Hey folks, here's another update on my geometric algebra things! This one is something completely different from the previous editors, which have been about creative coding. This one is about quantum computing:
04/12/2022, 1:27 AM
That was fascinating, and way over my head in about two or three different ways. I'm only vaguely familiar with GA (and Clifford algebras more specifically), and again only vaguely familiar with QC (at a pop-sci level). But I found this video fairly easy to follow and enjoyable. I don't have any domain-relevant feedback to offer, but I just wanted to share my enjoyment. I look forward to the next update!
04/13/2022, 3:56 AM
That would be fantastic if you could represent entangled qubits with spacetime algebra like that! I know some quantum computing from Michael Nielsen's and Andy Matuschak's mnuemonic medium pieces, and I agree it would be neat to be able to really visualize everything. I'm surprised you can visualize quantum states with the bloch sphere because that throws away all of the phase information. Does that have anything to do with using spacetime algebra to represent entangled qubits?
04/13/2022, 4:02 AM
If that crystal sphere is "a visualization two entangled qubits," what happens with more than two?
Likewise, with your circuit example, you have two inputs and two outputs. In the case where they're entangled, if you know the crystal sphere for one of the outputs, can you tell what the other one will be? Is each output picture a visualization of the same two qubit system, differing from the perspective of the corresponding input?
04/13/2022, 9:33 AM
@Robin Like the bloch sphere this representation throws away global phase - but that's ok, desirable even, since global phase isn't "experimentally meaningful" and therefore arguably nonexistant!
@wtaysom hrrrrrrrrrgh so I wanted to have a version of it that kiiiiind of scales to >2 qubits, this is part of my problem. I know that it implicitly involves a choice of whether it's a visualization of qubit1-entangled-with-qubit2 VERSUS qubit2-entangled-with-qubit1. And then I suspect that, this choice made, you can ask about qubit1-entangled-with-[the rest of a state of N qubits]
@wtaysom To your second question, yes, to your third question, yes
04/13/2022, 10:13 AM
As I still don’t know much about this topic, would the “shape” of many qubits entangled begin to reflect the problem being modeled?
04/13/2022, 10:14 AM
That's my hope, although I don't really know enough QC either!