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Can you construct a 3-qubit XOR state?

You wish to prepare your state into the uniform superposition of three qubits $\{q_1,q_2,q_3\}$ such that $q_3=q_1\oplus q_2$, starting from some canonical basis element (which is conventionally the ...
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Does quantum superposition allow to apply an algorithm to all bits possibly in one shot?

No, you're not missing something. Talking about being able to apply an algorithm for all possible inputs in a single shot is misleading. As you've found, you cannot read out all those answers; you can ...
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How does superposition in a quantum register work?

According to the Solovay-Kitaev theorm, the Clifford gates (which are generated by $H$, $S$ and $CNOT$), along with a non-Clifford gate - say the $T$ gate, can be used to approximate any unitary down ...
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