Rhythm is a Quantum Concatenated Code

I do believe this is the first time I've performed the paper dance on the scienceblogs incarnation of this blog. Yep, it's that time again: it's the paper dance!

"A far away light in the futuristic place we might be; It's a tiny world just big enough to support the kingdom of one knowledgeable; I feel a wave of loneliness and head back down I'm going too fast (I'm going too fast)"


The Stability of Quantum Concatenated Code Hamiltonians

Authors: D. Bacon

Abstract: Protecting quantum information from the detrimental effects of decoherence and lack of precise quantum control is a central challenge that must be overcome if a large robust quantum computer is to be constructed. The traditional approach to achieving this is via active quantum error correction using fault-tolerant techniques. An alternative to this approach is to engineer strongly interacting many-body quantum systems that enact the quantum error correction via the natural dynamics of these systems. Here we present a method for achieving this based on the concept of concatenated quantum error correcting codes. We define a class of Hamiltonians whose ground states are concatenated quantum codes and whose energy landscape naturally causes quantum error correction. We analyze these Hamiltonians for robustness and suggest methods for implementing these highly unnatural Hamiltonians.

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Dave, this is a good idea. Although I think you can do similar things with "natural" Hamiltonians also. In fact I think most Hamiltonians provide what can be thought of as passive quantum error correction. Your approach might help illuminate why / under what conditions this is true.

I am confused by the usage of 'we' in single-author papers. I know that 'I' is considered arrogant and turns a lot of people off, but 'we' is nonsensical.

I call it the "scientific we."

David Mermin once fought for using "I" in Physical Review Letters. He won, and then wrote the paper using "we."

I second Jon's comment (at least in principle). That is, while I'm not confused by it, I don't like it. I use "we" whenever possible to indicate "the reader and I", e.g. in "Now, by taking the square root of this negative number, we see that Chewbacca is a wookie." In other circumstances, though, I feel that "I" is just plain the right way to go -- and I propose a guerrilla group dedicated to the educated use of the first-person singular in papers...

By Robin Blume-Kohout (not verified) on 16 Jun 2008 #permalink

I'm going to point some of my buddy's at this paper as it seems to rhyme with things they are working on.

The whole construction smells of "mutually unbiased bases" or MUB theory, in that it considers tensor products of other than all spin-z states. And I think you can generalize from the Pauli algebra to other Clifford algebras. The ideals and primitive idempotents of a Clifford algebra are defined by maximal sets of commuting non trivial square roots of unity (other than -I). For example, with the Dirac algebra, given two Dirac bilinears A and B that commute and square to +1, a complete set of primitive idempotents is (1 +- A)(1 +- B)/4.

Also, "canonical choose" needs a change.

We find that it is a brilliant paper.

I am in a mixed state of humble and proud to have assisted in a tiny way with the error correction via the natural blog-dynamics of these systems.

I guarantee that my 4 arXiv papers have more insidious errors.

When last week's Caltech Commencement address by Robert Krulwich shows up on the Caltech web site, it would be well worth your mentioning on Quantum Pontiff. It was one of the best talks I've ever seen, on narrative in science, managing to quote Schrodinger, Heisenberg, Galileo, and episodes of "Friends."

Although I think you can do similar things with "natural" Hamiltonians also. In fact I think most Hamiltonians provide what can be thought of as passive quantum error correction.

Well there are a bunch of questions here. First I think that most Hamiltonians don't provide a degeneracy corresponding to a quantum error correcting code subspace. So I think it might be possible that generic ground states have quantum error correcting properties, they aren't necessarily good for protecting encoded quantum information. But the real question isn't whether the ground state is a good code state: the real question is what happens when you bump it. I suspect that systems which have quantum error correcting properties and which are also robust under perturbation aren't quite as ubiquitous.

What type of perturbation are you thinking of? Like unknown low frequency type perturbations on your control parameters during annealing?