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Quantum computer built by Google can instantly execute a task that would normally take 47 years (www.earth.com)

submitted 1 year ago by readbeanicecream@kbin.social to c/tech@kbin.social

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A new quantum computer can execute calculations in mere moments that would take the most advanced supercomputers 47 years to process.

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[–] hetscop@kbin.social 17 points 1 year ago* (last edited 1 year ago) (4 children)

This is article is missleading about how quantum computing works.

Superposition increases the computing power of a quantum computer exponentially. For example, two qubits can exist in four states simultaneously (00, 01, 10, 11), three qubits in eight states, and so on. This allows quantum computers to process a massive number of possibilities at once.

Quantum computers aren't faster because they "process" multiple "possibilities" at once. Quantum computers aren't any faster than regular computers when it comes to general purpose computing. You can exploit some interesting properties about quantum computing to solve certain problems asymptotically faster, like with Shor's algorithm.

This means that the time to solve a problem as the size of the problem grows scales better. Using Shor's algorithm, the time to factor a polynomial is proprtional to (log N)^2 log log N, where N is the size of the input data, instead of the fastest known non-quantum algorithm which takes time proportional to e^(1.9(log N)^(1/3)(log log N)^(2/3)). Note that the majority of problems that we would maybe like to solve using a computer don't have any fancy quantum algorithms asociated with them and as such are no faster than a normal computer,

Given a large enough problem that can be solved with a quantum algorithm, a quantum computer will eventually outperform a non-quantum computer. This does not mean that quantum computers can solve arbitrary problems quickly.

[–] DarkGamer@kbin.social 3 points 1 year ago (2 children)

Quantum computers aren't faster because they "process" multiple "possibilities" at once.

@hetscop I thought eigenstates/qbits were what made quantum computing faster and gave it its additional capabilities. For example, if you had an 8-bit integer represented by a bunch of qbits in a superposition of states, it would have every possible value from 0-256 and could be computed with as though it were every possible value at once until it is observed, the probability wave collapses, and a finite value emerges. Is this not the case?

I read up a bit on Shor's algorithm, and while I don't fully understand it all it seems to take advantage of superposition of states destructively, which sounds a lot like "processing multiple possibilities at once."

When we input a superposition through our system and measure the remainder, we get a superposition of all possible powers that result in only that remainder. And this remaining superposition repeats with a period of the power [math didn't paste nicely]

Just as a classical Fourier Transform translates a wave as a function of time into a function of frequency, so too does a Quantum Fourier Transform (QFT), with a superposition as an output with a frequency of the input.

So, if we input a single state into a QFT, the output will be a superposition of states with varying weights or probabilities that form a wave with the input state as the frequency. And if we input multiple states into a QFT, the output will be a superposition of superpositions - with destructive and constructive interference combining superpositions into one wave. And if our input to the QFT is a superposition with period [math didn't paste nicely] source

If my understanding is inaccurate, can you recommend a good source to understand this? Thanks!

[–] hetscop@kbin.social 2 points 1 year ago

(typed this out yesterday before @ZickZack s excellent answer, but couldn't post it at the time due to maintenance...)

No, you've got it wrong. This is a fairly common missunderstanding which is perpetuated by a lot of coverage about the topic being sloppy.

You could argue that there is a grain of truth to the idea of processing multiple possibilities at once, but it's a bit more complicated than that and the way it's usually presented leads to people building a bad intuition of how it works. If you do get in to the nitty-gritty of Shors algorithm it feels to me at least a bit like a weird hack that shouldn't work at all or at least not be faster than the normal way to compute prime factors. It isn't a general speedup, just in certain cases where you can exploit quantum mechanics in clever ways.

Of the top of my head the SMBC comic about it is actually pretty good. This article makes basically the same points, but a bit more elaborated (note that it was written a while ago so the part about the current state of quantum computing is outdated). I noticed that Veritasum put out a YouTube video which I haven't watched, but he is in my experience good at explaining physics and math so I think that there's a good chance that it'll hold up. I remember liking this Minute Physics video about Shor's algorithm too, if you wanna get a better understanding of it.

I should clarify that I'm not a quantum phycisist, I've just done a couple of internet deep dives on the topic but I can't say that I fully understand quantum computing at all. I do think my understanding of it is better than the one in this article and others like it.

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