math.stackexchange.com/questions/2382011/computational-complexity-of-modular-exponentiation-from-rosens-discrete-mathem mentions:
can be calculated in:
Remember that and are the lengths in bits of and , so in terms of the length in bits and we'd get:
Lemma (mathematics) Updated 2025-07-16
A theorem that is not very important on its own, often an intermediate step to proving something that the author feels deserves the name "theorem".
Cow Updated 2025-07-16
Ungulate Updated 2025-07-16
Ustad Updated 2025-07-16
Puriya Updated 2025-07-16
Video 1.
Raag Puriya Dhanashri performed on the Sitar by Shahid Parvez
. Source.
Evening raga Updated 2025-07-16
Raga Updated 2025-07-16
Empty circle control qubit notation Updated 2025-07-16
Some authors use the convention of:
Controlled quantum gate Updated 2025-07-16
Controlled quantum gates are gates that have two types of input qubits:
These gates can be understood as doing a certain unitary operation only if the control qubits are enabled or disabled.
The first example to look at is the CNOT gate.
Figure 1. . Source.
The black dot means "control qubit", and "U" means an arbitrary Unitary operation.
When the operand has a conventional symbol, e.g. the Figure "Quantum NOT gate symbol" for the quantum NOT gate to form the CNOT gate, that symbol is used in the operand instead.
Alps Updated 2025-07-16
Multi-qubit gate Updated 2025-07-16
The most common way to construct multi-qubit gates is to use single-qubit gates as part of a controlled quantum gate.

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