Delete comment from: Computational Complexity
Many practical computational problems are problems about simulation (there is even a point of view in which all computations are simulations).
And obviously, a pretty big subset of practical simulations are performed upon state-spaces that are small-dimension encodings of the large-dimension space that nature specifies.
The great advantage of learning quantum techniques comes when we ask questions like "Why does concentration work so well in real-world problems?" "What generic mechanism acts to algorithmically concentrate simulation trajectories?" For quantum systems this question can be phrased in Scott's language as "What physical mechanism accomplishes sure/Shor separations in real-world quantum systems?"
A good reason to learn quantum simulation is that (AFAICT) it is only for quantum systems that a reasonably generic mechanism (and mathematically well-posed) for algorithmic concentration known --- it is the physical mechanism that Zurek calls "einselection".
Now, if we ask, what mathematical aspects of quantum mechanics are necessary for einselection, then the mathematically natural answer is "the compatible triple of symplectic, Riemannian, and complex structure ... and as for the linear structure ... well ... that is merely a 'technical convenience' (according to the point of view of Ashtekar and Schilling)."
The resulting prediction is clear ... furture textbooks on quantum complexity will cover compatible triples first ... then cover linear structure. :)
The advantage of this approach is that complexity students end up speaking pretty much the same symplectic simulation language that biologists use ... and as simulation becomes more central to research at every scale of biology, this mathematical link-up increasingly benefits both disciplines.
Aug 12, 2009, 8:29:22 PM
Posted to Is Quantum the new Random ?