Optimal fermion-qubit mappings

Simulating fermionic systems on a quantum computer requires a high-performing mapping of fermionic states to qubits. The key characteristic of an efficient mapping is its ability to translate local fermionic interactions into local qubit interactions, leading to easy-to-simulate qubit Hamiltonians. Improvements in the locality of fermion-qubit mappings have traditionally come at higher resource costs elsewhere, such as in the form of a significant number of additional qubits. We present a new way to design fermion-qubit mappings by making use of the extra degree of freedom: the choice of numbering scheme for the fermionic modes, a feature all mappings must have. This allows us to minimse the average Pauli weight of a qubit Hamiltonian -- its average number of Pauli matrices per term. Our approach leads to a rigorous notion of optimality by viewing fermion-qubit mappings as functions of their enumeration schemes. Furthermore, finding the best enumeration scheme allows one to increase the locality of the target qubit Hamiltonian without expending any additional resources. Minimising the average Pauli weight of a mapping is an NP-complete problem in general. We show how one solution, Mitchison and Durbin's enumeration pattern, leads to a qubit Hamiltonian for simulating the square fermionic lattice consisting of terms with an average Pauli weight 13.9% shorter than previously any previously known. Adding just two ancilla qubits, we can reduce the average Pauli weight of Hamiltonian terms by 37.9% on square lattices compared to previous methods. Lastly, we demonstrate the potential of our techniques to polynomially reduce the average Pauli weight by exhibiting $n$-mode fermionic systems where optimisation yields patterns that achieve $n^{\frac{1}{4}}$ improvement in average Pauli weight over na\"ive enumeration schemes.Comment: 29 pages, 30 figure

Silicon uptake by a pasture grass experiencing simulated grazing is greatest under elevated precipitation

Background Grasses are hyper-accumulators of silicon (Si) and often up-regulate Si following herbivory. Positive correlations exist between Si and plant water content, yet the extent to which Si uptake responses can be mediated by changes in soil water availability has rarely been studied and never, to our knowledge, under field conditions. We used field-based rain-exclusion shelters to investigate how simulated grazing (shoot clipping) and altered rainfall patterns (drought and elevated precipitation, representing 50% and 150% of ambient precipitation levels, respectively) affected initial patterns of root- and shoot-Si uptake in a native Australian grass (Microlaena stipoides) in Si-supplemented and untreated soils. Results Si supplementation increased soil water retention under ambient and elevated precipitation but not under drought, although this had little effect on Si uptake and growth (tiller numbers or root biomass) of M. stipoides. Changes in rainfall patterns and clipping had strong individual effects on plant growth and Si uptake and storage, whereby clipping increased Si uptake by M. stipoides under all rainfall treatments but to the greatest extent under elevated precipitation. Moreover, above-ground–below-ground Si distribution only changed following elevated precipitation by decreasing the ratio of root:shoot Si concentrations. Conclusions Results highlight the importance of soil water availability for Si uptake and suggest a role for both active and passive Si transport mechanisms. Such manipulative field studies may provide a more realistic insight into how grasses initially respond to herbivory in terms of Si-based defence under different environmental conditions

Identification of 12 new susceptibility loci for different histotypes of epithelial ovarian cancer.

To identify common alleles associated with different histotypes of epithelial ovarian cancer (EOC), we pooled data from multiple genome-wide genotyping projects totaling 25,509 EOC cases and 40,941 controls. We identified nine new susceptibility loci for different EOC histotypes: six for serous EOC histotypes (3q28, 4q32.3, 8q21.11, 10q24.33, 18q11.2 and 22q12.1), two for mucinous EOC (3q22.3 and 9q31.1) and one for endometrioid EOC (5q12.3). We then performed meta-analysis on the results for high-grade serous ovarian cancer with the results from analysis of 31,448 BRCA1 and BRCA2 mutation carriers, including 3,887 mutation carriers with EOC. This identified three additional susceptibility loci at 2q13, 8q24.1 and 12q24.31. Integrated analyses of genes and regulatory biofeatures at each locus predicted candidate susceptibility genes, including OBFC1, a new candidate susceptibility gene for low-grade and borderline serous EOC

Pan-cancer analysis of whole genomes

Cancer is driven by genetic change, and the advent of massively parallel sequencing has enabled systematic documentation of this variation at the whole-genome scale(1-3). Here we report the integrative analysis of 2,658 whole-cancer genomes and their matching normal tissues across 38 tumour types from the Pan-Cancer Analysis of Whole Genomes (PCAWG) Consortium of the International Cancer Genome Consortium (ICGC) and The Cancer Genome Atlas (TCGA). We describe the generation of the PCAWG resource, facilitated by international data sharing using compute clouds. On average, cancer genomes contained 4-5 driver mutations when combining coding and non-coding genomic elements; however, in around 5% of cases no drivers were identified, suggesting that cancer driver discovery is not yet complete. Chromothripsis, in which many clustered structural variants arise in a single catastrophic event, is frequently an early event in tumour evolution; in acral melanoma, for example, these events precede most somatic point mutations and affect several cancer-associated genes simultaneously. Cancers with abnormal telomere maintenance often originate from tissues with low replicative activity and show several mechanisms of preventing telomere attrition to critical levels. Common and rare germline variants affect patterns of somatic mutation, including point mutations, structural variants and somatic retrotransposition. A collection of papers from the PCAWG Consortium describes non-coding mutations that drive cancer beyond those in the TERT promoter(4); identifies new signatures of mutational processes that cause base substitutions, small insertions and deletions and structural variation(5,6); analyses timings and patterns of tumour evolution(7); describes the diverse transcriptional consequences of somatic mutation on splicing, expression levels, fusion genes and promoter activity(8,9); and evaluates a range of more-specialized features of cancer genomes(8,10-18).Peer reviewe

Comprehensive analysis of chromothripsis in 2,658 human cancers using whole-genome sequencing

Chromothripsis is a mutational phenomenon characterized by massive, clustered genomic rearrangements that occurs in cancer and other diseases. Recent studies in selected cancer types have suggested that chromothripsis may be more common than initially inferred from low-resolution copy-number data. Here, as part of the Pan-Cancer Analysis of Whole Genomes (PCAWG) Consortium of the International Cancer Genome Consortium (ICGC) and The Cancer Genome Atlas (TCGA), we analyze patterns of chromothripsis across 2,658 tumors from 38 cancer types using whole-genome sequencing data. We find that chromothripsis events are pervasive across cancers, with a frequency of more than 50% in several cancer types. Whereas canonical chromothripsis profiles display oscillations between two copy-number states, a considerable fraction of events involve multiple chromosomes and additional structural alterations. In addition to non-homologous end joining, we detect signatures of replication-associated processes and templated insertions. Chromothripsis contributes to oncogene amplification and to inactivation of genes such as mismatch-repair-related genes. These findings show that chromothripsis is a major process that drives genome evolution in human cancer