Phi tensor Psi ... How hard could it be?

If you should stumble upon this page before I write the "Introductory" blog entry for this blog, my apologies for the lack of context. I just started typing. Introduction with purpose and resources coming soon.

Turns out, pretty hard :) In all seriousness, I understood most of it but was fuzzy on how the alpha-a term and beta-b term was being used - what they exactly represented. Like always, I turn to ChatGPT 4.0 for things like this. Its simply the quickest way to get the answer I am looking for. Straight to the core without any fluff. At the beginning of this journey, I would have to had watched several YouTube videos and Google a bunch of stuff from those videos to "get a hold" of a concept like this. But ChatGPT gives you beautiful answers like this:

This was a great answer, but, as ever, I had several follow up questions that generally start with "Considering your last answer ...". Side bar: Physics seems to be mostly, at least from my current take, just learning a whole bunch of new language. If you can learn that language, it seems you can be in the club. I don't want to give the impression that is is easy. It is an enormous language and some of the definitions are not simple.

I've gotten a lot of good answers from ChatGPT 4. 100's of fantastic, amazing answers but this answer below, which is a follow up from the answer above, is one of the most impactful answers I have ever gotten. For me, it tied a whole bunch of loose ends together:

So, I don't want to bore anyone who reads this to death with my question and answer sessions with ChatGPT4, but that is a big part of this journey for me at this point. Yes, I still watch tons of videos on YouTube for the many topics I am trying to learn but the advent of ChatGPT 4.0 has been transformational to my quantum journey. Here are a couple more follow up questions I had. Sometime I am 90% sure I know the answer, like this next one, but I just have to make sure. BTW, I never ... NEVER get an answer from ChatGPT that I don't record in my OneNote in organized sections by topic. This whole line of questioning/answers came from re-watching the extremely good series put on by IBM on their "Qiskit" YouTube channel titled "Understanding Quantum information and Computation" I cannot use strong enough language to impart how good this series is if you are interested in this part of Quantum Computing. By this part, I mean the nuts and bolts part of quantum information theory. Here is the link to this series.

Qiskit Series on Quantum Information and Computation on YouTube

Sorry, I saw a squirrel. Here is the continuation of the ChatGPT responses to the follow up questions I had asked. I'm showing just the answers because the way I ask the questions is sometimes a little strange but you can certainly glean the question from the answer.

And another follow up question that I vaguely knew the answer to which is to say, I dove deep on it at some point in the last year and got a moderately good handle on it but that was some months ago and, well, its not the simplest concept ... and I don't have the greatest memory:

Okay, one more for good measure. Clearly this blog is for no one other than me :)

It's funny how this whole series of questions started with me just wanting to get a handle on this tensor product of two quantum states, Phi and Psi thing (below). By good understanding I mean a basic understanding. This is very often how it goes for me when I am watching some video on Quantum stuff.

Update on 4/8/24:

I continued to ruminate on this for a bit to make sure I have it locked down. I asked ChatGPT to show me an example of solving this using the classical state set (0,1) for both sigma and gamma. Here is what I got as an answer. This is the way it turns out often for me with this physics notation. Understanding the abstraction of this notation is the challenging part. The actual concept (an the resulting answer that it produces) is easy comparatively speaking. Check this out from ChatGPT below. I now feel like I have a handle on this - like I could explain it to a group if I had to.

Here is the video that prompted this blog post. Start at the time mark of 16:44 in this video from the Qiskit channel on YouTube:

While not the same as the tensor product being talked about above, here are some YouTube resources that can help with what tensors are and do in other contexts. It took a long time to sort through a bunch of videos to come up with these awesome videos. That is one of my objectives with this blog, to present painstakingly curated resources from my journey to help separate the wheat from the chaff - to keep people from wasting their most valuable resource, time.