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<text>Shor's algorithm is an example of the standard model of quantum algorithms.</text>
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<text>A quantum oracle can be thought of as black box which produces an [mathjaxinline]n[/mathjaxinline]-qubit quantum state.</text>
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<text>Phase estimation is an example of the quantum oracle model of quantum algorithms category.</text>
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<text>Grover's algorithm is an example of the standard model of quantum algorithms category.</text>
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<h2 class="hd hd-2 unit-title">CQ: Abelian quantum Fourier transform</h2>
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Abelian quantum Fourier transform
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<p>
This is a concept question, provided to check your understanding of the previous lecture video clips. </p>
<p>
Which of the following are true? </p>
<p>
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<text>A character is a map from a group to complex numbers.</text>
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<text>The images of characters of abelian groups are roots of unity.</text>
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<text>[mathjaxinline]\mathbb {Z}_ N[/mathjaxinline] is abelian.</text>
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<text>The characters of [mathjaxinline]\mathbb {Z}_ N[/mathjaxinline] are the same as the characters of [mathjaxinline]\mathbb {Z}_ N^\times[/mathjaxinline].</text>
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Quantum Fourier transform over an Abelian group
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<p>
This is a concept question, provided to check your understanding of the previous lecture video clips. </p>
<p>
Which of the following are true? </p>
<p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div class="choicegroup capa_inputtype" id="inputtype_cq_M2L15_Quantum_Fourier_transform_over_an_Abelian_group_2_1">
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<text>The quantum Fourier transform over [mathjaxinline]\mathbb {Z}_{2^ n}[/mathjaxinline] is the conventional Fourier transform.</text>
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<text>The right group multiplication operator is defined according to [mathjaxinline]R_ g |{x}\rangle = |{g x}\rangle[/mathjaxinline].</text>
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<text>The quantum Fourier transform over [mathjaxinline]\mathbb {Z}^ n_{2}[/mathjaxinline] is the conventional Fourier transform.</text>
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<text>Phase estimation uses the conventional quantum Fourier transform.</text>
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<h2 class="hd hd-2 unit-title">A quick application of Fourier transform: quantum phase estimation</h2>
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