The ACM’s Ubiquity has been running a symposium on the question What is Computation?. Amusingly they let a slacker like me take a shot at the question and my essay has now been posted: Computation and Fundamental Physics. As a reviewer of the article said, this reads like an article someone would have written after attending a science fiction convention. Which I think was supposed to be an insult, but which I take as a blessing. For the experts in the audience, the fun part starts at the “Fundamental Physics” heading.
O brave new quantum world!
Science fiction can be very instructive. RE: concept of a universe as a computer, see TRON: LEGACY.
Thanks for pointing out the work by McCann and Pippenger; I’m excited now to look at McCann’s thesis and their paper.
I have a question about Preskil’s view that universe is a fault tolerant computer:
Usually the micro-processes where the information is lost, and the processes at larger scales where information is preserved, are described by different physical descriptions – the latter being some kind of approximation or coarse graining of the former.
But in Preskill’s argument, the micro and macro processes are both based on the same process – quantum unitary evolution.
This doesn’t seem likely IMHO.
Daniel, I too particularly liked the passage in Dave’s essay that read:
Moreover, the extension of this concept to concrete calculations is well underway, as follows.
(1) Lindblad dynamics has provided us with a mathematically well-posed description of information-destroying quantum processes (indeed, the entirety of Nielsen and Chuang’s textbook is founded on the postulate that Lindblad dynamics is the sole means by which quantum information can be destroyed).
(2) Thanks to QIT pioneers like Howard Carmichael (who invented the term “quantum unraveling”), Carlton Caves, and Stephen Adler, we know how to unravel discrete Lindblad processes, in complete generality, as continuous (stochastic) dynamical processes.
(3) Thanks to the analytic insights of Morse theory, the physical insights of QIT pioneers like Wojciech Zurek, and the informatic and thermodynamic insights of mathematicians like Terry Tao, we appreciate that Lindbladian dynamical processes compress quantum trajectories onto low-dimension state-spaces that (fortunately!) inherit all of the (beautiful!) Kählerian structure of Hilbert space, while being far richer geometrically.
(4) Thanks to mid-20th century dynamics pioneers like Cartan, Arnold, Smale, Kolmogorov, Mac Lane, and Marsden, and their (subsequent) quantum counterparts—in particular Abhay Ashtekar and Troy Schilling—we have all the mathematical tools we need to pullback Lindbladian dynamics onto non-Hilbert state-spaces … by methods that are geometrically natural and are computationally efficient.
Thus, if we follow-through on Dave’s line of inquiry (and that Preskill/ Ogburn/Â Hawking etc.), we are led to appreciate that quantum dynamics generically occurs on non-Hilbert state-spaces, according to all that we already know about quantum dynamical processes.
As for whether Nature’s own state-space is Hilbert-flat versus Kähler-curved … or Hilbert-flat versus Einstein-dynamic … well … in the short term these issues are immaterial, because insofar as practical computations are concerned, the issue is decided: the viewpoint of modern dynamics is that all state-spaces (both classical and quantum) are effectively non-flat and dynamical.
If you think about it, this represents an unexpected transformation in our understanding of quantum dynamics, that is substantially more radical in its implications for mathematics, science, and engineering, than anything that ARDA’s QIST panels conceived back in 2002.
We thus appreciate that the post-Hilbert quantum world that Dave’s essay envisions is not some future dream: that post-Hilbert world is right here, right now, and it is burgeoning exponentially in its practical scope and global strategic consequence.
The overall point is simply this: the advent of post-Hilbert quantum dynamics is good news for everyone on the planet … and especially, it’s very good news for young CT/QIT/QSE researchers.
And on that optimistic note, please let me extend my best wishes … for Happy Holidays to all! 🙂