[MUSIC] Okay, in this example let's take n=10. Then N would be 2 to the power of 10. Which is 1,024. And the square root of n will be 32. And suppose that we run Shor's algorithm and we get y equal to 139. So we have this value, 139 divided by 1,024, and we search for some fraction near it in this proximity of it. Which has the denominator less than 32. So how do we do it? We wrote this fraction like this. Which equals to 7 here, plus 51 divided by 139. And this is our first estimation, 1/7. It is close to this fraction. And if it is not close enough we continue this. So if one seventh doesn't meet our requirement to be close enough to our original fraction, we go further. 7 plus 1 divided 139 divided by 51. Which is 7 plus 1 divided by 2, and plus 37 divided by 51. So our next estimation is this. And if you multiply both numerator and denominator by 2 you get the second destination, 2 divided by 15, which is closer to this original fraction. And still it has the denominator less than 32. If it does not fit, if it's still not close enough, we continue this infinite fraction. And then next value we will get 3 divided by 22, which I think meet our conditions. And if it don't, the next value would be 8 divided by 59, which is very close to the original fraction, but it does not meet the condition of the denominator to be less than 32. And if it happens we might conclude, we might conclude that the y that we have measured is not a good y. Okay, on this slide here you see the implementation of the Shor's algorithm and the quantum computer simulator, link to which you can find the materials for the course. I can write it right here, that's, http://qc-sim.appssupport.com. Okay, and p and q are chosen here like 3 and 5. So their product is 15 here. And we randomly choose 7 as this a. So the function f(a) is function f(7) here. And we see the implementation of QFT. We already discussed before on this week. So this QFT, and this is our, You have operator. Here you have a demo, and how to implement your operator. You'll understand if you do the exercises for this week. So probably that's all with this example. And you can try it yourself on this Internet address, or you can try it for different numbers of numbers p and q. And you will need to implement the separator you have differently. Maybe you will try monthly bits. So you would have to implement this quantum free transform differently. So good luck with that. Well to conclude, imagine we have this big composite number, that product of two big price and we want to factor it. So we choose some random number a, we define this function f(a) and we search for its period. We employ Shor's algorithm and we get some y is probability almost to one half. It is good y. So we search for this k divided by r in a proximity of this value in a shot proximity. And if we find then we try to use it as a period. If it doesn't fit we can think that it is one of the denominator. So we have to run Shor's algorithm many times and to re-combine these values that we get. And we try to build the value of period. And finally when we succeed, this period may happen to be odd, and we have to start all over. All this seems a little bit time consuming, but it's not if compared to the classical approach to this problem. Because for the Shor's algorithm, even if you have to run it several times, maybe many times, it is only n squared where n is number of bits and all known classical algorithm to this time are over polynomial at this parameter. So for big N for classical computing this problem is untractable. And for quantum computation, it's just a little bit time consuming. So what I'm trying to say is that Shor's algorithm provides us with exponential speed up over the classical computing for this task of factoring and period finding. I want to wish you good luck with your control test and I hope to see you next week, bye.