Optimal resources for topological two-dimensional stabilizer codes : Comparative study
By H. Bombin, Miguel Angel Martin-Delgado. 2007
197 citations recorded by the source corpus.
We study the resources needed to construct topological two-dimensional stabilizer codes as a way to estimate in part their efficiency, and this leads us to perform a comparative study of surface codes and color codes. This study clarifies the similarities and differences between these two types of stabilizer code. We compute the topological error-correcting rate C:=n/d{sup 2} for surface codes C{sub s} and color codes C{sub c} in several instances. On the torus, typical values are C{sub s}=2 and C{sub c}=3/2, but we find that the optimal values are C{sub s}=1 and C{sub c}=9/8. For planar codes, a typical value is C{sub s}=2, while we find that the optimal values are C{sub s}=1 and C{sub c}=3/4. In general, a color code encodes twice as many logical qubits as does a surface code.
Subfields: Artificial Intelligence, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/cc6f74e24d2464df093a61e1c5dacf580871fd03
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In Artificial Intelligence
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- Joschka Roffe
- Kyungjoo Noh
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In Computational Theory and Mathematics
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- Peter Zoller
- Joschka Roffe
- G. Pupillo
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Citations in the corpus
- Engineered Open Systems and Quantum Simulations with Atoms and Ions (2012, background): “These ideas can be readily generalized to more complex stabilizer states and to setups in higher dimensions, as in, e.g., the color codes developed in Bombin and Martin-Delgado (2006, 2007), and the simulation of a three-dimensional U(1) lattice gauge theory, which will be discussed in Sect.”
- Quantum error correction: an introductory guide (2019, methodology): “surface code is that resource intensive methods are required to obtain a universal encoded gate set. Alternatives to the surface code have been proposed based on different tilings of the qubit lattice [80], as well as extensions to higher dimensions [70,81]. These constructions typically have lower t”
- Fault-tolerant bosonic quantum error correction with the surface–Gottesman-Kitaev-Preskill code (2019, methodology): “[38] H.”