4 ms·

Note its not strictly-speaking necessary to learn any linear algebra to "understand" quantum computing, there is a very simple but universal set of string-rewri

Note its not strictly-speaking necessary to learn any linear algebra to "understand" quantum computing, there is a very simple but universal set of string-rewriting rules. I realise for this audience most people wouldn't get much from it, but I find these rules useful for explaining quantum theory without annoying and fluffy analogies to high school students. You can find the rules in my book _Q is for Quantum_ - Part I which covers quantum computing is a free download on the book website (and the rest will be if I ever get around to producing a corrected pdf, bleh, but if you read part I and don't want to pay for the rest let me know and I'll get it to you...)

gus_massa 6y ago
Are you sure the easy rewriting rules are not just 2x2 matrix multiplication?
- abdullahkhalids 6y ago
  I looked at the book and it is. His way is perhaps useful for not scaring off amateurs from learning quantum theories, but ultimately he is tricking them into learning a part of linear algebra without a foundation upon which more complex concepts can be built.
  - magsnus 6y ago
    I hate people that trick others in to learning stuff. :) This book really looks nice and short to me and I really wish the other parts comes online to.
  - Q_is_4_Quantum 6y ago
    Actually its not quite that simple. The approaches are "equivalent" (in terms of operational/statistical predictions) but not "isomorphic" (even if we restrict the regular linear algebra approach to the same gates as I use in the book). Basically (because of not implementing normalization/unitarity) in certain situations the "mist" retains a count of the number of "Feynman paths" that led to the output state. For example, concatenate two PETE boxes (hadamard gates) and the output is [W,W], concatenate four and its [W,W,W,W]. Operationally identical (you only observe the ball to be certainly white!) and applying a suitable simplification rule you "drop the extras" of course. But if someone (unlike me!) wants to think of these states as having ontological status maybe they would think the distinction is relevant. A much more interesting example of something similar happens in the Deutch-Hayden version of Heisenberg picture style quantum theory. There from looking at the "state of the world" you can determine which total unitary evolution occurred to get you there. In the Schroedinger picture, if I give you the inital and final states there are many possible unitaries that get you between them. Its possible to go further and come up with versions where not only the total unitary connecting initial and final state is discernable, but also the sequence of Hamiltonian's that implemented it are too. These things are mainly of interest to people in foundations of course (since they like to play the game of blurring the line between our math and what is "really out there"). I tried to be very careful in the book to maintain the distinction.
    - GuiA 6y ago
      Downloaded part 1 of your book last night and read it, as a fellow computer scientist and educator, very very solid work! I bought the book! Are you aware of anyone who made an interactive version (eg in the browser) of the boxes and balls model? Would be really fun to mess around with it interactively.
      - Q_is_4_Quantum 6y ago
        Thanks for buying! Any money I make eventually works its way back to Malawi where I grew up, so it not going to be squandered :) A few weeks ago a high school physics teacher who used the book for some extension classes sent me some python code he says will do all of the calculations. I have asked the family friend who maintains the book webpage to put it on there, and I am sure she will when she gets a chance. However if you email me - terry @ qisforquantum.org - it would be great to have someone look at it - I don't know python at all and can't even run it to check it. (I also have some atrocious octave/matlab code of my own which anyone is also welcome to.)
jimhefferon 6y ago
An excellent book, thank you. I picked it up on Scott Aaronson's recommendation and it is very good indeed.

gus_massa 6y ago

Are you sure the easy rewriting rules are not just 2x2 matrix multiplication?

abdullahkhalids 6y ago
I looked at the book and it is. His way is perhaps useful for not scaring off amateurs from learning quantum theories, but ultimately he is tricking them into learning a part of linear algebra without a foundation upon which more complex concepts can be built.
- magsnus 6y ago
  I hate people that trick others in to learning stuff. :) This book really looks nice and short to me and I really wish the other parts comes online to.
- Q_is_4_Quantum 6y ago
  Actually its not quite that simple. The approaches are "equivalent" (in terms of operational/statistical predictions) but not "isomorphic" (even if we restrict the regular linear algebra approach to the same gates as I use in the book). Basically (because of not implementing normalization/unitarity) in certain situations the "mist" retains a count of the number of "Feynman paths" that led to the output state. For example, concatenate two PETE boxes (hadamard gates) and the output is [W,W], concatenate four and its [W,W,W,W]. Operationally identical (you only observe the ball to be certainly white!) and applying a suitable simplification rule you "drop the extras" of course. But if someone (unlike me!) wants to think of these states as having ontological status maybe they would think the distinction is relevant. A much more interesting example of something similar happens in the Deutch-Hayden version of Heisenberg picture style quantum theory. There from looking at the "state of the world" you can determine which total unitary evolution occurred to get you there. In the Schroedinger picture, if I give you the inital and final states there are many possible unitaries that get you between them. Its possible to go further and come up with versions where not only the total unitary connecting initial and final state is discernable, but also the sequence of Hamiltonian's that implemented it are too. These things are mainly of interest to people in foundations of course (since they like to play the game of blurring the line between our math and what is "really out there"). I tried to be very careful in the book to maintain the distinction.
  - GuiA 6y ago
    Downloaded part 1 of your book last night and read it, as a fellow computer scientist and educator, very very solid work! I bought the book! Are you aware of anyone who made an interactive version (eg in the browser) of the boxes and balls model? Would be really fun to mess around with it interactively.
    - Q_is_4_Quantum 6y ago
      Thanks for buying! Any money I make eventually works its way back to Malawi where I grew up, so it not going to be squandered :) A few weeks ago a high school physics teacher who used the book for some extension classes sent me some python code he says will do all of the calculations. I have asked the family friend who maintains the book webpage to put it on there, and I am sure she will when she gets a chance. However if you email me - terry @ qisforquantum.org - it would be great to have someone look at it - I don't know python at all and can't even run it to check it. (I also have some atrocious octave/matlab code of my own which anyone is also welcome to.)

jimhefferon 6y ago

An excellent book, thank you. I picked it up on Scott Aaronson's recommendation and it is very good indeed.