Digital quantum simulation is a promising application of computers where dynamics simulated by using gate operations. Many techniques for decomposing time-evolution operator into simulatable operations have been proposed, whereas these methods cause some errors. To evaluate errors, we derive lower bound overlap between true and digital at the final time. Our result enables us to guarantee how o...

Nonconstructive existence results are obtained for block error-correcting codes whose codewords lie in a given constrained system. Each such system is defined as a set of words obtained by reading the labels of a finite directed labelled graph. For a prescribed constrained system and relative minimum distance δ, the new lower bounds on the rate of such codes improve on those derived recently by...

For nonbinary codes it is proved that the Hamming bound is asymptotically sharp in some range of the code rate.

R~sum~. On inlroduit une classe de codes lintaires de la famille des codes de Reed-Muller, les codes de Reed-Muller projectifs. Ces codes sont des extensions des codes de Reed-Muller gtntralists ; les codes de Reed-Muller projectifs d'ordre I atteignent la borne de Plotkin. On donne les traram&res des codes de Reed-Muller projecfifs d'ordre 2. 1.Introduction We note pm(Fq) the projective space ...

In many machine learning applications, crowdsourcing has become the primary means for label collection. In this paper, we study the optimal error rate for aggregating labels provided by a set of non-expert workers. Under the classic Dawid-Skene model, we establish matching upper and lower bounds with an exact exponent mI(π) in which m is the number of workers and I(π) the average Chernoff infor...