[Quantum Computing] Quantum Parallelism State Calculation

In summary, the resulting state of applying the operator for quantum parallelism should be (1/sqrt(2^4)) * (|0, f(0)> + |0, f(1)> + |1, f(1)> + |1, f(0)>). However, this would be useless to measure and to understand where you are going wrong, it is recommended to apply the operator over the base states and use linearity to get the final state.
  • #1
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Nielsen and Chuang state calculation isn't the full tensor product? But a full tensor product would be useless to measure?
Hi, I'm going through Nielsen and Chuang's Quantum Computation and Quantum Information textbook and I don't really understand this part about quantum parallelism:
1626469417681.png


Shouldn't the resulting state be (1/sqrt(2^4)) * (|0, f(0)> + |0, f(1)> + |1, f(1)> + |1, f(0)>), since the resulting state would be the (normalized) tensor product of (1/sqrt(2)) * (|0> + |1>) and (1/sqrt(2)) * (|f(0)> + f(1)>)?

I understand that would be pretty useless to measure, so I know I'm wrong, but I don't understand where I'm going wrong. Thanks in advance.
 
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  • #2
A state of two qubits can be written in the base ##\left|00\right>, \left|01\right>, \left|10\right>, \left|11\right>##. I would recommend you to apply the operator over these 4 states such that you really understand how the operator works, after that you can write the initial state as a linear combination of those states and use linearity and the previous result to get the final state.
 

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