Nielsen, Michael A., and Chuang, Isaac L. Quantum Computation and Quantum Information / Michael A. Nielsen and Isaac L. Includes bibliographical references and index. ISBN 0-521-63503-9 1. QA401.G47 2000 5110.8dc9 CIP ISBN 0 521 63235 8 hardback ISBN 0 521 63503 9 paperback.

The quantum fourier transform on an orthonormal basis $ket{0}, cdots ,ket{N - 1}$ is defined to be a linear operator with the following action on the basis states, How to view encrypted password.

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Nielsen and Chuang Solutions This is a non-official, still expanding solution manual to Nielsen and Chuang's Quantum Computation and Quantum Information. I use the 10th Anniversary Edition for problem numbering. By using this site, you consent to the use of cookies. For more information, please see our Cookie Policy.

(5.2) Explicitly compute the Fourier transform of the $n$ qubit state $ket{00cdots 0}$.

Nielsen And Chuang Solutions Manual 14th Edition

Nielsen And Chuang Solutions Manual Pdf

$ket{00 cdots 0 }$ corresponds to state $ket{0}$ in the size $N = 2^n$ computational basis. Hence, using the formula above we have

(5.7) Additional insight into the circuit above may be obtained by showing, as you should now do, that the effect of the sequence of controlled-$U$ operations like that in the figure is to take the state $ket{j}ket{u}$ to $ket{j} U^jket{u}$. (Note that this does not depend on $ket{u}$ being an eigenstate of $U$.)

Nielsen And Chuang Solutions Manual 5th

Consider an arbitrary $j$ in its binary representation $j_0j_1 cdots j_{t-1}$ where $j_i in { 0, 1}$. Hence, for each $ket{j_i}$, the control-$U$ acts on $ket{j_i}ket{u}$ such that $ket{j_i}ket{u} mapsto ket{j_i}U^{j_i 2^i}ket{u}$. Therefore, the final state is given by