# How "fundamental" is quantum information/computation?

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I am wondering how fundamental the study of quantum information theory and computation is, in the sense of contributing to our understanding of the basic laws of nature. Will quantum information theory give us exciting new insights into fundamental physics, or is it "merely" an application of quantum mechanics to information theory and computation? I find this to be a very interesting question, but can find very few sources that comment on it. I am currently reading Nielsen and Chuang's quantum information textbook, but I haven't seen this point addressed. There's a 2012 article by Aram Harrow (Why now is the right time to study quantum computing) which posits in the abstract that "quantum computing is not merely a recipe for new computing devices, but a new way of looking at the world", but sadly it is behind a paywall. In section 5 of this 1999 article, John Preskill briefly talks about how he thinks quantum information will contribute to fundamental physics, and says "I am anticipating a much broader interface between quantum information science and fundamental physics in the future". I am basically wondering what the current status of this interface is 15 years later, if there is any at all, and if the quantum information community believes that quantum information will play an important role in fundamental physics.

Well, as a PhD students in this field, I feel sometimes a little repentant to come into the field, just as your question, it seems not so "fundamental" as theories such as quantum gravity and string. While it really bring some new perspectives to view the nature, a charming question is that "can the nature be built upon a first principle about "information"? In another words, you can ask yourself, can we derive the known equations starting from such principle, rather than the principle of relativity? Will these ideas someday change the current physics? However, most researchers are developing applications with the quantum theory established about 90 years ago. And for the foundations, physicists are now in a bottle－neck .

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In the notes "Quantization via Linear homotopy types" (arXiv;1402.7041) I describe a perspective unifying fundamental aspects of physics with quantum logic that is based on founding logic itself in type theory (which is more fundamental than logic), or rather in homotopy type theory (which is still more fundamental), and quantum logic in linear type theory. It is observed that if one further goes to dependent linear type theory, which the article introduces ("semantically"), then the resulting quantum logic captures also the process of geometric quantization from classical physics via cohesive homotopy types to linear homotopy types, aka quantum state spaces. The central technical result expressing this is that pull-push in twisted generalized cohomology (such as in K-theory, in elliptic cohomology, etc.) has a neat linear-type-theoretic (hence quantum logical) expression (here) as a "secondary integral transform" which is manifestly in the form of a path integral, providing a kind of generalized cohomological motivic quantization. Examples discussed are holographic geometric quantization of Poisson manifolds and quantization of D-brane charge in string theory, also a little bit of elliptic cohomology. The article provides some further comments on the relation of all this to the foundations of pre-quantum ("classical") physics in cohesive homotopy type theory  for readers interested in yet "more fundamentalness" and some further technical results regarding anomaly cancellation, for those readers who are rather not.

answered Dec 20, 2014 by (5,925 points)
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Physics, in particular, condensed matter physics, is a very old field. Many people are thinking that the exciting time of physics has passed. We enter the begining of the end of physics. The only important things in physics are its engineering applications, such as optical fiber and blue LED.

However, I feel that we only see the end of the begining. The exciting time is still ahead of us. In particular, now is a very exciting time in physics, like 1900 - 1930.

Historically, physics has experienced  four revolutions: mechanical revolution, electromagnetic revolution, general relativity revolution, and quantum revolution. Each revolution unifies seemingly unrelated phenomena. Each revolution requires new mathematics to describe the new theory. Each revolution changes our world view.  Now we are seeing/making the second quantum revolution which unifies (quantum) information, matter and geometry:

Wheeler's "it from bit" represents a deep desire to unify matter and information. In fact, it happend before at a small scale. We introduced electric field to informationally (or pictorially) describe Coulomb law. But later, electric field became real matter with energy and momentum, and even a particle associated with it.

However, in our world, "it" are very complicated. (1) Most "it" are fermions, while "bit" are bosonic. Can fermionic "it" come from bosonic "bit"? (2) Most "it" also carry spin-1/2. Can spin-1/2 arises from "bit"? (3) All "it" interact via a spectial kind of interaction -- gauge interaction. Can "bit" produce gauge interaction? Can "bit" produce waves that satisfy Maxwell equation? Can "bit" produce photon?

More generally, there are Eight wonders in our universe (ie "it" has eight wonders)::
(1) Locality.
(2) Identical particles.
(3) Gauge interactions.
(4) Fermi statistics and spin-1/2.
(5) Chiral fermions.
(6) Small mass of fermions. (Much less than Planck mass)
(7) Lorentz invariance.
(8) Gravity.

It turns out that we can only produce two out of eight wonders (1 -- 2) from bits.

However, if we start with qubits, we can obtain Fermi statistics, spin-1/2, Maxwell equation, Yang-Mills equation, and the corresponding gauge interations. So far, we can  unify seven out of eight wonders (1 -- 7) by qubits, and we are trying to add the gravity (see http://arxiv.org/abs/0907.1203 ).

So It from qubit, not bit.  Bit is too classical to produce Gauge interactions, Fermi statistics, and Chiral fermions.Those phenomena (or properties) come from quantum many-body entanglement, which exists only for qubits. (For more deails see http://blog.sciencenet.cn/blog-1116346-736093.html )

answered Dec 21, 2014 by (3,475 points)
edited Dec 21, 2014

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