It's great that "AND" is not taken by itself. It very much helps that AND comes from our language. The AND gate is named after "and" which is an English concept.
The word 'and' is used to group two things that will happen together. For example: "I will go to the park and go to the pool." This is much like the AND gate which only turns on after the two inputs turn on.
Unfortunately "Hadamard" is not part of the English language.
> The problem is that nearly everything on quantum physics is so profoundly unfamiliar that we cannot map these concepts and operations to familiar words
There is no simple way to explain this in laymen terms? From what the Wikipedia article says I doubt that [1].
Why not just call it a "map basis states" operations? That's what the Wikipedia article implies it does.
[1] - https://en.wikipedia.org/wiki/Hadamard_transform#Quantum_com...
Note that the full description in your linked Wikipedia article " a one-qubit rotation, mapping the qubit-basis states |0⟩ and |1⟩ to two superposition states with equal weight of the computational basis states |0⟩ and |1⟩".
If I had to choose a descriptive name, I might call it the "equal superposition" operation; but I'm not a quantum physicist either, so that might be wrong as well.
Of course "Hadamard operation" is part of the English language. If you didn't allow proper nouns and foreign terms to be added to a language, none of the contemporary languages would exist.
True, but the difference is that most people able to communicate with a modern language have an intuitive grasp on the concept of conjunction, and can use that intuition to guess what an "AND" or "OR" or "NOT" might mean, as well as more easily remember what "XOR" or "NAND" or "NOR" might do as long as they can remember that "X" stands for "eXclusive" and "N" stands for "Not".
In other words, to even a basic English speaker, the name "AND" shouldn't really be all that opaque. Any basic English speaker should be able to guess what "AND" means.
In contrast, naming such things after dead mathematicians makes their meanings unintuitive and unguessable to anyone who hasn't memorized said mathematicians and their notable discoveries. As one of those people, I'll take "the lemma where you plug that thing into this mapping and then this thing becomes frobnicated" over "Zorn's lemma" any day; the latter may be more concise, but it's also significantly more opaque, leaving me with absolutely zero starting point to guess what this "lemma" does.
In the context of quantum logic gates/operators, I'd propose some alternative names for things currently named after random people (disclaimer: I'm no expert on quantum mathematics, so my names are probably not really accurate depictions of what such gates do, but rather what I currently understand them to do based on what I can glean about them):
- "Hadamard gate" -> "equally-maybe gate" (gate that ensures equal probability - "maybe" - of a qubit's potential states)
- "Pauli-X gate" -> "maybe-not gate" (gate that inverts the probabilities of a qubit's potential states) / "X flip gate" (gate that rotates the qubit's state space along the X axis)
- "Pauli-Y gate" -> "Y flip gate" (gate that rotates the qubit's state space along the Y axis)
- "Pauli-Z gate" -> "Z flip gate" or "phase flip gate" (gate that rotates the qubit's state space along the Z axis)
- "Toffoli gate" -> "and maybe-not gate" (inverts the third qubit if the first two are both in the |1> state)
- "Fredkin gate" -> "maybe swap gate" (swaps the second and third qubits if the first qubit is in the |1> state)
These possible names are arguably much more intuitive than the names currently assigned to these operators/gates, especially once you're familiar with representing qubits as Bloch spheres (which is another thing that needs renamed; maybe "qubit sphere" or "state sphere" or "state space" like I've put it above would be more appropriate?).
The name "AND" is just as opaque as "Hadamard", if taken by itself. It just doesn't appear as such to you because you already have an intuitive grasp on the concept of conjunction.
The problem is that nearly everything on quantum physics is so profoundly unfamiliar that we cannot map these concepts and operations to familiar words. At that point, it doesn't matter if we call it "the florb operator" or if we name it after some pioneer of the field.
EDIT: Math actually has sort of the opposite problem. They use everyday words for very concrete objects with very concrete definitions. The most notable exception is theorems, but I hope you won't argue that a name like "Zorn's lemma" is more practical than something like "the lemma where you plug that thing into this mapping and then this thing becomes frobnicated".