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Paper 1
Ultra Low Overhead Syndrome Extraction for the Steane code
Boldizsár Poór, Benjamin Rodatz, Aleks Kissinger
- Year
- 2025
- Journal
- arXiv preprint
- DOI
- arXiv:2511.13700
- arXiv
- 2511.13700
We establish a new performance benchmark for the fault-tolerant syndrome extraction of [[7, 1, 3]] Steane code with a dynamic protocol. Our method is built on two highly optimized circuits derived using fault-equivalent ZX-rewrites: a primary fault-tolerant circuit with 14 CNOTs and an efficient non-fault-tolerant recovery circuit with 11 CNOTs. The protocol uses an adaptive response to internal faults, discarding flagged measurements and falling back to the recovery circuit to correct potentially detrimental errors. Monte Carlo simulations confirm the efficiency of our protocol, reducing the logical error rate per cycle by an average of ~14.3% relative to the optimized Steane method [arXiv:2506.17181] and ~17.7% compared to the Reichardt's three-qubit method [arXiv:1804.06995], the leading prior techniques.
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Localization of low-energy eigenfunctions in Seba billiards
Minjae Lee
- Year
- 2014
- Journal
- arXiv preprint
- DOI
- arXiv:1407.7077
- arXiv
- 1407.7077
We investigate localization of low-energy modes of the Laplacian with a point scatterer on a rectangular plate. We observe that the point scatterer acts as a barrier confining the low-level modes to one side of the plate while assuming the Dirichlet boundary condition at a point does not induce this type of localization. This low-energy phenomenon extends to higher modes as we increase the eccentricity of the plate.
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