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Quantum Computing - Interview Questions
What about Inputs and outputs of quantum circuits in Quantum Computing?

The previous examples have had precisely the same number of wires (qubits) input to a quantum gate as the number of wires out from the quantum gate. It may at first seem reasonable that quantum circuits could have more, or fewer, outputs than inputs in general. This is impossible, however, because all quantum operations, save measurement, are unitary and hence reversible. If they did not have the same number of outputs as inputs they would not be reversible and hence not unitary, which is a contradiction. For this reason any box drawn in a circuit diagram must have precisely the same number of wires entering it as exiting it.

Multi-qubit circuit diagrams follow similar conventions to single-qubit ones. As a clarifying example, a two-qubit unitary operation B can be defined to be (HS⊗X), so the equivalent quantum circuit is:

Circuit diagram of a two-qubit unitary operation

You can also view B as having an action on a single two-qubit register rather than two one-qubit registers depending on the context in which the circuit is used.

Perhaps the most useful property of such abstract circuit diagrams is that they allow complicated quantum algorithms to be described at a high level without having to compile them down to fundamental gates. This means that you can get an intuition about the data flow for a large quantum algorithm without needing to understand all the details of how each of the subroutines within the algorithm work.

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