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I'd like to know what rung of the math ladder one need be on to grasp how a quantum computer computes.

I realize this might not be a simple answer, so I'm just looking for an idea of the broad topics required.


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Linear algebra gets used a lot in quantum computing. – Srivatsan Nov 10 '11 at 3:52
Fourier analysis on groups. – anon Nov 10 '11 at 4:07
To all that are interested in Quantum Information: The Quantum Information and Foundations proposal is currently in commitment phase. – draks ... May 8 '12 at 17:48
up vote 2 down vote accepted

For the foundation you need to understand linear algebra, projective geometry and how to build circuits out of AND, OR, NOT gates. For the algorithms themselves, you need to know a little about rational approximations and the Fourier transformation. You can start to learn about Quantum Computing from here but I also recommend working through the book he wrote.

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Since all quantum algorithms I know, deal with finite dimensional system, knowledge of unitary groups $\text{U}(N)$ is important, because it governs the evolution of the finite quantum system without relaxation. For the QA to approximate the Jones Polynomial, it doesn't hurt to know something about knot theory.

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