# What is a ket

November 4, 2014 6:41 PM Subscribe

Quantum physicists of MeFi: I want to know all the quantum mechanics I need to know to understand quantum computing. I am mathematically literate and willing to learn more math, but I want to minimize my need to study physical phenomena or experimental results.

I'm coming from a theoretical CS perspective. Success would be when I can understand and explain to someone else at least Grover's algorithm (Shor's algorithm also relies on some number theory which is kind of a separate domain).

I basically just want the mathematical and notational background to understand what's going on in the texts I'm reading; I can sort of follow them but it always feels like I'm missing some assumed prior knowledge. E.g. what precisely does |a> denote; what is the difference between |a>|b> and |ab>, etc.? I don't care about "spin", or what that means, or anything involving double slits or wave/particle duality or hydrogen. It's too specific. I just want to understand quantum algorithms independent of the implementation of qubits. I am (as far as I know) comfortable with math at the level required.

If you have an explanation, that's great; any helpful texts are also good.

I'm coming from a theoretical CS perspective. Success would be when I can understand and explain to someone else at least Grover's algorithm (Shor's algorithm also relies on some number theory which is kind of a separate domain).

I basically just want the mathematical and notational background to understand what's going on in the texts I'm reading; I can sort of follow them but it always feels like I'm missing some assumed prior knowledge. E.g. what precisely does |a> denote; what is the difference between |a>|b> and |ab>, etc.? I don't care about "spin", or what that means, or anything involving double slits or wave/particle duality or hydrogen. It's too specific. I just want to understand quantum algorithms independent of the implementation of qubits. I am (as far as I know) comfortable with math at the level required.

If you have an explanation, that's great; any helpful texts are also good.

Alright, I spent a lot of time on Wikipedia reading about this and somehow never looked for that article directly. It is pretty comprehensive. Still, other resources are appreciated.

posted by vogon_poet at 7:22 PM on November 4, 2014

posted by vogon_poet at 7:22 PM on November 4, 2014

Sounds like you're looking for Sakurai. It's a standard grad school textbook, for a second course in QM, not a first one. We used this version, but I see that there's a newer version with a posthumous reviser.

From a review on Amazon:

If you want to buy a cheap copy, look for international editions - or your university library certainly has this book.

(And as a personal prejudice, I really think people should anchor their theoretical work by understanding the experimental results. The results are weird and wonderful and expose fundamental shortcomings in our understanding of the world where the physics of very large and very small scales make contact.)

posted by RedOrGreen at 7:35 PM on November 4, 2014 [1 favorite]

From a review on Amazon:

*"In the 21st century, perhaps it would be better to start off with one foot planted firmly in the weird, axiomatic and algebraic land of QM first, and to make contact with classical observations later. This is the approach of Sakurai. A quote from Julian Schwinger appropriately summarizes this idea, that this is a "non-historical approach" that "goes to the heart of the quantum experience."*If you want to buy a cheap copy, look for international editions - or your university library certainly has this book.

(And as a personal prejudice, I really think people should anchor their theoretical work by understanding the experimental results. The results are weird and wonderful and expose fundamental shortcomings in our understanding of the world where the physics of very large and very small scales make contact.)

posted by RedOrGreen at 7:35 PM on November 4, 2014 [1 favorite]

I prefer Shankar over Sakurai for general QM but if you only want to understand two-level systems, neither of them exactly cuts to the chase.

posted by Herr Zebrurka at 8:05 PM on November 4, 2014

*Quantum Computation and Quantum Information*by Nielsen and Chuang would probably be useful to you. It's used in many classes and was written with both physicists and computer scientists in mind. Chapter 2 gives an overview of quantum mechanics that should be sufficient to understand the rest of the book.posted by Herr Zebrurka at 8:05 PM on November 4, 2014

Susskind's Theoretical Minimum lectures give a ground up intro to the maths, though they also cover the physics bases.

posted by StephenF at 1:48 AM on November 5, 2014 [1 favorite]

posted by StephenF at 1:48 AM on November 5, 2014 [1 favorite]

the problem with this question is that you are kind of asking how can I learn just enough vocabulary of $FOREIGNLANGUAGE to read this article... but you can't "read" without at least a rudimentary grasp of the language, rather than just the vocabulary.

the mathematical answer to what is bra-ket knowledge is actually really simple:

given vectors "x" and "y," < x| y > is an inner product of "x" and "y" and < x| and |y > are linear operators defined by inserting "x" or "y" into the left and right slots of (bilinear form defining) the inner product (note that "linear operators" so defined also form a vector space.) (note that < x| and |y > don't live in the same vector space)

you can see how convoluted wikipedia articles tend to be on mathematical topics. on the other hand and what this has to with quantum computing or quantum mechanics in general is opaque. unfortunately, depending upon the context, a and b could be vectors in an infinite dimensional vector space... which accounts for the verbosity and confusion of the wikipedia article linked above. the wikipedia article on Grover's Algorithm seems sane, but quantum mechanics tends to use linear algebra over complex vectors spaces, which brings in things like "unitary" operators, which you don't see in real vector spaces, if that's what you are familiar with.

probably the cleanest introduction to quantum mechanics at an undergraduate level that is still mathematical is "Introduction to Quantum Mechanics" by "David J. Griffiths." personally, i find Griffiths to be kind of annoying to read, but it is both concise and mathematical.

tldr; quantum mechanics for quantum computing depends on an intermediate understanding of complex linear algebra and a basic understanding of quantum mechanics.

posted by ennui.bz at 3:42 AM on November 5, 2014 [1 favorite]

the mathematical answer to what is bra-ket knowledge is actually really simple:

given vectors "x" and "y," < x| y > is an inner product of "x" and "y" and < x| and |y > are linear operators defined by inserting "x" or "y" into the left and right slots of (bilinear form defining) the inner product (note that "linear operators" so defined also form a vector space.) (note that < x| and |y > don't live in the same vector space)

you can see how convoluted wikipedia articles tend to be on mathematical topics. on the other hand and what this has to with quantum computing or quantum mechanics in general is opaque. unfortunately, depending upon the context, a and b could be vectors in an infinite dimensional vector space... which accounts for the verbosity and confusion of the wikipedia article linked above. the wikipedia article on Grover's Algorithm seems sane, but quantum mechanics tends to use linear algebra over complex vectors spaces, which brings in things like "unitary" operators, which you don't see in real vector spaces, if that's what you are familiar with.

probably the cleanest introduction to quantum mechanics at an undergraduate level that is still mathematical is "Introduction to Quantum Mechanics" by "David J. Griffiths." personally, i find Griffiths to be kind of annoying to read, but it is both concise and mathematical.

tldr; quantum mechanics for quantum computing depends on an intermediate understanding of complex linear algebra and a basic understanding of quantum mechanics.

posted by ennui.bz at 3:42 AM on November 5, 2014 [1 favorite]

For someone with a mathematical education, it should be possible to get into quantum information without learning about wave functions, angular momentum, or harmonic oscillators. A book like Nielsen and Chuang is written to provide that shortcut. It should get you to a point where you can understand the details of the algorithms. I had it as a course book long ago, and factorizing 15 with Shore's algorithm on paper was one of the exam problems.

However, if you find that the mathematical foundation there is insufficient, I can't think of a better resource than Shankar's book,

posted by Herr Zebrurka at 11:18 AM on November 5, 2014

However, if you find that the mathematical foundation there is insufficient, I can't think of a better resource than Shankar's book,

*Principles of Quantum Mechanics*. Both Griffiths and Sakurai dive straight into the physics and develop the notation as they go. In contrast, Shankar postpones all the physics (not just the experiments) until after he's gone through the mathematical framework and notation where the physics is later going to fit in. As a quantum physicist I like that approach, and for someone in your situation it should be close to ideal.posted by Herr Zebrurka at 11:18 AM on November 5, 2014

This might be a little light on detail but: http://arxiv.org/abs/quant-ph/9809016

posted by piyushnz at 11:44 AM on November 5, 2014

posted by piyushnz at 11:44 AM on November 5, 2014

All of these resources are great. I've marked as "best answer" those that really get at the heart of my question.

Susskind's "Theoretical Minimum" lectures come at physics from a perspective I find a lot easier to understand and more interesting than the sort of engineering-motivated problems you usually see in a physics class. I'll probably watch them because why not get the background.

posted by vogon_poet at 12:35 PM on November 5, 2014

Susskind's "Theoretical Minimum" lectures come at physics from a perspective I find a lot easier to understand and more interesting than the sort of engineering-motivated problems you usually see in a physics class. I'll probably watch them because why not get the background.

posted by vogon_poet at 12:35 PM on November 5, 2014

Another option that might be interesting for you, if you want to learn QM from a linear algebra point of view, rather than from a differential equations point of view, is "The Physics of Quantum Mechanics" by James Binney. His lecture series based on the book is on youtube, so maybe try them out to see if it's for you before buying anything. I think his approach is worth following if you're happy to really dig into the maths, and it should give you a better perspective on quantum computing than starting from the Schrodinger equation, but if you just want to understand a few results, maybe it's overkill.

posted by Ned G at 5:21 AM on November 6, 2014

posted by Ned G at 5:21 AM on November 6, 2014

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posted by Dmenet at 6:52 PM on November 4, 2014