**Douglas Knight** remarks: “Chemistry (eg, spectral lines) is supposed to be possible to be derived from known physical theories.”

As a technical point, spectral lines are associated to periodic orbits of Hamiltonian flows. The theory of such orbits is well-developed for quantum flows on (flat) Hilbert state-spaces; less well-developed for **general Hamiltonian flows.**

As large-scale quantum simulations migrate onto algebraic state-spaces of increasingly geometric sophistication, these once-abstract mathematical questions are gaining in physical and even engineering consequence. In particular, it can happen (and increasingly *does* happen) that chemical observations are in reasonable accord with computational simulations, and yet we don’t understand either of them.

**Conclusion** ** “Allez en avant, et la foi vous viendra“** (Set forth and faith will come to you).

Here’s a similar question. Chemistry (eg, spectral lines) is supposed to be possible to be derived from known physical theories, but we don’t know how to carry out the computation of the physical theory on classical computers. But is there an interactive protocol that we could use to verify that chemistry is what we think it is?

I’m sure that people have done lots of consistency checks on theories of chemistry, but the point of view of quantum computing and interactive proofs can probably suggest new consistency checks.

]]>The part I find interesting (if I am understanding it correctly) is that the undecidability part comes from wanting arbitrary precision. This reminds me of the kind of the potential separation of BPP and P… Think they might be related?

]]>I’m weighing the probabilities of you being full of it against the probabilities of LW being full of it. Once again, not a formally rigourous argument as I’m not quantifying it precisely, but the evidence is so overwhelming that I don’t need to.

]]>Thanks for the links!

]]>To the best of my knowledge, by any reasonable measure, these squeezed LIGO light-beams will constitute the most macroscopic non-classical dynamical state ever created, and a wonderful example of scalable engineering applications of fundamental quantum research.

]]>Quantum effects that are remarkable when observed with individual photons become (as it seems to me) truly *incredible* when these same effects are scaled to Avogadro’s Number of photons, and Carlton Caves is deserving of our appreciation and thanks for being among the first to foresee both the technical feasibility and the practical applications of this macroscopic quantum scaling.

]]>http://physics.illinois.edu/people/kwiat/interaction-free-measurements.asp

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