The quantum computing paradigm has attracted much attention recently and implementations of simple but real quantum computers are happening faster than people expected. While the principles and intuition underlying quantum mechanics are profound and deep, quantum computation as a formal mathematical model is relatively straightforward to understand in terms of ideas well-known to applied mathematicians. Unfortunately, most developments of quantum computing are couched in the language and symbolism of physics, not the traditional mathematics of functional analysis and matrix algebra.
The first part of this talk will be an overview of quantum computing using simple linear algebra and probability ideas leading to some of the important quantum algorithms people have discovered. We will then present some results about the reducibility of quantum computations to simple quantum gate operations using Givens-like rotations applied to unitary matrices. We will finish with some results about the encrypted execution of encrypted quantum computations.
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