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Update week11.do.txt
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doc/src/week11/week11.do.txt

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@@ -7,7 +7,7 @@ DATE: April 2, 2025
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===== Plans for the week of March 31-April 4, 2025 =====
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o Discrete Fourier transforms (DFTs, reminder from last week) ) and the fast Fourier Transform (FFT)
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o Discrete Fourier transforms (DFTs, reminder from last week) ) and the fast Fourier Transform (FFT) (additional slides)
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o Quantum Fourier transforms (QFTs), reminder from last week
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o Setting up circuits for QFT
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o Quantum phase estimation algorithm
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that, for example, it was known to Gauss back in 1805.
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To read more about Fast Fourier transforms and similar topics, see for example "Fast Fourier Transform - Algorithms and Applications":"https://link.springer.com/book/10.1007/978-1-4020-6629-0". See also URL:"https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/Textbooks/fastfourier.pdf"
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Our emphasis is on the link between discrete Fourier transforms and quantum Fourier transforms. We will not discuss FFT in this course.
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For a discussion of FFT, see additional slides at (address to be added)
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!et
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===== Fast Fourier transform and polynomial multiplication =====
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The FFT algorithm is an $O(n\log{n})$ divide and conquer algorithm for DFT, used by
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Gauss circa 1805, and popularized by Cooley and Turkey and 1965. Gauss used the
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algorithm to determine periodic asteroid orbits, while Cooley and Turkey used it to
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detect Soviet nuclear tests from offshore readings.
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A practical implementation of FFT is FFTW, which was described by Frigo and
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Johnson at MIT. The algorithm is often implemented directly in hardware, for fixed $n$.
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===== From DFT to QFT =====
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