History states of one-dimensional quantum walks

We analyze the application of the history state formalism to quantum walks. The formalism allows one to describe the whole walk through a pure quantum history state, which can be derived from a timeless eigenvalue equation. It naturally leads to the notion of system-time entanglement of the walk, which can be considered as a measure of the number of orthogonal states visited in the walk. We then focus on one-dimensional discrete quantum walks, where it is shown that such entanglement is independent of the initial spin orientation for real Hadamard-type quantum coins and real initial states (in the standard basis) with definite site-parity. Moreover, in the case of an initially localized particle it can be identified with the entanglement of the unitary global operator that generates the whole history state, which is related to its entangling power and can be analytically evaluated. Besides, it is shown that the evolution of the spin subsystem can also be described through a spin history state with an extended clock. A connection between its average entanglement (over all initial states) and that of the operator generating this state is also derived. A quantum circuit for generating the quantum walk history state is as well provided.Comment: 12 pages, 7 figure

Entwicklung und Herstellung von Verpackungsformteilen aus Getreidekleie Abschlussbericht

Available from TIB Hannover: F01B1221 / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDeutsche Bundesstiftung Umwelt, Osnabrueck (Germany)DEGerman

Noninvasive prenatal diagnosis of genetic diseases induced by triplet repeat expansion by linked read haplotyping and Bayesian approach

International audienceAbstract The field of noninvasive prenatal diagnosis (NIPD) has undergone significant progress over the last decade. Direct haplotyping has been successfully applied for NIPD of few single-gene disorders. However, technical issues remain for triplet-repeat expansions. The objective of this study was to develop an NIPD approach for couples at risk of transmitting dynamic mutations. This method includes targeted enrichment for linked-read libraries and targeted maternal plasma DNA sequencing. We also developed an innovative Bayesian procedure to integrate the Hoobari fetal genotyping model for inferring the fetal haplotype and the targeted gene variant status. Our method of directly resolving parental haplotypes through targeted linked-read sequencing was smoothly performed using blood samples from families with Huntington’s disease or myotonic dystrophy type 1. The Bayesian analysis of transmission of parental haplotypes allowed defining the genotype of five fetuses. The predicted variant status of four of these fetuses was in agreement with the invasive prenatal diagnosis findings. Conversely, no conclusive result was obtained for the NIPD of fragile X syndrome. Although improvements should be made to achieve clinically acceptable accuracy, our study shows that linked-read sequencing and parental haplotype phasing can be successfully used for NIPD of triplet-repeat expansion diseases. Trial registration: NCT04698551_date of first registration: 07/01/2021