Characterizing quantum supremacy in near-term devices

© 2018 Macmillan Publishers Limited, part of Springer Nature. All rights reserved. A critical question for quantum computing in the near future is whether quantum devices without error correction can perform a well-defined computational task beyond the capabilities of supercomputers. Such a demonstration of what is referred to as quantum supremacy requires a reliable evaluation of the resources required to solve tasks with classical approaches. Here, we propose the task of sampling from the output distribution of random quantum circuits as a demonstration of quantum supremacy. We extend previous results in computational complexity to argue that this sampling task must take exponential time in a classical computer. We introduce cross-entropy benchmarking to obtain the experimental fidelity of complex multiqubit dynamics. This can be estimated and extrapolated to give a success metric for a quantum supremacy demonstration. We study the computational cost of relevant classical algorithms and conclude that quantum supremacy can be achieved with circuits in a two-dimensional lattice of 7 × 7 qubits and around 40 clock cycles. This requires an error rate of around 0.5% for two-qubit gates (0.05% for one-qubit gates), and it would demonstrate the basic building blocks for a fault-tolerant quantum computer

The development of path integration: combining estimations of distance and heading

Efficient daily navigation is underpinned by path integration, the mechanism by which we use self-movement information to update our position in space. This process is well-understood in adulthood, but there has been relatively little study of path integration in childhood, leading to an underrepresentation in accounts of navigational development. Previous research has shown that calculation of distance and heading both tend to be less accurate in children as they are in adults, although there have been no studies of the combined calculation of distance and heading that typifies naturalistic path integration. In the present study 5-year-olds and 7-year-olds took part in a triangle-completion task, where they were required to return to the startpoint of a multi-element path using only idiothetic information. Performance was compared to a sample of adult participants, who were found to be more accurate than children on measures of landing error, heading error, and distance error. 7-year-olds were significantly more accurate than 5-year-olds on measures of landing error and heading error, although the difference between groups was much smaller for distance error. All measures were reliably correlated with age, demonstrating a clear development of path integration abilities within the age range tested. Taken together, these data make a strong case for the inclusion of path integration within developmental models of spatial navigational processing

Plant communities affect arbuscular mycorrhizal fungal diversity and community composition in grassland microcosms

The diversity of arbuscular mycorrhizal (AM) fungi was investigated in an unfertilized limestone grassland soil supporting different synthesized vascular plant assemblages that had developed for 3 yr. The experimental treatments comprised: bare soil; monocultures of the nonmycotrophic sedge Carex flacca; monocultures of the mycotrophic grass Festuca ovina; and a species-rich mixture of four forbs, four grasses and four sedges. The diversity of AM fungi was analysed in roots of Plantago lanceolata bioassay seedlings using terminal-restriction fragment length polymorphism (T-RFLP). The extent of AM colonization, shoot biomass and nitrogen and phosphorus concentrations were also measured. The AM diversity was affected significantly by the floristic composition of the microcosms and shoot phosphorus concentration was positively correlated with AM diversity. The diversity of AM fungi in P. lanceolata decreased in the order: bare soil > C. flacca > 12 species > F. ovina. The unexpectedly high diversity in the bare soil and sedge monoculture likely reflects differences in the modes of colonization and sources of inoculum in these treatments compared with the assemblages containing established AM-compatible plants

Autosomal dominant optic atrophy and cataract “plus” phenotype including axonal neuropathy

Objective To characterize the phenotype in individuals with OPA3-related autosomal dominant optic atrophy and cataract (ADOAC) and peripheral neuropathy (PN). Methods Two probands with multiple affected relatives and one sporadic case were referred for evaluation of a PN. Their phenotype was determined by clinical ± neurophysiological assessment. Neuropathologic examination of sural nerve and skeletal muscle, and ultrastructural analysis of mitochondria in fibroblasts were performed in one case. Exome sequencing was performed in the probands. Results The main clinical features in one family (n = 7 affected individuals) and one sporadic case were early-onset cataracts (n = 7), symptoms of gastrointestinal dysmotility (n = 8), and possible/confirmed PN (n = 7). Impaired vision was an early-onset feature in another family (n = 4 affected individuals), in which 3 members had symptoms of gastrointestinal dysmotility and 2 developed PN and cataracts. The less common features among all individuals included symptoms/signs of autonomic dysfunction (n = 3), hearing loss (n = 3), and recurrent pancreatitis (n = 1). In 5 individuals, the neuropathy was axonal and clinically asymptomatic (n = 1), sensory-predominant (n = 2), or motor and sensory (n = 2). In one patient, nerve biopsy revealed a loss of large and small myelinated fibers. In fibroblasts, mitochondria were frequently enlarged with slightly fragmented cristae. The exome sequencing identified OPA3 variants in all probands: a novel variant (c.23T>C) and the known mutation (c.313C>G) in OPA3. Conclusions A syndromic form of ADOAC (ADOAC+), in which axonal neuropathy may be a major feature, is described. OPA3 mutations should be included in the differential diagnosis of complex inherited PN, even in the absence of clinically apparent optic atrophy

Reciprocity as a foundation of financial economics

This paper argues that the subsistence of the fundamental theorem of contemporary financial mathematics is the ethical concept ‘reciprocity’. The argument is based on identifying an equivalence between the contemporary, and ostensibly ‘value neutral’, Fundamental Theory of Asset Pricing with theories of mathematical probability that emerged in the seventeenth century in the context of the ethical assessment of commercial contracts in a framework of Aristotelian ethics. This observation, the main claim of the paper, is justified on the basis of results from the Ultimatum Game and is analysed within a framework of Pragmatic philosophy. The analysis leads to the explanatory hypothesis that markets are centres of communicative action with reciprocity as a rule of discourse. The purpose of the paper is to reorientate financial economics to emphasise the objectives of cooperation and social cohesion and to this end, we offer specific policy advice

The quantitative ADAM questionnaire: a new tool in quantifying the severity of hypogonadism

Androgen deficiency is a pervasive problem in the older male population and is thought to be responsible for many symptoms once considered to be the result of normal aging. Numerous methods have been proposed to facilitate the detection of men at risk for androgen deficiency. In this article, we propose a novel screening tool, the quantitative Androgen Deficiency in the Aging Male (qADAM) questionnaire and report its successful use in quantifying the severity of androgen deficiency in a group of older men. Fifty-seven males scheduled to undergo radical prostatectomy for prostate cancer completed the qADAM as well as the Sexual Health Inventory for Men (SHIM) and the Expanded Prostate Cancer Index Composite hormonal/sexual (EPICh/EPICs) questionnaires. Thirty-four men also had serum testosterone levels measured for comparison. The qADAM showed statistically significant correlation to the SHIM (P=0.001), EPICh (P=0.016), EPICs (P=<0.001), and serum testosterone (P=0.046). The qADAM represents a viable alternative to existing questionnaires used to detect androgen deficiency and to assess response to treatment

An excess of niche differences maximizes ecosystem functioning

Ecologists have long argued that higher functioning in diverse communities arises from the niche differences stabilizing species coexistence and from the fitness differences driving competitive dominance. However, rigorous tests are lacking. We couple field-parameterized models of competition between 10 annual plant species with a biodiversity-functioning experiment under two contrasting environmental conditions, to study how coexistence determinants link to biodiversity effects (selection and complementarity). We find that complementarity effects positively correlate with niche differences and selection effects differences correlate with fitness differences. However, niche differences also contribute to selection effects and fitness differences to complementarity effects. Despite this complexity, communities with an excess of niche differences (where niche differences exceeded those needed for coexistence) produce more biomass and have faster decomposition rates under drought, but do not take up nutrients more rapidly. We provide empirical evidence that the mechanisms determining coexistence correlate with those maximizing ecosystem functioning. It is unclear how biodiversity-ecosystem functioning and species coexistence mechanisms are linked. Here, Godoy and colleagues combine field-parameterised competition models with a BEF experiment to show that mechanisms leading to more stable species coexistence lead to greater productivity, but not necessarily to enhanced functions other than primary production