How Shor's Algorithm Factors 314191

This video explains how Shor’s Algorithm factors the pseudoprime number 314191 into its prime factors using a quantum computer. The quantum computation relies on the number-theoretic analysis of the factoring problem via modular arithmetic mod N (where N is the number to be factored), and finding the order or period of a random coprime number mod N. The exponential speedup comes in part from the use of the quantum fast fourier transform which achieves interference among frequencies that are not related to the period (period-finding is the goal of the QFT FFT).

REFERENCES

RSA Numbers (sample large numbers to try factoring)

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[markorezic]

I understood all of those words separately

[SzanyiAtti]

I guess this is one of those 5 minute videos that I have to watch for an hour to understand

[jacobr]

Protip: watch at 0.25 speed. You won't understand anything, just like now, but at least you get to hear your computer make some fun sounds!

[PMW]

you just wanted to see how many numbers you could say in a single video

[TheVoidPhantom]

What a fun coincidence. This video was published just one day after I had to implement Shor’s algorithm for my quantum computing class at university.

[meatloaf]

I understood it completely but I like apple pie more.

[JRizzo-lidr]

This example makes the original video make much more sense! Thanks!

[shunyat]

Instruction is unclear, accidentally generated wormhole to the pie dimension.

[WayneBraack]

Great! Scrambled brains for breakfast. Now if I could figure out how to tie my slipons I could walk the cabbage. Anyone got coffee? And aspirin?

[francesco]

These kinds of worked out examples are so great. Keep it up!

[KevinHorecka]

This video was very clear and helpful. The previous video left a lot of open questions, but this one was excellent. Still not sure I understand exactly how the QFT and remainder operations work, but knowing those are the functions being implemented means that can be treated as a separate issue. Great job!

[SaberTooth]

This is a really great follow up to the previous video. Really helps to illustrate just how powerful this algorithm is.

[nietschecrossout]

One of the few video channels that I don't need to speed up, lmao nice one

[irwainnornossa]

The number 16129 is one I will recognize instantly.
If you have base 210 (2×3×5×7), and you want the square of prime following square of following prime after last prime in base 210, this is the number you get.
I've seen this number so many times…
For similar purpose. Faktoring. Not big numbers, but a lot of them (at once). Not using super effective algorithm, but my own.
Why? I was bored once on job interview. And I asked myself „what is the chance of specific prime being the lowest factor of any given number?“, after which I came up with theory. I've not stopped there. I went deep, into numbers and factoring. Found unexpected things and realized that expected things were in fact stupid.

[xatnu]

Great video, directly answered all the questions I had from last video :)

[francoisrd]

4:36 I can have my pie, but can I eat it too?







Answer: yes, because of superposition

[renantequezon]

I'm just gonna pretend I understand a thing of what he is saying

[angaj]

Great work. One of the best explanations I have seen.

[linguinelabs]

This was so complex but you made me understand it so you did a good job

[electronicsNmore]

You want a video with 100M views? Do one about YouTube's algorithm. LOL