Decoding Algorithms for Correction of X-Zand Spatially Correlated Errors in Topological Quantum Computing

Overview

Topological quantum error correction uses the topology of surfaces like the plane or torus to correct quantum errors, helping quantum computing to be successful. However, topological quantum error correction assumes that all errors occur independently. In this project, both spatial correlation and X-Zcorrelation are considered. In the error model used, staircase-shaped errors of fixed unknown length are considered, providing the spatial correlation. Also, instead of treating Pauli Yerrors as a combination of Xand Zerrors, they are considered separately by having X, Y, and Zchains occur with equal probability. This forces the decoder to consider X-Z correlation. The decoder is a variation of the minimum-weight perfect matching (MWPM) algorithm. Instead of using the taxicab distance on the lattice as the weight of an edge, weight is defined using a combination of functions on distance and the overlap of chains. The distance function has a spike at the predicted staircase distance. The overlap function peaks at no overlap and maximum overlap to account for Yerrors. This algorithm is applied twice; once for Xsyndromes and once for Zsyndromes. This information is combined to give the most likely error chains. The traditional MWPM decoder has an error threshold at ~11%, beyond which the success rate dramatically declines. The revised decoder has a higher success rate and remains useful beyond this threshold, to as much as 17%. Both of the weight functions used in this research can be generalized to broader forms of spatial and X-Zcorrelation Conserving Water Through the Filtration and Recyclation of Greywater in a Domestic System Bryce Goodin* Bartlesville High School Bartlesville, Oklahoma Supervisor/Teacher: Mrs. Henderson, AP Biology This project aims to produce and test a prototype aid in water conservation within a domestic, consumer context. A specialized recirculating faucet system was built using direct filtration techniques: two carbon filters and an adapted Biosand Filter. The system was tested by filtering solutions of decreasing particulate sizes through the system and comparing the contamination after filtration to the initial contamination levels. The final goal of this project is to create a system that conserves water before it leaves the consumer. The system was made to be modular for easy installment and be able to filter sediments such as soil, graphite powder, vegetable oil, and soap content. E. coli was tested to assess the microbial-filtration ability of the system. The results for microbial-filtration suggested there were E. coli remnants after filtration and new methods will need to be applied to reach the desired function of the system. This will include an activated carbon and zeolite filter. One gallon of water was successfully recycled for an extended period of time within standard flow-rates for household faucets. This system, if implemented in the average American household, would save the consumer significant amounts of money in water costs and conserve up to 50 gallons daily in the American home with the potential for further conservation within commercial environments.

Competition history

• JSHS 2020 Category not listed

Resources

• National JSHS abstract book ↗

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