope, example to show the difference:

CLARIFICATION: The following is a general motivation of the possible advantage of a Quantum network. It may not apply to any particular algorithm like Shor's Algorithm or gate-based algorithms. It does apply to the method of quantum annealing.

Suppose you had to find the 1 right combination of ten zero/one values to decode a message.
A conventional computer can test the combinations, one at a time. It might have to test all ##2^{10}=1024## before it got an answer. But a basic property of quantum computers is that it can have 10 qbits hooked together (all in simultaneous zero/one states) that can settle into a solution that fits the problem in a single step.

Now suppose you needed to find the right combination of 1000 zero/one values to decode a message. That is over ##2^{1000}=10^{301}## possible combinations. If a conventional computer can test one billion possible combinations every second, it would still take over ##3\cdot 10^{284}## years to get through them all. Meanwhile, a quantum computer with 1000 qbits (ideally arranged) could still settle into the solution in one step.

 

[gentzen]

Meanwhile, a quantum computer with 1000 qbits (ideally arranged) could still settle into the solution in one step.

A classical computer could randomly guess solutions, and if it is (very) lucky, it too could find a solution in a few steps. Therefore the "could still settle" in your answer makes the explanatory value of it quite small. We don't get any idea for which type of problem a quantum computer with 1000 qbits typically manages to "settle into the solution in one step", and for which problems it has no significant advantage over a classical computer.

Take everything I say with a grain of salt. I know nothing.

Good to know.

Explaining how a quantum computer works (and why it is fast for some problems, for example "period finding") is not an easy task. It gets even more challenging when it is unclear how deep the asker actually wants to dive into details.

If somebody wants to answer with understandable thoughts first, fine. But if this is all he can offer, even in case the asker wants to know some more detail, then I am not convinced that it was a good idea to offer his understandable thoughts.

 

[fresh_42]

We don't get any idea for which type of problem a quantum computer with 1000 qbits typically manages to "settle into the solution in one step", and for which problems it has no significant advantage over a classical computer.

Read the paper I linked to. The one titled "The limits of quantum computers". As a rule of thumb: Algorithms that can be parallelized like the NP-complete 3-SAT, or breaching a code with a brute-force attack will be faster by many magnitudes. A simple addition remains a simple addition. The gain here is only due to the lack of switches, aka chips or transistors. That contributes to a linear speed-up. I read it by a factor of 100. The significant factor in almost all applications are I/O operations. If you can read all inputs at once, you will save computation time already there. You cannot solve the RH but you can test even more zeros than we can today. Distributed computing will no longer be necessary. I expect that OR will be revolutionized since you can evaluate all routes of the traveling salesman in one step. Algorithms that cannot be parallelized will only be slightly faster.

 

[gentzen]

Read the paper I linked to. The one titled "The limits of quantum computers".

Maybe a bit more interesting is the following article (University of Virginia, Department of Computer Science):
https://www.cs.virginia.edu/~robins/The_Limits_of_Quantum_Computers.pdf

@KingGambit This is indeed a good paper. By Scott Aaronson. And it is very readable too! Do read it, really!

As a rule of thumb: Algorithms that can be parallelized like the NP-complete 3-SAT, or breaching a code with a brute-force attack will be faster by many magnitudes.

This is wrong, and is not supported by the linked paper.

The gain here is only due to the lack of switches, aka chips or transistors. That contributes to a linear speed-up. I read it by a factor of 100. You cannot solve the RH but you can test even more zeros than we can today.

The assumption that quantum computers would work faster for classical operations like a simple addition is not correct. They are typically slower, even those using superconducting qubits. (I could look up the actual cycle time of existing superconducting quantum chips. I guess it was around 300 MHz).

 

[FactChecker]

A classical computer could randomly guess solutions, and if it is (very) lucky, it too could find a solution in a few steps.

Yes. The expected number of tries before a solution is found would be half of the total, assuming that nothing about a failed try gives a hint to the solution. For the 1000 bit example, testing 1 billion a second that would still take over ##10^{284}## years on average.

Therefore the "could still settle" in your answer makes the explanatory value of it quite small. We don't get any idea for which type of problem a quantum computer with 1000 qbits typically manages to "settle into the solution in one step", and for which problems it has no significant advantage over a classical computer.

There are different approaches with different details. I am not about to get into quantum annealing versus quantum computing and different approaches to error correction on an introductory question. (I am not sufficiently expert on this subject anyway.)

Good to know.

Please don't be a wise- .

Explaining how a quantum computer works (and why it is fast for some problems, for example "period finding") is not an easy task. It gets even more challenging when it is unclear how deep the asker actually wants to dive into details.

Then he can ask some follow-up questions.

If somebody wants to answer with understandable thoughts first, fine. But if this is all he can offer, even in case the asker wants to know some more detail, then I am not convinced that it was a good idea to offer his understandable thoughts.

I am doing the best I can. If you don't like my answers, then please provide better ones of your own.

 

[FactChecker]

Explaining how a quantum computer works (and why it is fast for some problems, for example "period finding") is not an easy task. It gets even more challenging when it is unclear how deep the asker actually wants to dive into details.

I don't think you need to get buried in the details when answering the question of how superposition gives a quantum computer an advantage over traditional computers. It's a good, basic question and the answer does not have to fill in all details, especially since many details are the subject of current research.

 

[fresh_42]

lgorithms that can be parallelized like the NP-complete 3-SAT, or breaching a code with a brute-force attack will be faster by many magnitudes.

This is wrong, and is not supported by the linked paper.

You are right. I should have been less enthusiastic. The relation between BQP and NP is not known.
https://en.wikipedia.org/wiki/BQP. At least there is a little light at the end of the tunnel, Grover's algorithm

Charles H. Bennett, Ethan Bernstein, Gilles Brassard, and Umesh Vazirani proved that any quantum solution to the problem needs to evaluate the function ##\Omega(\sqrt{N})## times, so Grover's algorithm is asymptotically optimal. Since classical algorithms for NP-complete problems require exponentially many steps, and Grover's algorithm provides at most a quadratic speedup over the classical solution for unstructured search, this suggests that Grover's algorithm by itself will not provide polynomial-time solutions for NP-complete problems (as the square root of an exponential function is still an exponential, not a polynomial, function).

 

[FactChecker]

While bit has 1 or 0 value, qubit can be anything from 0 to 1. Such as 0.001, 0.002, 0.0003, etc...

It's better to think of it as having both 0 and 1 as its only possible values that it will only decide on when it fits the situation.
When several qbits are linked together, they are keeping all possibilities open until they can reach a compatible state with each qbit deciding on its 0/1 value. If a problem is presented to the network (it is like defining the boundary values) the entire network of qbits can decide on 0/1 values simultaneously that is compatible with the problem and gives the solution of the problem. So it is (ideally) a single-step solution.

So 1 qubit can replace several bits. But that's not the case.

Correct.

From those articles, to read 1 qubit, we have to colapse its wave function (do I understand it right), and this qubit is fixed to 0 or 1.
But then again, 1 qubit is equal to 1 bit (ordinary computer).

Right

So again, how can quantum computer be much faster?

Because an entire network of qbits decide on their 0 or 1 values which are compatible with the problem solution simultaneously.

Or, perhaps to change 1 qubit status it takes much, much faster than ordinary computer clock.
1 clock cycle in x86 family, in Pentium I7 about 2 Ghz,

So instruction such as, say. mov AX, BX takes about 1 or 0.5 nano seconds
Or perhaps a quantum computer can process mov AX, BX (or should I say mov QAX, QBX ) in some pico second??
And I also read that a quantum computer can crack, say RSA private key or SHA256 in matter of minutes. Then again, its speed must be in the order of trillion by trillion of ordinary computer.

The speed of the single step of a quantum computer is not critical even if it took an hour. Its advantage is on problems that could take a conventional computer thousands of years.

To be clear, IMO most home computer/internet users have no use for quantum computers, except for one case -- quantum computers can threaten to break passwords quickly. That is the type of problem where finding the right combination in one step gives the quantum computer an advantage. (There are people developing quantum security procedures to defeat hackers who might use quantum computers to break passwords. I am not an expert on that subject.) Other than that, normal home uses of computers/internet are the type of things that quantum computers are not better for, and would probably be much worse for.

 

[KingGambit]

Here is a crude, back of the envelope, example to show the difference:

Suppose you had to find the 1 right combination of ten zero/one values to decode a message.
A conventional computer can test the combinations, one at a time. It might have to test all ##2^{10}=1024## before it got an answer. But a basic property of quantum computers is that it can have 10 qbits hooked together (all in simultaneous zero/one states) that can settle into a solution that fits the problem in a single step.

Now suppose you needed to find the right combination of 1000 zero/one values to decode a message. That is over ##2^{1000}=10^{301}## possible combinations. If a conventional computer can test one billion possible combinations every second, it would still take over ##3\cdot 10^{284}## years to get through them all. Meanwhile, a quantum computer with 1000 qbits (ideally arranged) could still settle into the solution in one step.

Wow, Mr. @FactChecker, thank you very much for your answer.
I'll study it.

 

[PeroK]

Here is a crude, back of the envelope, example to show the difference:

Suppose you had to find the 1 right combination of ten zero/one values to decode a message.
A conventional computer can test the combinations, one at a time. It might have to test all ##2^{10}=1024## before it got an answer. But a basic property of quantum computers is that it can have 10 qbits hooked together (all in simultaneous zero/one states) that can settle into a solution that fits the problem in a single step.

The classical computer not only has to guess the right key but presumably decode part of the message using the key to check whether the guess is correct. And if the message has not been decoded correctly, then move on to the next possible key.

It's not immediately clear how a quantum computer does that for all possible keys simultaneously.

 

[pbuk]

The classical computer not only has to guess the right key but presumably decode part of the message using the key to check whether the guess is correct. And if the message has not been decoded correctly, then move on to the next possible key.

No, that is not how quantum (or classical) computers break RSA encryption. This is done by finding the factors of the public key.

Factorising large numbers (e.g. 2,048 bits) is something that quantum computers can in theory do much faster than classical computers, but in practice it takes many more than 2,048 qbits to factor a 2,048 bit number - probably a few million. The largest QCs currently have a few thousand so this is some distance away.

 

[PeroK]

No, that is not how quantum (or classical) computers break RSA encryption. This is done by finding the factors of the public key.

Please read the message I was responding to. That was about hypothetically finding a 10-digit key to decode a message. Not about RSA encryption.

 

[Hornbein]

I have read that quantum computers cannot solve the traveling salesman problem. I think their main use will be simulating quantum systems like big atoms and molecules. It could revolutionize chemistry.

 

[FactChecker]

The classical computer not only has to guess the right key but presumably decode part of the message using the key to check whether the guess is correct. And if the message has not been decoded correctly, then move on to the next possible key.

It's not immediately clear how a quantum computer does that for all possible keys simultaneously.

That's a very good point. The task of representing the problem to a quantum computer is very challenging. The network connections of qbits in a quantum computer further restricts how a problem can be represented. That subject is far beyond my knowledge base. I do know that conventional computers were used to set up the problem for a quantum computer.
My experience was about 12 years ago and was only related to a qbit network that used quantum annealing. I don't know what the current situation is or what it would be like on other types of quantum computers.

 

[FactChecker]

I have read that quantum computers cannot solve the traveling salesman problem.

Very interesting. I don't know why that would be true. Can you remember where you read that?
ADDED: I would have thought that the traveling salesman problem would be an ideal application.

I think their main use will be simulating quantum systems like big atoms and molecules. It could revolutionize chemistry.

Good point. Using quantum computers to study other quantum problems seems to be very rich with possible applications.

 

[Hornbein]

Very interesting. I don't know why that would be true. Can you remember where you read that?
ADDED: I would have thought that the traveling salesman problem would be an ideal application.

It was some time ago. Ten years? A quick look shows me this very interesting 2024 paper, "

"Solving The Travelling Salesman Problem Using A Single Qubit"​

I do a lot with 3-spheres and just got interested in the Hopf fibration so I'm going to put some effort into attempting to "get it." "Rotating a qubit," well I never. This is theory and not practice. They simulate solving with four to nine cities. They're at the University of Hamburg. It is hard to believe this could work in real life, but I'll have some intellectual titillation with it I hope.

https://arxiv.org/abs/2407.17207

Good point. Using quantum computers to study other quantum problems seems to be very rich with possible applications.

That was Richard Feynman's goal. He initiated all this.

 

[gentzen]

I have read that quantum computers cannot solve the traveling salesman problem. I think their main use will be simulating quantum systems like big atoms and molecules. It could revolutionize chemistry.

The point is that the traveling salesman problem is NP-complete, and we currently don't know of any quantum algorithm which would solve NP-complete problems in polynomial time.
But we cannot prove the opposite either, i.e. assuming P ≠ NP show that there is no quantum algorithm which would solve NP-complete problems in polynomial time.

 

[Hornbein]

The point is that the traveling salesman problem is NP-complete, and we currently don't know of any quantum algorithm which would solve NP-complete problems in polynomial time.
But we cannot prove the opposite either, i.e. assuming P ≠ NP show that there is no quantum algorithm which would solve NP-complete problems in polynomial time.

Yes the word "solving" is ambiguous. I guess they are saying they can do much better than a conventional computer, but maybe that is nothing to get all that excited about.

 

[.Scott]

A classical computer can check one solution per program execution which makes it slow for testing whether a certain key is valid for RSA or not. A quantum computer can check exponentially many solutions simultaneously per program execution which makes RSA vulnerable to a brute force attack.

When using a quantum computer to crack RSA, you would use Shor's Algorithm or more specifically, his factoring algorithm. The quantum computer needs to be slaved to the main processor - which will be a Von Neumann device - ie, classical, instruction-oriented - like your laptop. The classical computer will then guess at an answer, ie, a factor of 'N'. We'll call that guess G. In the highly unlikely event that G is correct, then it's done. More likely, it will discover that the G and N are coprime - which is exactly what the quantum computer needs. If you operate with modulo arithmetic and your base is N, the any coprime of N (such as G) when raised to a high enough power will result in 1. So, for some r, G^r=1. What the quantum computer is programmed to do is to find the 'r'. If you need to know exactly how it does this, study the wiki article and work through all three of what they call the "quantum subroutines". If I had to describe it in simple terms, I would try this: It creates a superposition of G^r for all possible r's and then looks for a repeating pattern that will show up in the QFT (Quantum Fourier Transform). That 'r' then goes back to your laptop (or whatever) and if 'r' is even, it will use it to find the answer. Otherwise, it picks another G and tries again.

My points are this:
1) Although the QM computer is solving the G^r=1 problem with simultaneous multiplications, it really isn't doing any of the "checking".
2) It seems to me that "QM solutions" seem to be developed more by asking "what can I do with these qubit modules" that by asking "how would I program a solution to this problem".

 

[.Scott]

While bit has 1 or 0 value, qubit can be anything from 0 to 1. Such as 0.001, 0.002, 0.0003, etc...
So 1 qubit can replace several bits. But that's not the case.

Correct. That's not the case.

If I have 8 bits, I can have any of 256 possible codes.
But with 8 qubits:
1) I perform some quantum operations to generate an 8 qubit result:
2) I perform the same operations a million time and each time I measure the result and get an 8-bit result.
3) I generate a 256-bin histogram with the results and discover that although any of the 8 qubits can be either 0 or 1, many of the 8-bit combinations are impossible.

Based on the method for preparing those 8 qubits, all 8 qubits can become entangled - so that they share a single common state that can be described as the probabilities of measuring each of those 256 codes.

Before I take the measurement, those 8 qubits can contain at least 1 bit per histogram bin (256 bits), but when I make a measurement, I only get one code. In order to take full advantage of the massive amount of information in a set of qubits, I need to stay in the quantum domain until I have some useful final result.

I said "at least 1 bit per histogram bin", but here is the take from Peter Shor, 1996 :
-------------------------------
Consider a system with n components, each of which can have two states. Whereas in classical physics, a complete description of the state of this system requires only n bits, in quantum physics, a complete description of the state of this system requires ##2^{n − 1}## complex numbers. To be more precise, the state of the quantum system is a point in a ##2^n##-dimensional vector space.
-------------------------------

 

[fresh_42]

My points are this:
1) Although the QM computer is solving the G^r=1 problem with simultaneous multiplications, it really isn't doing any of the "checking".
2) It seems to me that "QM solutions" seem to be developed more by asking "what can I do with these qubit modules" that by asking "how would I program a solution to this problem".

Yes. The article about the Grover algorithm and the links therein is a better description than my naive and partly wrong intuition of what can be done:
https://en.wikipedia.org/wiki/Grover's_algorithm

 

[.Scott]

Even when QM circuitry contains logic components that are topologically sequential, the processing itself is not sequential in the "one step at a time" sense.

When I try to imagine "what's actually going on", I think of it like a standing wave that's working itself out through the quantum circuitry. The Wiki article has a paragraph titled "The bottleneck" that touches on the actual QM circuitry implementation. It describes QM circuitry that "mimic conventional arithmetic circuits with reversible gates". In other words, schematically identical to standard digital multiplication logic but using AND/OR/XOR gates that can carry quantum information in both directions (factors to product and product to factors). So each of those multiplication blocks that square the input still have a classical propagation delay - but they also need to wait a bit of time for that propagation to complete through the remainder of the circuitry including the QFT. At that point, the entire circuit has a single shared state that can be "measured". In the general case of QM circuitry, that shared state would be a superposition of many potential states. But for this circuit, only one answer is correct - so, even before the measurement, with an ideal circuit, there would be only a single result available for measurement.

 

[KingGambit]

First of all, I'd like to thanks all members here who help me understanding quantum computing.

There's is something scary about Google!
How the hell do they know, that I was just asking QM in PF Forum?
This link pops up in my Youtube Feed.
Explaining quantum computer to different level
1. Toddler
2. Teenager
3. Under grad student, only knows computing not QM
4. Grad student, but I think he understand "just fair" about QM.
5. Professional

Here, the IBM lady is explaining quantum computer to 5 different level people. It's very good.
And in 5:23, the IBM lady tells the teenanger that if she (IBM) measures her penny to be a head, then the teenager would measures her (teenanger) penny to a head also.
But, that's not how entanglement work, right . If the measured electron is spin up, the other would be spin down .
And in graduate session 10:37, I think I can grab a few things there.
1. To take the advantage of quantum computing, you have to have a "quantum" algorithm, "...the key is to come up with algorithm where the result is deterministic"
2. QC needs like 1 millions error corrected qubit, (now we can only come up with 50 error corrected qubit).

14:20 A professional
At least, here. We can watch a dialog where both participants understand each other (but I don't understand them! )

But I keep watching, watching this video to grab the essence about of quantum computing.
[Edit] about -> of sorry my English.

 

[FactChecker]

First of all, I'd like to thanks all members here who help me understanding quantum computing.

There's is something scary about Google!
How the hell do they know, that I was just asking QM in PF Forum?
This link pops up in my Youtube Feed.
Explaining quantum computer to different level
1. Toddler
2. Teenager
3. Under grad student, only knows computing not QM
4. Grad student, but I think he understand "just fair" about QM.
5. Professional

Here, the IBM lady is explaining quantum computer to 5 different level people. It's very good.

I love that video and that approach to introducing a new subject!

And in 5:23, the IBM lady tells the teenanger that if she (IBM) measures her penny to be a head, then the teenager would measures her (teenanger) penny to a head also.
But, that's not how entanglement work, right . If the measured electron is spin up, the other would be spin down .

The point is that the two results would be coordinated, whether consistently identical or consistently opposite.

And in graduate session 10:37, I think I can grab a few things there.
1. To take the advantage of quantum computing, you have to have a "quantum" algorithm, "...the key is to come up with algorithm where the result is deterministic"
2. QC needs like 1 millions error corrected qubit, (now we can only come up with 50 error corrected qubit).

Fault tolerance is currently the "Holly Grail" of gate-based quantum computer research. But it is not required in all applications. If you were trying to solve the Traveling Salesman problem, a "near optimal" solution might be acceptable. Quantum annealing (see this) is an approach where the energy on the quantum network starts at a ground state and is slowly "morphed" into a state that is compatible with the problem solution. That solution might have a little energy above the ground state, but it is likely to be "nearly optimal". The company D-Wave does research in that approach. In fact, for some applications it might be better if the solution has some randomness among "near optimal" results. You might want to keep an enemy country guessing at your solution.

Getting back to your original question about the speed. Suppose you have an algorithm of two parts, A and B, where A produces an output 0/1 value that B needs to do its part. In a conventional computer, A would have to execute in one (or more) step to get a value. Then B would have to execute in a second step using that value. But if A and B were entangled in a quantum computer, as soon as A arrives at a value, B also arrives at a compatible value due to entanglement. Now suppose you had a network of hundreds of interrelated parts. A conventional computer might require years to work through combinations whereas a quantum computer might get the right combination in one step due to entanglement. Even if the single step of the quantum computer takes an hour it can still be much faster than the conventional computer.