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Here, we have exhibited that the logical failure rate can be enhanced by manipulating the lattice size of surface codes that they can show an enormous improvement in the number of physical qubits for a noise model where dephasing errors dominate over relaxation errors. We estimated the logical error rate in terms of the lattice size and physical error rate. When the physical error rate was high, the parameter estimation method was applied, and when it was low, the most frequently occurring logical error cases were considered. By using the minimum weight perfect matching decoding algorithm, we obtained the optimal lattice size by minimizing the number of qubits to achieve the required failure rates when physical error rates and bias are provided .<\/jats:p>","DOI":"10.1007\/s11128-021-03130-z","type":"journal-article","created":{"date-parts":[[2021,7,7]],"date-time":"2021-07-07T05:02:46Z","timestamp":1625634166000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Rectangular surface code under biased noise"],"prefix":"10.1007","volume":"20","author":[{"given":"Jonghyun","family":"Lee","sequence":"first","affiliation":[]},{"given":"Jooyoun","family":"Park","sequence":"additional","affiliation":[]},{"given":"Jun","family":"Heo","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,7,7]]},"reference":[{"key":"3130_CR1","doi-asserted-by":"crossref","unstructured":"Multiple-particle interference and quantum error correction: Proceedings of the Royal Society of London. 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