Consider the single bit flip error detecting and correcting…

Consider the single bit flip error detecting and correcting circuit as shown below. (Note that, the choice of convention does not affect the answer in this problem.) Given that the error gate ‘E’ is of the form I1⊗X2⊗I3{“version”:”1.1″,”math”:”\(I_1 \otimes X_2 \otimes I_3\)”}.What is the state of the ancillary qubit A1{“version”:”1.1″,”math”:”\(A_1\)”} at the ‘Stage’ marked in red?

Consider the linear adiabatic evolution path taking us from…

Consider the linear adiabatic evolution path taking us from a single qubit Hamiltonian Hinitial=(I+σx)/2{“version”:”1.1″,”math”:”\(H_{initial} = (I+\sigma_x)/2\) “} at time t=0{“version”:”1.1″,”math”:”\(t=0\)”} to a final Hamiltonian Hfinal=(I−σz)/2{“version”:”1.1″,”math”:”\(H_{final} = (I-\sigma_z)/2\)”} at time t=tf{“version”:”1.1″,”math”:”\(t=t_f\)”} such that H(t)=(t/tf)Hfinal+(1−t/tf)Hinitial{“version”:”1.1″,”math”:”\(H(t) = (t/t_f) H_{final} + (1- t/t_f) H_{initial}\)”} for 0≤t≤tf{“version”:”1.1″,”math”:”\(0 \leq t \leq t_f\)”}.  What are the ground states of the qubit at the initial and final times, i.e. at t=0{“version”:”1.1″,”math”:”\(t=0\)”} and t=tf{“version”:”1.1″,”math”:”\(t=t_f\)”}?

In the following circuit, what is the probability for the me…

In the following circuit, what is the probability for the measurement outcome of Qubit 1 to be in state |1⟩? Here, the states are expressed in the convention |Qubit2⊗Qubit1⟩{“version”:”1.1″,”math”:”\(\vert Qubit_2 \otimes Qubit_1 \rangle\)”}.