11:16 AM
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If we have a physical qubit with energy eigenstates $|0\rangle$ and $|1\rangle$ with energy separation $\Delta E$ its Hamiltonian in the absence of any interaction is $$H=\hbar\frac{\Delta E}{2}\sigma_z$$ the time evolution operator is $U=e^{-iHt/\hbar}$, so why doesn't a qubit left to itself ...

11:36 AM
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Given a complex matrix $M = \begin{pmatrix} c & 0\\ 0 & c^* \end{pmatrix}$, where $c$ is a complex number. How can one express $M$ in terms of the fundamental quantum logic gates?