Ex7 1

$\def\abs#1{|#1|}\def\i{\mathbf {i}}\def\ket#1{|{#1}\rangle}\def\bra#1{\langle{#1}|}\def\braket#1#2{\langle{#1}|{#2}\rangle}\mathbf{Exercise\ 7.1}$

In the standard circuit model of section 5.6, the computation takes place by applying quantum gates. Only at the end are measurements performed. Imagine a computation that proceeds instead as follows. Gates $G_{0}, G_{1}, \dots, G_{n}$ are applied, then qubit $i$ is measured in the standard basis and never used again. If the result of the measurement is $0$, the gates $G_{01}, G_{02}, \dots, G_{0k}$ are applied. If the result is $1$, then gates $G_{11}, G_{12}, \dots, G_{1l}$ are applied. Find a single quantum circuit in the standard circuit model, with only measurement at the very end, that carries out this computation.

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