It didn't say their exam was an entire postgraduate exam. It said they passed an exam consisting of questions from a postgraduate exam.
I'd guess that if someone tried to take the entire exam it would include things that do require "complex math" (whatever that is). But you don't have to get to the parts of QM that require such math in order to cover things that exhibit the meat of QM, such as superposition, entanglement, and uncertainty principles. I'd guess that it was those kinds of things covered for these students and that is what they were tested on.
I have doubt that anyone with a high school maths would even understand any of these (2023 MSc QM level Oxford exam) [1] . but reading the original source on the study [2] it seems like it is not this or any of what we expect.
> This article is concerned with a new language for quantum, to which we refer as quantum picturalism (QPict) [5]. It
is the subject of two books written by some of the authors, respectively entitled Picturing Quantum Processes [10] and
Quantum in Pictures (QiP) [9]. The first one is the text book of an Oxford University postgraduate course that has been
running for well over ten years now. The second one, remarkably, has no mathematical prerequisites beyond what is already
taught to 6-7 year olds in the UK, namely angles
String diagrams of category theory potentially make working with invariants easier by embedding them in graphical transformations, so they "just maintain themselves". Eg, electric circuit laws.[2] Or here, ZX-calculus/diagrams for QM.[3]
Major milestone for ZX-alike calculi: now for all finite dimensions, with completeness theorem. I.e. for all dimensions any equation derivable using Hilbert space maths, is derivable with pictures! ZXW moreover allows for differentiation, integration and exponentiation.
One of the high school student went on publishing a paper applying what he learned during the course, but I can't find it anymore.
A sibling comment posted a 900 page pdf textbook[0] on the subject which mentions the word hydrogen once (discussing the Stern-Gerlach experiment). It doesn't mention atomic spectra at all. It doesn't mention the word "chemistry" at all.
Here's the eigenfunctions and energy levels of the wavefunction for a hydrogen-like atom[1], equations derivable in the Hilbert space formalism which explain the Rydberg formula[2] and offer a path toward understanding molecular bonding. This stuff is usually covered in an introductory quantum mechanics course, which immediately requires you to work with infinite dimensional Hilbert spaces.
The process calculus stuff is neat, but it's not really covering what you might call "quantum physics". The mentioned textbook says it's "about telling the story of quantum theory entirely in terms of pictures", but it doesn't even mention what quantum theory is about. It starts with saying a photon or an electron might be a typical system, but what's a photon and why do we think they exist? What does it mean to say electrons are quantum systems, and why do we think they are?
A standard introductory text like Griffiths (which is also kind of unmotivated but at least covers the material) has e.g. this problem 5.11a: "Figure out electron configuration for the first two rows of the periodic table (up to neon)".
