Everybody do the new paper dance, quant-ph/0506023

**Quantum Error Correcting Subsystems and Self-Correcting Quantum Memories**

**Authors:** D. Bacon

**Comments:** 16 pages

The most general method for encoding quantum information is not to encode the information into a subspace of a Hilbert space, but to encode information into a subsystem of a Hilbert space. In this paper we use this fact to define subsystems with quantum error correcting capabilities. In standard quantum error correcting codes, one requires the ability to apply a procedure which exactly reverses on the error correcting subspace any correctable error. In contrast, for quantum error correcting subsystems, the correction procedure need not undo the error which has occurred, but instead one must perform correction only modulo the subsystem structure. Here we present two examples of quantum error correcting subsystems. These examples are motivated by simple spatially local Hamiltonians on square and cubic lattices. In three dimensions we provide evidence, in the form a simple mean field theory, that our Hamiltonian gives rise to a system which is self-correcting. Such a system will be a natural high-temperature quantum memory, robust to noise without external intervening quantum error correction procedures.

Your paper has interesting-looking examples of subsystem-based quantum error correction. If I may respond with a bit of self-promotion as well: Many people are not aware that a structure theorem on idempotent maps on C^*-algebras obtained by Choi and Effros in the 1970s is equivalent to the notion of a decoherence-free subsystem. See quant-ph/0203105 for details.

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Grgrgrg…

You scooped me with that “self-correcting” word in the title. I was going to use it for my own paper, grgrgrg.

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