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Author Archives: hecker
Quantum Country exercise 6
This is one in a series of posts working through the exercises in the Quantum Country online introduction to quantum computing and related topics. The exercises in the original document are not numbered; I have added my own numbers for … Continue reading
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Quantum Country exercise 5
This is one in a series of posts working through the exercises in the Quantum Country online introduction to quantum computing and related topics. The exercises in the original document are not numbered; I have added my own numbers for … Continue reading
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Quantum Country exercise 4
This is one in a series of posts working through the exercises in the Quantum Country online introduction to quantum computing and related topics. The exercises in the original document are not numbered; I have added my own numbers for … Continue reading
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Quantum Country exercise 3
This is one in a series of posts working through the exercises in the Quantum Country online introduction to quantum computing and related topics. The exercises in the original document are not numbered; I have added my own numbers for … Continue reading
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Quantum Country exercise 2
This is one in a series of posts working through the exercises in the Quantum Country online introduction to quantum computing and related topics. The exercises in the original document are not numbered; I have added my own numbers for … Continue reading
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Quantum Country exercise 1
This is the first in a series of posts working through the exercises in the Quantum Country online introduction to quantum computing and related topics. The exercises in the original document are not numbered; I have added my own numbers … Continue reading
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Variance and the sum of squared pairwise differences
The variance of a set of values is usually expressed in terms of squared differences between those values and the mean of those values. However the sum of squared differences between the values and the mean can also be expressed … Continue reading
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All lengthpreserving matrices are unitary
I recently read the (excellent) online resource Quantum Computing for the Very Curious by Andy Matuschak and Michael Nielsen. Upon reading the proof that all lengthpreserving matrices are unitary and trying it out myself, I came to believe that there … Continue reading
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Linear Algebra and Its Applications, Exercise 3.4.28
Exercise 3.4.28. Given the plane and the following vectors in the plane, find an orthonormal basis for the subspace represented by the plane. Report the dimension of the subspace and the number of nonzero vectors produced by GramSchmidt orthogonalization. Answer: … Continue reading
Linear Algebra and Its Applications, Exercise 3.4.27
Exercise 3.4.27. Given the subspace spanned by the three vectors find vectors , , and that form an orthonormal basis for the subspace. Answer: We can save some time by noting that and are already orthogonal. We can normalize these … Continue reading