Hadamard gate by Ciro Santilli 37 Updated 2025-07-16
The Hadamard gate takes or (quantum states with probability 1.0 of measuring either 0 or 1), and produces states that have equal probability of 0 or 1.
Equation 1.
Hadamard gate matrix
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Figure 1.
Hadamard gate symbol
. Source.
Some authors use the convention of:
Lemma (mathematics) by Ciro Santilli 37 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".
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:
Sum of three cubes by Ciro Santilli 37 Updated 2025-07-16
Compared to Waring's problem, this is potentially much harder, as we can go infinitely negative in our attempts, there isn't a bound on how many tries we can have for each number.
In other words, it is unlikely to have a Conjecture reduction to a halting problem.
Video 1.
3 as the sum of the 3 cubes by Numberphile (2019)
Source.
Waring's problem by Ciro Santilli 37 Updated 2025-07-16
And when it can't, attempt to classify which subset of the integers can be reached. E.g. Legendre's three-square theorem.

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