Abstract: Let N be a (large) positive integer, and let b < N be a positive integer relatively prime to N whose order modulo N is large. Let QC be a quantum computer whose input register has the size specified in Shor’s original description of his order-finding algorithm. We show that when Shor’s algorithm is implemented on QC, then the probability of obtaining a divisor of the order of b modulo...

Vote-tabulation audits can be used to collect evidence that the set of winners (the outcome) of an election according to the machine count is correct—that it agrees with the outcome that a full hand count of the audit trail would show. The strength of evidence is measured by the p-value of the hypothesis that the machine outcome is wrong. Smaller p-values are stronger evidence that the outcome ...

A bstract We continue to develop Bootstrability — a method merging Integrability and Conformal Bootstrap extract CFT data in integrable conformal gauge theories such as $$ \mathcal{N} N = 4 SYM. In this paper, we consider the 1D defect defined on \frac{1}{2} 1 2 <...

California has experienced increasingly severe autumn wildfires over the past several decades, which have exacted a rising human and environmental toll. Recent fire climate science research demonstrated clear link between worsening change, mainly though vegetation-drying effect of temperatures shifting precipitation seasonality. New work by Lukovi? et al. (2021) explores observed changes in Cal...