Topological Subsystem Codes
arXiv:0908.4246 · doi:10.1103/PhysRevA.81.032301
Abstract
We introduce a family of 2D topological subsystem quantum error-correcting codes. The gauge group is generated by 2-local Pauli operators, so that 2-local measurements are enough to recover the error syndrome. We study the computational power of code deformation in these codes, and show that boundaries cannot be introduced in the usual way. In addition, we give a general mapping connecting suitable classical statistical mechanical models to optimal error correction in subsystem stabilizer codes that suffer from depolarizing noise.
16 pages, 11 figures, explanations added, typos corrected
References in corpus (8)
- Topological Quantum Distillation
- Topological fault-tolerance in cluster state quantum computation
- A no-go theorem for a two-dimensional self-correcting quantum memory based on stabilizer codes
- Topological Computation without Braiding
- On thermalization in Kitaev's 2D model
- Exact Topological Quantum Order in D=3 and Beyond: Branyons and Brane-Net Condensates
- Error Threshold for Color Codes and Random 3-Body Ising Models
- Homological Error Correction: Classical and Quantum Codes
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