dorsal/arxiv
View SchemaOperator Quantum Error Correcting Subsystems for Self-Correcting Quantum Memories
| Authors | Dave Bacon |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0506023 |
| URL | https://arxiv.org/abs/quant-ph/0506023 |
| DOI | 10.1103/PhysRevA.73.012340 |
| Journal | Phys. Rev. A 73, 012340 (2006) |
Abstract
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. Recently this notion has led to a more general notion of quantum error correction known as operator quantum error correction. 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 operator 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. This does not lead to codes which differ from subspace codes, but does lead to recovery routines which explicitly make use of the subsystem structure. Here we present two examples of such operator 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.
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"abstract": "The most general method for encoding quantum information is not to encode the\ninformation into a subspace of a Hilbert space, but to encode information into\na subsystem of a Hilbert space. Recently this notion has led to a more general\nnotion of quantum error correction known as operator quantum error correction.\nIn standard quantum error correcting codes, one requires the ability to apply a\nprocedure which exactly reverses on the error correcting subspace any\ncorrectable error. In contrast, for operator error correcting subsystems, the\ncorrection procedure need not undo the error which has occurred, but instead\none must perform correction only modulo the subsystem structure. This does not\nlead to codes which differ from subspace codes, but does lead to recovery\nroutines which explicitly make use of the subsystem structure. Here we present\ntwo examples of such operator error correcting subsystems. These examples are\nmotivated by simple spatially local Hamiltonians on square and cubic lattices.\nIn three dimensions we provide evidence, in the form a simple mean field\ntheory, that our Hamiltonian gives rise to a system which is self-correcting.\nSuch a system will be a natural high-temperature quantum memory, robust to\nnoise without external intervening quantum error correction procedures.",
"arxiv_id": "quant-ph/0506023",
"authors": [
"Dave Bacon"
],
"categories": [
"quant-ph",
"cond-mat.str-el"
],
"doi": "10.1103/PhysRevA.73.012340",
"journal_ref": "Phys. Rev. A 73, 012340 (2006)",
"title": "Operator Quantum Error Correcting Subsystems for Self-Correcting Quantum Memories",
"url": "https://arxiv.org/abs/quant-ph/0506023"
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