Quantum Computing is a new and exciting field at the intersection of mathematics, computer science and physics. It concerns a utilization of quantum mechanics to improve the efficiency of computation. Here we present a gentle introduction to some of the ideas in quantum computing. The paper begins by motivating the central ideas of quantum mechanics and quantum computation with simple toy models. From there we move on to a formal presentation of the small fraction of (finite dimensional) quantum mechanics that we will need for basic quantum computation. Central notions of quantum architecture (qubits and quantum gates) are described. The paper ends with a presentation of one of the simplest quantum algorithms: Deutsch's algorithm. Our presentation demands neither advanced mathematics nor advanced physics.
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OP Here:
I just wanted to give some context to how I found this page, and why I thought it would be good to post.
I may be putting myself on the spot here: I never took a linear algebra course in undergrad. It was a heavily encouraged option, of course, but I felt I understood the basic rules enough to not really need formal study. I opted to study other areas, partially motivated by a fear I wouldn't do well and would hurt my GPA (my god was I vain, I feel I could do so much more studying full-time with my current world-view).
As time has gone on, and ML and quantum computing have simply blown up since I graduated in 2014, I quickly realized the magnitude of my mistake.…
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I have frantically self-studied for years to try to make up the gaps in my mathematical understanding, and linear algebra has come up time and time again. I can do the processes, but they never clicked, I had no intuition.
I want to help others in my position cut to the chase, and study the highest yield, most intuition giving resources.
I actually developed the mental model shared in this guide on my own, and was positively delighted to find to this while thinking over a comment I was drafting on here. This page lays things out so clearly. The component steps are intuitive and I can commit them to memory/recall what they mean without needing to dig up my notes to self!
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I find this page gives an excellent foundation, and goes great with these resources:
* A web site which clearly shows how to do matrix multiplication in a way that's easy to recall, it makes the procedure like riding a bike:
http://matrixmultiplication.xyz/
Huge thanks to Jeremy Howard of fast.ai for mentioning this in one of his lectures, this tool is how I finally got matrix multiplication to click
* A paper named "An Introduction to Quantum Computing" (bear with me, it's superbly well written and very approachable):
https://arxiv.org/abs/0708.0261
Page 3 of that paper lays out matrix multiplication (e.g.: applying a "transformation matrix" in the spatial parlance of 3blue1brown's videos) as a traversal of a directed graph. A very useful understanding, and shows how generalizable the tools of linear algebra really are in my opinion.
* The essence of linear algebra, by 3blue1brown (fantastic for a geometric/"transformation of space" view of linear alg):
https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2x...
Linear Algebra is very important for Quantum Computing. You have a masters in engineering, so you shouldn't have any problems with the math. I suggest you review the basics of Linear Algebra if you haven't applied that knowledge in a while.
John Preskill's lecture notes are invaluable. They start from the basics of Quantum Computing, to Quantum Theory, all the way to advanced concepts such as Topological Quantum Computation:http://www.theory.caltech.edu/people/preskill/ph229/
You can also look over the Quantum Computation course that is hosted at OCW. The instructor for this course was Peter Shor who invented the seminal "Shor's…
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Algorithm":https://ocw.mit.edu/courses/mathematics/18-435j-quantum-comp...
These will be enough to get you started, but it is good apply your knowledge by implementing the quantum algorithms that you have learned.There is a huge list of simulators you can use:https://www.quantiki.org/wiki/list-qc-simulators
I know you want references to open courses, but reading papers shouldn't hurt either. I don't know how much experience you have with Quantum Mechanics, but this paper:https://arxiv.org/abs/0708.0261 explains Quantum Computing very well by referring to concepts in Classical Computing. You should read this first if you are not familiar with Quantum Mechanics.
Let me know if you have any questions and good luck!
The paper http://arxiv.org/abs/0708.0261 is a reasonably good introduction with a fair amount of math.
If you're looking for a non-technical overview, you might try https://uwaterloo.ca/institute-for-quantum-computing/quantum... but I don't think English alone is precise enough to explain anything really interesting about quantum computing.
I gained some great intuition from http://matrixmultiplication.xyz/ and (of all things) a paper named "An Introduction to Quantum Computing"[0].
Page 3 of that paper lays out matrix multiplication (e.g.: applying a "transformation matrix" in the spatial parlance of 3blue1brown's videos) as a traversal of a directed graph.
This isn't super readable (it's from my notes to self), but my intuition is:
Matrix multiplication is a graph traversal:
* Each i,j in transform matrix (on left) pulls N (the value at that index) times the j-th value in the input vec (on right) into the i-th output vec index
* This is equivalent to an N weighted vertex from the j-th node to i-th node, so i takes N of j's previous value
* The input (right side) is a matrix? It's just multiple column vectors next to each other, repeat the above process and make a new output vector for each iteration
[0]: https://arxiv.org/abs/0708.0261
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.