Electrons do not orbit.

For the simple case of an electron in a hydrogen atom, energy-stable wavefunctions are products of three separate functions: exponential function, a laguerre polynomial function and a spherical harmonic.

Presumably the GP meant orbitals.

It's an important distinction. A lot of people would like to think electrons orbit the nucleus like planets orbit a star.

Yes, but someone thinking in terms of the Bohr model would not ask is the orbits are (described by) spherical harmonics.

Yes.

More details: The orbitals are the product of an Harmonic Orbital and a radial function. More details in https://en.wikipedia.org/wiki/Atomic_orbital#Types_of_orbita... and https://en.wikipedia.org/wiki/Hydrogen-like_atom#Non-relativ...

Note that this is the initial selection of orbitals. The "real"[1] orbitals are linear combinations of them. In some cases it's good enough to mix them using some easy combinations like in https://en.wikipedia.org/wiki/Orbital_hybridisation but in the general cases you must use a computer to calculate the best combination https://en.wikipedia.org/wiki/Hartree%E2%80%93Fock_method .

[1] It get's more complicated.

How might spherical harmonics be relevant for quantum computing? I’m on the hunt for visualizations. (Not to be confused with the Bloch Sphere!)

Spherical harmonics are a useful mathematical basis set for eigenfunctions of a Schrodinger equation describing a hydrogen atom like system.

There's nothing particularly special about them, and they fail to be a good basis set for solutions of other types of quantum systems. Conversely, they can be useful for non-quantum systems - any sort of wave equation in a sphere.

It's not an intrinsically quantum mechanical thing.

Idk… seems intrinsic in so far as waves are intrinsic to Quantum Mechanics.

Check out these visuals from “the orbitron”: https://winter.group.shef.ac.uk/orbitron/