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Anyone interested in learning quantum mechanics should first learn/review their linear algebra. Understanding quantum states and quantum measurements is really

by ivan_ah 10y ago

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_preview.pdf#page=143 https://minireference.com/static/excerpts/noBSguide2LA_previ... Available electronically here https://gum.co/noBSLA https://gum.co/noBSLA and the print version is coming soon.

GFK_of_xmaspast 10y ago
See also Lipton&Regan: https://mitpress.mit.edu/books/quantum-algorithms-linear-algebra https://mitpress.mit.edu/books/quantum-algorithms-linear-alg...
mathgenius 10y ago
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.
- Ar-Curunir 10y ago
  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.
- groovy2shoes 10y ago
  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.
dn2k 10y ago
do u accept bitcoin for the digital version? is it DRM protected, can I lend it to a friend then?
- ivan_ah 10y ago
  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.
  - dn2k 10y ago
    I'd use electrum
  - dn2k 10y ago
    sending you an email
  - kobeya 10y ago
    Green Address is really good: greenaddress.it
dekhn 10y ago
I think most people would say that functional analysis is the key to working comfortably in quantum, rather than linear algebra.
- krastanov 10y ago
  I am a PhD student in physics and I would definitely say that linear algebra is more important.
  - dekhn 10y ago
    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.
    - mathgenius 10y ago
      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!)
      - dekhn 10y ago
        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.
  - stOneskull 10y ago
    What should I learn if I'm interested in learning linear algebra?
    - jps359 10y ago
      algebra?
stOneskull 10y ago
Just start learning quantum mechanics, I reckon.
deleted 10y ago
[deleted]
jobu 10y ago
SMBC did a pretty interesting comic about quantum computing a few weeks ago: "The Talk" - http://www.smbc-comics.com/comic/the-talk-3 http://www.smbc-comics.com/comic/the-talk-3 It was a collaboration with Scott Aaronson ( http://scottaaronson.com/ http://scottaaronson.com/ ), so hopefully it's as accurate an intro to quantum computing as any webcomic could be.
- crazy2be 10y ago
  "Quantum computing and consciousness are both weird and therefore equivalent" -- Scott Aaronson
Analemma_ 10y ago
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.
- dangirsh 10y ago
  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 http://www.lassp.cornell.edu/mermin/qcomp/CS483.html
  - themgt 10y ago
    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.
stared 10y ago
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-school-students.html 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.
unit91 10y ago
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 https://github.com/tpope/vim-foreplay
- ivan_ah 10y ago
  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...
  - kayoone 10y ago
    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 :)
sleekdesign 10y ago
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.

by ivan_ah 10y ago

GFK_of_xmaspast 10y ago

See also Lipton&Regan: https://mitpress.mit.edu/books/quantum-algorithms-linear-algebra https://mitpress.mit.edu/books/quantum-algorithms-linear-alg...

mathgenius 10y ago

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.

Ar-Curunir 10y ago
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.
groovy2shoes 10y ago
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.

dn2k 10y ago

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

ivan_ah 10y ago
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.
- dn2k 10y ago
  I'd use electrum
- dn2k 10y ago
  sending you an email
- kobeya 10y ago
  Green Address is really good: greenaddress.it

dekhn 10y ago

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

krastanov 10y ago
I am a PhD student in physics and I would definitely say that linear algebra is more important.
- dekhn 10y ago
  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.
  - mathgenius 10y ago
    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!)
    - dekhn 10y ago
      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.
- stOneskull 10y ago
  What should I learn if I'm interested in learning linear algebra?
  - jps359 10y ago
    algebra?

stOneskull 10y ago

Just start learning quantum mechanics, I reckon.

deleted 10y ago

[deleted]

jobu 10y ago

SMBC did a pretty interesting comic about quantum computing a few weeks ago: "The Talk" - http://www.smbc-comics.com/comic/the-talk-3 http://www.smbc-comics.com/comic/the-talk-3 It was a collaboration with Scott Aaronson ( http://scottaaronson.com/ http://scottaaronson.com/ ), so hopefully it's as accurate an intro to quantum computing as any webcomic could be.

crazy2be 10y ago
"Quantum computing and consciousness are both weird and therefore equivalent" -- Scott Aaronson

Analemma_ 10y ago

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.

dangirsh 10y ago
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 http://www.lassp.cornell.edu/mermin/qcomp/CS483.html
- themgt 10y ago
  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.

stared 10y ago

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-school-students.html 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.

unit91 10y ago

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

ivan_ah 10y ago
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...
- kayoone 10y ago
  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 :)

sleekdesign 10y ago

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.