A proposal for self-correcting stabilizer quantum memories in 3 dimensions (or slightly less)
arXiv:1411.7046 · doi:10.1088/1367-2630/18/1/013050
Abstract
We propose a family of local CSS stabilizer codes as possible candidates for self-correcting quantum memories in 3D. The construction is inspired by the classical Ising model on a Sierpinski carpet fractal, which acts as a classical self-correcting memory. Our models are naturally defined on fractal subsets of a 4D hypercubic lattice with Hausdorff dimension less than 3. Though this does not imply that these models can be realised with local interactions in 3D Euclidean space, we also discuss this possibility. The X and Z sectors of the code are dual to one another, and we show that there exists a finite temperature phase transition associated with each of these sectors, providing evidence that the system may robustly store quantum information at finite temperature.
16 pages, 6 figures. In v2, erroneous argument about embeddability into R3 was removed. In v3, minor changes to match journal version
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Cited by in corpus (15)
- Quantum memories at finite temperature
- Fractal symmetries: Ungauging the cubic code
- Topological Order, Quantum Codes and Quantum Computation on Fractal Geometries
- Locality-Preserving Logical Operators in Topological Stabiliser Codes
- Symmetry-protected self-correcting quantum memories
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- Topological Order and Memory Time in Marginally Self-Correcting Quantum Memory
- Quantum storage in quantum ferromagnets
- Self correction requires Energy Barrier for Abelian quantum doubles
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