Hitting the Books

I’ve recently(-ish) been doing some self-study using textbooks, and I’m briefly capturing some reflections on the process here. As far as I can tell most of the actual learning happens as a result of:

1. my own note-taking, where I re-structure or re-schema what I’m reading into my own terms. This is an active process on multiple levels. First, I need to do some editorial curation in terms of what to capture, elide, or emphasize. Second, I reflect on what I’m jotting down: does this really make sense, are claims seem fully supported, what are the implications of this theorem, and so on. The final artifacts (pages of notes) are a nice encapsulation of my understanding, and I do occasionally revisit and review these. However, I suspect that most of the value I am getting out of the exercise comes from the process itself, where the active engagement with the material makes the content dramatically more “sticky” for me.
2. doing the exercises, where applicable. Generally it seems that the textbook authors have carefully constructed these to test and stretch the reader’s understanding in incremental and valuable ways. I usually choose some sampling of intermediate-difficulty problems, as these feel like the best ROI on my time. I also work through the inline proofs myself, although I generally don’t do them myself from scratch. It would be more accurate to say that I follow along very closely, working out each individual step and convincing myself that it is correct, at roughly the level of a code review. On occasion, I will try to fill in the blanks, either guessing ahead at what the next step should be, or looking ahead at a later step and trying to fill in the intermediate steps myself. This is less challenging than trying to develop a proof entirely on my own, but involves more attention and effort than simply reading it.

I would be remiss not to briefly mention my significant usage of ChatGPT in this process. This topic merits its own entire writeup, but I use the tool as a kind of “Teaching Assistant” on problems where I get stuck, proof steps that don’t make sense, stress-testing intuitions or connections I am developing, and other general questions that come up. An example of this was when I was doing some exercises in Quantum Computing and I kept noticing that certain matrices had the property $AB=-BA$, so I asked about this and learned the proper name for the property (anticommutative) and its connection to the Pauli matrices. For particularly interesting or tricky ideas, I’ve also begun vibe-coding simple simulations or short animated visualizations of concepts using the manim ”community edition” library. As before, the process of developing one of these scripts is itself a productive exercise in terms of building intuitions. So for me, somewhat surprisingly, ChatGPT (or similar) ends up being a very nice complementary resource for self-study alongside traditional textbooks.

That all being said, I should also mention the time I mis-transcribed some of the instructor’s handwriting on the whiteboard from the Quantum Information Coursera and mistakenly asked ChatGPT about the “CHZ quantum state” (which does not exist) instead of the “GHZ state” the instructor was actually talking about. Rather than asking me if I had intended to ask about the Greenberger–Horne–Zeilinger (GHZ) state, ChatGPT confidently hallucinated a plausible sounding explanation centered on 3 quantum researchers (who did indeed exist) with the appropriate initials “CHZ” along with a related-ish paper one of them had written (see below). The fake state and its supposed properties were even somewhat similar to the real one! I found this failure mode to be pretty incredible. This experience underscored the importance of using these tools as a supplement to, but not substitute for, standard textbooks and other canonical resources.

The CHZ quantum state is named after its inventors: Cabello, Hardy, and Zukowski. The CHZ state is a three-qubit entangled state that has some interesting properties that make it useful for various quantum information processing tasks, such as quantum teleportation and quantum key distribution. The state was introduced in a 1999 paper by Antonio Cabello, Lucien Hardy, and Marek Zukowski titled “Bell’s Theorem for General N-Qubit States and Quantum Mechanics of Classical-Like States”.

Written on July 17th, 2025 by David M. Andrzejewski