A strategy is suggested for teaching mathematically literate students, with no background in physics, just enough quantum mechanics for them to understand and develop algorithms in quantum computation and quantum information theory. Although the article as a whole addresses teachers of physics, well versed in quantum mechanics, the central pedagogical development is addressed directly to computer scientists and mathematicians, with only occasional asides to their teacher. Physicists uninterested in quantum pedagogy may be amused (or irritated) by some of the views of standard quantum mechanics that arise naturally from this unorthodox perspective.
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David Mermin has written a very good introduction specifically targeted towards computer scientists and mathematicians looking to learn and contribute to this field. His book "Quantum Computer Science" is really great, and I highly recommend reading it if you're interested in learning more. Basic linear algebra is pretty much all that's required, although familiarity with mathematical notation definitely helps.
A good place to start might be this paper by Mermin, which defines classical computing bits (Cbits) in a specific mathematical framework and then expands that definition to define Qbits and their states: https://arxiv.org/pdf/quant-ph/0207118.pdf
An accessible quick introduction. This abstract links to a 19-page pdf:
From Cbits to Qbits: Teaching computer scientists quantum mechanics N. David Mermin
https://arxiv.org/abs/quant-ph/0207118
After that, the textbook by Nielsen and Chuang, Quantum Computation and Quantum Information. It's a big book but
the first couple of chapters, 60 pages or so, are self-contained and make a good introduction.
Sure. Here are a few resources; they vary in technical complexity and depth of coverage, but they're all rigorous:
Scott Aaronson has a good introductory article in Scientific American[1], and he also wrote a short, accessible article aimed at high school students in 2002[2].
Then there's Berkeley's CS 191 Qubits, Quantum Mechanics and Computers syllabus and lectures[3].
Tel Aviv University has lecture notes for the 1997 Quantum Information Processing course online[4]. These are old, but the information is still fundamentally accurate if what you're looking for is a breadth-wise introduction to the topic.
There's the paper, From Cbits to Qbits: Teaching Computer…
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Scientists Quantum Mechanics on arXiv[5].
I assume you have a computer science background; if that's the case, you might want to start with for light reading on the meta between classical and quantum computing, then dive into one of the lecture notes series. The first two resources are much more digestible; if you're looking for something to read in 10 minutes or so and come away with a basic understanding of the field, those are what you want to read.
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1. http://www.cs.virginia.edu/~robins/The_Limits_of_Quantum_Com...
2. http://www.scottaaronson.com/writings/highschool.html
3. http://www-inst.eecs.berkeley.edu/~cs191/sp05/
4. http://www.tau.ac.il/~tsirel/Courses/QuantInf/syllabus.html
5. https://arxiv.org/abs/quant-ph/0207118
Here is a nice short (19 page) introduction:
From Cbits to Qbits: Teaching computer scientists quantum mechanics by N. David Mermin
http://arxiv.org/abs/quant-ph/0207118
The standard (very big) textbook is Nielsen and Chuang, Quantum Computing and Quantum Information. It answers all your questions and much more. Much of it is an advanced college physics textbook, but some of the chapters are quite accessible.
In response to Jaffe and Quinn [math.HO/9307227], the author discusses forms of progress in mathematics that are not captured by formal proofs of theorems, especially in his own work in the theory of foliations and geometrization of 3-manifolds and dynamical systems.
Artificial intelligence (AI) researchers have been developing and refining large language models (LLMs) that exhibit remarkable capabilities across a variety of domains and tasks, challenging our understanding of learning and cognition.
The Fermi paradox is the conflict between an expectation of a high {\em ex ante} probability of intelligent life elsewhere in the universe and the apparently lifeless universe we in fact observe.