Hacker News Reader

Comment by ivansavz | Hacker News Reader

Anyone interested in learning quantum mechanics should first learn/review their linear algebra. Understanding quantum states and quantum measurements is really not that complicated once you're comfortable with vectors and matrices.

Shameless plug: I wrote a linear algebra book that discusses applications to quantum mechanics, including quantum computing. Check out an extended preview here: https://minireference.com/static/excerpts/noBSguide2LA_previ... Available electronically here https://gum.co/noBSLA and the print version is coming soon.

View on HN

SMBC did a pretty interesting comic about quantum computing a few weeks ago: "The Talk" - http://www.smbc-comics.com/comic/the-talk-3

It was a collaboration with Scott Aaronson ( http://scottaaronson.com/ ), so hopefully it's as accurate an intro to quantum computing as any webcomic could be.

"Quantum computing and consciousness are both weird and therefore equivalent" -- Scott Aaronson

Looks like really solid work on the math end, with good explanations. If I may, the profanity seems gratuitous, however. Also, since a book recommendation is in part a reflection of the reader, it would be difficult to recommend this text to a colleague. Maybe something to consider.

ETA: reminds me of Tim Pope renaming Vim Foreplay to Vim Fireplace a few years ago. Apparently, that really helped him [1].

1. https://github.com/tpope/vim-foreplay

Do you mean the title or the content of the book? I'm asking because I thought the main LA content is rather clean—the first book on MATH&PHYS had much more of the "juvenile" stuff. Also is bullshit really that bad? I never saw it as a swearword, but I guess it's borderline...

You're not the first to point out the limited recommendation potential. At the same time, I think the title is really what makes people stop and look in the first place. There are so many good math, physics, and LA textbooks out there, so it's important to stand out. I'm thinking I might release a PG13 version that cuts down on the edgy subjects, but I fear something will be lost in the process...

I don't share ops sentiment. As a software developer studying math part time, the title really made me interested in the preview. Will buy :)

N. David Mermin's "Quantum computer science: An introduction" is also a really good text for people with a CS background. It's a dead-tree book but I think the lecture notes he used to make the book are free online.

Agreed - I used Mermin's book in my undergrad. Not as comprehensive as Nielson and Chuang, but I love Mermin's style. The lecture notes you mentioned are here: http://www.lassp.cornell.edu/mermin/qcomp/CS483.html

I hate to be "that quantum consciousness guy", but one of the first sentences of the first lecture stood out to me: For a computer to be a quantum computer the physical systems that encode the individual bits must have no physical interactions whatever that are not under the complete control of the program.

What if we relaxed/paraphrased this as: For a biological system to be a mind the physical systems that underlie the mental substrate must have limited/circumscribed physical interactions that are not under the complete control of the mind.

For anyone wanting to learn quantum mechanics, there is a list of resources and pointers: http://p.migdal.pl/2016/08/15/quantum-mechanics-for-high-sch... (I have been teaching it to... high-school students).

Yes, linear algebra (and complex numbers) are necessary. Though, complex numbers are fun on its own, and linear algebra is crucial for other cool things, e.g. artificial neural networks.

Ivan, thanks for writing this book on Linear Algebra. It's been a while since I took a course in it and your book looks perfect for a thorough review. I'm writing this as someone that loves mathematical rigor and intends to pursue a PhD in Computer Science. I'll read every chapter of this book and can't wait to get to the chapter on QM applications.

Just start learning quantum mechanics, I reckon.

I think most people would say that functional analysis is the key to working comfortably in quantum, rather than linear algebra.

I am a PhD student in physics and I would definitely say that linear algebra is more important.

What should I learn if I'm interested in learning linear algebra?

3Blue1Brown has a great video intro series on the topic. https://www.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw/vid...

terrific! thank you.

I made notes some time ago that cover the linear algebra needed for Quantum Mechanics in some details and then go on to introduce basic QM at the end:

https://graybits.biz/notes/quantum_mechanics/preface

cool stuff. thank you.

Your question is rather tautological... You can pick a text book or even an online tutorial.

Understanding diagonalization (and more generally, spectral theory), scalar products, and norms would be a great start. Then you can pick any quantum information textbook.

algebra?

But what should I learn if I'm interested in learning algebra?

N.B. My maturity level is normally only a half step above the average 12-year-old. I can play this game all day ;)

hey! you got me ;)

My PhD is in biophysics. The Hamiltonion is a functional, pretty much all QM is application of Hamiltonians. I know both LA and FA; LA is basically introduction to FA.

It really depends on the area. For quantum computing and quantum info theory it seems that mostly it is just linear algebra. The functional stuff is left for the really really clever people only (not me btw!)

The way you describe it sounds analogous to computers: like saying "you only need to know C, not transistor physics, to program a computer". You can code on an existing machine, port your code to a new machine, but you'll never invent a new machine or architecture.

I think most would say that functional analysis is a generalization of linear algebra and that you absolutely need your linear algebra first. (Functional analysis is often thought of as infinite dimensional linear algebra.) Moreover, (finite dimensional) linear algebra is sufficient for learning theoretical quantum computing where there is a finite number of states.

do u accept bitcoin for the digital version? is it DRM protected, can I lend it to a friend then?

Not yet, but I'll be happy to get a wallet going to make this happen. Any recommendation for a good bitcoin wallet provider? I don't care about mobile app: web-only is good enough for me. Ideally fully offline.

Green Address is really good:

greenaddress.it

I'd use electrum

sending you an email

That's so boring! I recommend people learn whatever they want, and then if needed go and read a maths book. Much more fun that way. (Btw, I don't mean to dis your book, it looks good to me.)

Edit: just to elaborate on this. I hear often from people "what math do i need to learn so i can do X?" And I just think that alot of the time people should just do X and this will force them to figure out the math as needed. Learning math from a book is brutally difficult! Just like learning a programming language, what is the best way to do that? You start with a project that you want to do. People who want to read the "pre-requisite book" often-times just seem to be deferring the real crunch that happens when you actually get down to the business of actually learning X.

I'm reminded of the film "October Sky" where Jake Gyllenhaal's character (and I feel like a terrible nerd for not recalling the character, who is (was?) an actual NASA engineer, iirc), upon witnessing Sputnik-1 on a clear night, became obsessed with space flight and rocketry in particular. Got himself a bunch of really advanced texts on the subject and just powered through them, lazily learning the necessary math as needed, as you suggest. Once a poor student (bit of a slacker), he went on to make himself some rockets in relatively short order.

Excellent flick. If you haven't seen it, I recommend giving it a watch.

I can understand your approach. It helps to learn a topic (like linear algebra) when you can immediately see it's applications. However, I'm not sure it would work here; for one, quantum mechanics is not an "easily" understood application, like, say PCA, or DFT, or other such things.

Reply on news.ycombinator.com