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Bell circuit

A quantum circuit which when fed with input produces the Bell state.
In Qiskit at: qiskit/hello.py.
Figure 7.
Quantum circuit that generates the Bell state
. Source.
The fundamental intuition for this circuit is as follows.
First the Hadamard gate makes the first qubit be in a 50/50 state.
Then, the CNOT gate gets controlled by that 50/50 value, and the controlled qubit also gets 50/50 chance as a result.
However, both qubits are now entangled: the result of the second qubit depends on the result of the first one. Because:
  • if the first qubit is 0, cnot is not active, and so the second qubit remains 0 as its input
  • if the first qubit is 1, cnot is active, and so the second qubit is flipped to 1

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