On the convex characterisation of the set of unital quantum channels

In this paper, we consider the convex set of $d$ dimensional unital quantum channels. In particular, we parametrise a family of maps and through this parametrisation we provide a partial characterisation of the set of unital quantum maps with respect to this family of channels. For the case of qutrit channels, we consider the extreme points of the set and their classification with respect to the Kraus rank. In this setting, we see that the parametrised family of maps corresponds to maps with Kraus rank three. Furthermore, we introduce a novel family of qutrit unital quantum channels with Kraus rank four to consider the extreme points of the set over all possible Kraus ranks. We construct explicit examples of these two families of channels and we consider the question of whether these channels correspond to extreme points of the set of quantum unital channels. Finally, we demonstrate how well-known channels relate to the examples presented.Comment: 18 page

On a generalized quantum SWAP gate

The SWAP gate plays a central role in network designs for qubit quantum computation. However, there has been a view to generalize qubit quantum computing to higher dimensional quantum systems. In this paper we construct a generalized SWAP gate using only instances of the generalized controlled-NOT gate to cyclically permute the states of d qudits for d prime

Towards an optimal swap gate

We present a novel approach that generalizes the well known quantum SWAP gate to higher dimensions and construct a regular quantum gate composed entirely in terms of the generalized CNOT gate that cyclically permutes the states of d qudits for d prime. We also investigate the case for d other than prime. A key feature of the construction design relates to the periodicity evaluation for a family of linear recurrences which we achieve by exploiting generating functions and their factorization over the complex reals

On swapping the states of two qudits

The SWAP gate has become an integral feature of quantum circuit architectures and is designed to permute the states of two qubits through the use of the well-known controlled-NOT gate. We consider the question of whether a two-qudit quantum circuit composed entirely from instances of the generalised controlled-NOT gate can be constructed to permute the states of two qudits. Arguing via the signature of a permutation, we demonstrate the impossibility of such circuits for dimensions $d \equiv 3$ (mod 4)

Quantum Sign Permutation Polytopes

Convex polytopes are convex hulls of point sets in the $n$-dimensional space \E^n that generalize 2-dimensional convex polygons and 3-dimensional convex polyhedra. We concentrate on the class of $n$-dimensional polytopes in \E^n called sign permutation polytopes. We characterize sign permutation polytopes before relating their construction to constructions over the space of quantum density matrices. Finally, we consider the problem of state identification and show how sign permutation polytopes may be useful in addressing issues of robustness

InterMEL: An international biorepository and clinical database to uncover predictors of survival in early-stage melanoma

We are conducting a multicenter study to identify classifiers predictive of disease-specific survival in patients with primary melanomas. Here we delineate the unique aspects, challenges, and best practices for optimizing a study of generally small-sized pigmented tumor samples including primary melanomas of at least 1.05mm from AJTCC TNM stage IIA-IIID patients. We also evaluated tissue-derived predictors of extracted nucleic acids’ quality and success in downstream testing. This ongoing study will target 1,000 melanomas within the international InterMEL consortium.Medicin

Retrospective evaluation of whole exome and genome mutation calls in 746 cancer samples

Funder: NCI U24CA211006Abstract: The Cancer Genome Atlas (TCGA) and International Cancer Genome Consortium (ICGC) curated consensus somatic mutation calls using whole exome sequencing (WES) and whole genome sequencing (WGS), respectively. Here, as part of the ICGC/TCGA Pan-Cancer Analysis of Whole Genomes (PCAWG) Consortium, which aggregated whole genome sequencing data from 2,658 cancers across 38 tumour types, we compare WES and WGS side-by-side from 746 TCGA samples, finding that ~80% of mutations overlap in covered exonic regions. We estimate that low variant allele fraction (VAF < 15%) and clonal heterogeneity contribute up to 68% of private WGS mutations and 71% of private WES mutations. We observe that ~30% of private WGS mutations trace to mutations identified by a single variant caller in WES consensus efforts. WGS captures both ~50% more variation in exonic regions and un-observed mutations in loci with variable GC-content. Together, our analysis highlights technological divergences between two reproducible somatic variant detection efforts

Sex differences in oncogenic mutational processes

Sex differences have been observed in multiple facets of cancer epidemiology, treatment and biology, and in most cancers outside the sex organs. Efforts to link these clinical differences to specific molecular features have focused on somatic mutations within the coding regions of the genome. Here we report a pan-cancer analysis of sex differences in whole genomes of 1983 tumours of 28 subtypes as part of the ICGC/TCGA Pan-Cancer Analysis of Whole Genomes (PCAWG) Consortium. We both confirm the results of exome studies, and also uncover previously undescribed sex differences. These include sex-biases in coding and non-coding cancer drivers, mutation prevalence and strikingly, in mutational signatures related to underlying mutational processes. These results underline the pervasiveness of molecular sex differences and strengthen the call for increased consideration of sex in molecular cancer research.Sex differences have been observed in multiple facets of cancer epidemiology, treatment and biology, and in most cancers outside the sex organs. Efforts to link these clinical differences to specific molecular features have focused on somatic mutations within the coding regions of the genome. Here we report a pan-cancer analysis of sex differences in whole genomes of 1983 tumours of 28 subtypes as part of the ICGC/TCGA Pan-Cancer Analysis of Whole Genomes (PCAWG) Consortium. We both confirm the results of exome studies, and also uncover previously undescribed sex differences. These include sex-biases in coding and non-coding cancer drivers, mutation prevalence and strikingly, in mutational signatures related to underlying mutational processes. These results underline the pervasiveness of molecular sex differences and strengthen the call for increased consideration of sex in molecular cancer research.Peer reviewe