Majorization in Quantum Adiabatic Algorithms

The majorization theory has been applied to analyze the mathematical structure of quantum algorithms. An empirical conclusion by numerical simulations obtained in the previous literature indicates that step-by-step majorization seems to appear universally in quantum adiabatic algorithms. In this paper, a rigorous analysis of the majorization arrow in a special class of quantum adiabatic algorithms is carried out. In particular, we prove that for any adiabatic algorithm of this class, step-by-step majorization of the ground state holds exactly. For the actual state, we show that step-by-step majorization holds approximately, and furthermore that the longer the running time of the algorithm, the better the approximation.Comment: 7 pages;1 figur

Optimal conclusive discrimination of two states can be achieved locally

This paper constructs a LOCC protocol that achieves the global optimality in conclusive discrimination of any two states with arbitrary a priori probability. This can be interpreted that there is no ``non-locality'' in the conclusive discrimination of two multipartite states.Comment: 9 pages, RevTeX, no figure. Comments, criticisms and suggestions are welcom

Upregulation of Functional Kv11.1 Isoform Expression by Inhibition of Intronic Polyadenylation with Antisense Morpholino Oligonucleotides

The KCNH2 gene encodes the Kv11.1 potassium channel that conducts the rapidly activating delayed rectifier current in the heart. KCNH2 pre-mRNA undergoes alternative processing; intron 9 splicing leads to the formation of a functional, full-length Kv11.1a isoform, while polyadenylationwithin intron 9 generates a non-functional, Cterminally truncated Kv11.1a-USO isoform. The relative expression of Kv11.1 isoforms plays an important role in the regulation of Kv11.1 channel function and the pathogenesis of long QT syndrome. In this study,we identified cis-acting elements that are required for KCNH2 intron 9 poly(A) signal activity. Mutation of these elements decreased Kv11.1a-USO expression and increased the expression of Kv11.1a mRNA, protein and channel current. More importantly, blocking these elements by antisense morpholino oligonucleotides shifted the alternative processing of KCNH2 intron 9 from the polyadenylation to the splicing pathway, leading to the predominant production of Kv11.1a and a significant increase in Kv11.1 current. Our findings indicate that the expression of the Kv11.1a isoform can be upregulated by an antisense approach. Antisense inhibition of KCNH2 intronic polyadenylation represents a novel approach to increase Kv11.1 channel function

Upregulation of Functional Kv11.1a Isoform Expression by Modified U1 Small Nuclear RNA

The KCNH2 or human ether-a go-go-related gene (hERG) encodes the Kv11.1 potassium channel that conducts the rapidly activating delayed rectifier potassium current in the heart. The expression of Kv11.1 C-terminal isoforms is directed by the alternative splicing and polyadenylation of intron 9. Splicing of intron 9 leads to the formation of a functional, full-length Kv11.1a isoform and polyadenylation of intron 9 results in the production of a non-functional, C-terminally truncated Kv11.1a-USO isoform. The relative expression of Kv11.1a and Kv11.1a-USO plays an important role in regulating Kv11.1 channel function. In the heart, only one-third of KCNH2 pre-mRNA is processed to Kv11.1a due to the weak 5′ splice site of intron 9. We previously showed that the weak 5′ splice site is caused by sequence deviation from the consensus, and that mutations toward the consensus sequence increased the efficiency of intron 9 splicing. It is well established that 5′ splice sites are recognized by complementary base-paring with U1 small nuclear RNA (U1 snRNA). In this study, we modified the sequence of U1 snRNA to increase its complementarity to the 5′ splice site of KCNH2 intron 9 and observed a significant increase in the efficiency of intron 9 splicing. RNase protection assay and western blot analysis showed that modified U1 snRNA increased the expression of the functional Kv11.1a isoform and concomitantly decreased the expression of the non-functional Kv11.1a-USO isoform. In patch-clamp experiments, modified U1 snRNA significantly increased Kv11.1 current. Our findings suggest that relative expression of Kv11.1 C-terminal isoforms can be regulated by modified U1 snRNA