The Mathematics of Quantum Computers | Infinite Series

What is the math behind quantum computers? And why are quantum computers so amazing? Find out on this episode of Infinite Series.

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Previous Episode - How the Infinite Explains the Finite

Written and Hosted by Kelsey Houston-Edwards
Produced by Rusty Ward
Graphics by Ray Lux

Sources and further references:

For a great linear algebra tutorial, check out 3Blue1Brown's:

Some of the people who wrote awesome programs that compute Goodstein Sequences:

Donald Hobson
David Franco
Jeronimo Spuri Murguia
Nathan Soufflet
Ivan Hop
Max Goldstein

Comments answered by Kelsey:

Cybernetic Qualinaut

Eric Saumar

Bob C

[shubhamshinde]

Infinite series and spacetime are the best thing to happen to youtube...

[Lonewolf-]

She: Quantum computer's don't exist yet
Me: in 2021 jumps into to description box to see when was the video uploaded 😂

[notmadeofpeople]

In this video we'll be using numbers. You probably don't know what those are but for the purposes of this video you just need to know they are squiggly things that math people like.

[tesseraph]

This was maybe the most well-put explanation of quantum computing I've seen on Youtube or really anywhere. Thanks for this!

[MrHimanshun]

_2017: Nobody has ever built a Quantum Computer!!_
_2019: Hold my Qubits_

[wiadroman]

2:11 "Actually, qubits are not made of cats" - my world collapsed like a wave function :-(

[nernaykumar]

One of the best explanation of quantum I have seen in yt, cuz there are many expensive courses online which teach quantum but fail to develop a visual intuition of how quantum looks like, PBS infinite series doing a great job

[quilan]

One thing that should be noted is that while computations on the entire quantum state are exponentially quicker than classical, there is still an exponential number of states that you have to observe, if you're not clever about setting things up. The reason that very specific algorithms (Shor, Grover, etc) are so much quicker is because they're able to manipulate the probabilities in a very specific manner that makes the correct answers tend to "jump out" of the final state (having a higher probability). For normal calculations, a quantum computer would be of no better use than classical.

[whatdamath]

in reality, there are already plenty of quantum computer out there. D wave is a Canadian company that provides quantum services to organization and Intel recently announced a 49qubit processor.

[kevinchau]

I'm a senior in electrical and computer engineering at the UofA, I just understood everything she was talking about! OMG, this is amazing! Everything boils down to basics and how we can do basic things better... crazy!

[lellyparker]

Quantum SatNav computer. "Turn left at the next junction. Probably".

[RubbberRabbbit]

I love this channel! This is the first video on the subject that's made real sense to me, actually explaining beyond the concept of Schrödinger's Cat. Good job!

[thezebraherd]

It's so weird that these things exist now looking at this video from 2 years ago (still not mass produced but significantly better than when the video was made)

[dragonfyre]

Thank you so much for this. I have seen so many videos that jump straight from explaining to superposition to the 2^N states thing without explaining WHY superpositions give quantum computers this power. Your vector explanation was the first thing I've seen that actually helped me understand this.

[noodleiv]

This is the best short explanation of quantum computing. Thank you!

[Kyzyl_Tuva]

Just started rewatching these videos. Thank you Kelsey.

[Julian-tfnj]

great video! One of the best intros to qubits and quantum computing (especially its underlying math) that I have seen. Thank you!

[nemotaylor]

Finally a video on quantum computing that didn’t skip over the math and dumb it down too much. THANK YOU.

[MrPhaedrusx]

I love whomever is coaching your hand movements between this and Spacetime. No Sarcasm. Your shows are incredible. :)

[fbarousse]

Excellent explanation!
Too bad this is outdated already: starts with "Quantum computers do not exist YET ".... couldn't be so false now in October 2019. Hope we could get an update of the video.