Almost-linear time decoding algorithm for topological codes

In order to build a large scale quantum computer, one must be able to correct errors extremely fast. We design a fast decoding algorithm for topological codes to correct for Pauli errors and erasure and combination of both errors and erasure. Our algorithm has a worst case complexity of O(nα(n)), where n is the number of physical qubits and α is the inverse of Ackermann's function, which is very slowly growing. For all practical purposes, α(n)≤3. We prove that our algorithm performs optimally for errors of weight up to (d−1)/2 and for loss of up to d−1 qubits, where d is the minimum distance of the code. Numerically, we obtain a threshold of 9.9% for the 2d-toric code with perfect syndrome measurements and 2.6% with faulty measurements.

Compelling Evidence Suggesting the Codon Usage of SARS-CoV-2 Adapts to Human After the Split From RaTG13

SARS-CoV-2 needs to efficiently make use of the resources from hosts in order to survive and propagate. Among the multiple layers of regulatory network, mRNA translation is the rate-limiting step in gene expression. Synonymous codon usage usually conforms with tRNA concentration to allow fast decoding during translation. It is acknowledged that SARS-CoV-2 has adapted to the codon usage of human lungs so that the virus could rapidly proliferate in the lung environment. While this notion seems to nicely explain the adaptation of SARS-CoV-2 to lungs, it is unable to tell why other viruses do not have this advantage. In this study, we retrieve the GTEx RNA-seq data for 30 tissues (belonging to over 17 000 individuals). We calculate the RSCU (relative synonymous codon usage) weighted by gene expression in each human sample, and investigate the correlation of RSCU between the human tissues and SARS-CoV-2 or RaTG13 (the closest coronavirus to SARS-CoV-2). Lung has the highest correlation of RSCU to SARS-CoV-2 among all tissues, suggesting that the lung environment is generally suitable for SARS-CoV-2. Interestingly, for most tissues, SARS-CoV-2 has higher correlations with the human samples compared with the RaTG13-human correlation. This difference is most significant for lungs. In conclusion, the codon usage of SARS-CoV-2 has adapted to human lungs to allow fast decoding and translation. This adaptation probably took place after SARS-CoV-2 split from RaTG13 because RaTG13 is less perfectly correlated with human. This finding depicts the trajectory of adaptive evolution from ancestral sequence to SARS-CoV-2, and also well explains why SARS-CoV-2 rather than other viruses could perfectly adapt to human lung environment.