Mine too ...
I did this research while working at the Institute for Interdisciplinary Information Sciences in Beijing for about 5 months.
How it all works (and what's going on behind the scenes) really takes awhile to sink in.
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I can read the words, even get a sense of coherence but I have to accept some of the more interesting areas of human discovery, like quantum physics and math, are far beyond me. I'm just thankful for all the people like you who have these incredible brains which can operate at the bleeding edge whilst I can enjoy wrestling with comprehension at a concept level!
Thanks. I meant to make the post entertaining and an introduction into the subject area. It's really a pre-lude to a talk that I'll be giving in Boston at SIAM.
I want to point out that coherency is key. I hope it wasn't lost on anyone. I didn't even know how to begin to describe the work I did in developing some algorithms that would turn on or off various q-bits in such a way as they relate to their entangled states.
From what I could understand, if you have k q-bits that are entangled in an n q-bit system, then the corresponding matrix that represents the Hamiltonian will be a 2^n x 2^n system, with a 2^k x 2^k block submatrix (under an appropriate transformation) realizing the underlying subspace of the Hamiltonian that represents the k entangled q-bits.
So, if you have a 3 q-bit system with 2 q-bits entangled, then you have a 4 x 4 block diagonal matrix that represents the entangled state of the two q-bits. Now, because we assume that only 2 q-bits are entangled that means one of them isn't interacting with the other two at all.
How does this translate to the representation in the matrix? 1 q-bit that isn't being entangled with 2 others doesn't fit in a 4 x 4 submatrix on its own? It really ought to be a 2 x 2 submatrix.
So, what's going on with those other 2 dimensions in the row / column space of the matrix?
I'm not entirely sure, but I intend to find out.
Oh I think you did a fantastic job of communicating the subject. I can't wait to hear more! Really good luck with your talk!