Journal
NEW JOURNAL OF PHYSICS
Volume 18, Issue -, Pages -Publisher
IOP Publishing Ltd
DOI: 10.1088/1367-2630/18/1/013050
Keywords
quantum memory; topological order; topological codes
Categories
Funding
- ERC grant QFTCMPS
- cluster of excellence Quantum Engineering and Space-Time Research [EXC 201]
- Deutsche Forschungsgemeinschaft
- Open Access Publishing Fund of Leibniz Universitat Hannover
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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 realized with local interactions in R-3, 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.
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