Quantum Computing Questions
The controlled-V gate, also known as the controlled-phase gate or controlled-R gate, is a quantum gate that applies a phase shift to the target qubit based on the state of the control qubit. It is represented by the matrix:
[[1, 0, 0, 0],
[0, 1, 0, 0],
[0, 0, 1, 0],
[0, 0, 0, V]],
where V is a complex number representing the phase shift applied to the target qubit when the control qubit is in the state |1⟩. When the control qubit is in the state |0⟩, no phase shift is applied. The controlled-V gate is a fundamental building block in quantum algorithms and quantum error correction codes.