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Given a paramterised quantum circuit with adjustable gates, why do you need (why is it common) to initialise the qubits of the circuit at $|0\rangle$. What is the classical interpretation of this?

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To be able to initialize a quantum computer with some initial state is one of DiVincenzo criteria of quantum computing. To start with all qubits in state $|0\rangle$ seems reasonable, as it is an analog to initialize a numeric variable to zero on a classical computer (of course, some languages like C++ starts with some garbage in the variable but e.g. Visual Basic initialize numeric variables to zero).

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