Full classical: physical quantities are scalars (x, p), fields are classical fields (E, B)
Semiclassical (first quantization): physical quantities are now operators.
Full quantum (second quantization): all fields are now field operators.
from wikipedia, second quantization is a misnomer:
> The term "second quantization" is a misnomer that has persisted for historical reasons. At the origin of quantum field theory, it was incorrectly thought that the Dirac equation described a nrelativistic wave function (hence the mistaken "Dirac sea" interpretation), rather than a classical spinor field which, when quantized (like the scalar field), yielded a fermionic quantum field (vs. a bosonic quantum field).
> One is not quantizing "again", as the term "second" might suggest; the field that is being quantized is not a Schrödinger wave function that was produced as the result of quantizing a particle, but is a classical field (such as the electromagnetic field or Dirac spinor field) that was not previously quantized. One is merely shifting from a semiclassical treatment of the system to a fully quantum-mechanical one.
I would love to see one in rust there'd be real advantages for asynchronous parallelism in some of the most sophisticated models.
Could you expand on this? it's my understanding that these engines already use lapack/blas for higher dimension numerical calculations, which are already parallelized.