It is conventional to assume that the state input to the circuit is a computational basis state, usually the state consisting of all $|0\rangle$s. This rule is broken frequently in the literature on quantum computation and quantum information, but it is considered polite to inform the reader when this is the case.

What does this mean?

Source: M. Nielsen and I. Chuang. Quantum Computation and Quantum Information. Cambridge UniversityPress, 2000. (1.3.4 Quantum Circuits)

  • $\begingroup$ What are you confused about? $\endgroup$ – psitae Dec 30 '18 at 11:32
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    $\begingroup$ Are you just confused about the notation? The starting state could be anything depending upon the basis, it is just convenient to use $|0\rangle$s. The book just says that it may be different and that will be informed to the reader. That is not even a scientific issue. $\endgroup$ – Siddhant Singh Dec 30 '18 at 14:35

You have some quantum algorithms assuming you prepared a special input state which is not represented as a superposition of bitstrings.

For example, you can just say you start in the $| + \rangle$ state for all your qubits. Another one is starting in a state where you have encoded your input in the amplitudes of a quantum state (this type of encoding is called amplitude encoding). This is used in quantum linear system solvers (originally HHL) to input a vector in a quantum form to solve a linear system.


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