Multi-qubit Randomized Benchmarking Using Few Samples

Randomized benchmarking (RB) is an efficient and robust method to characterize gate errors in quantum circuits. Averaging over random sequences of gates leads to estimates of gate errors in terms of the average fidelity. These estimates are isolated from the state preparation and measurement errors that plague other methods like channel tomography and direct fidelity estimation. A decisive factor in the feasibility of randomized benchmarking is the number of sampled sequences required to obtain rigorous confidence intervals. Previous bounds were either prohibitively loose or required the number of sampled sequences to scale exponentially with the number of qubits in order to obtain a fixed confidence interval at a fixed error rate. Here we show that, with a small adaptation to the randomized benchmarking procedure, the number of sampled sequences required for a fixed confidence interval is dramatically smaller than could previously be justified. In particular, we show that the number of sampled sequences required is essentially independent of the number of qubits and scales favorably with the average error rate of the system under investigation. We also show that the number of samples required for long sequence lengths can be made substantially smaller than previous rigorous results (even for single qubits) as long as the noise process under investigation is not unitary. Our results bring rigorous randomized benchmarking on systems with many qubits into the realm of experimental feasibility.Comment: v3: Added discussion of the impact of variance heteroskedasticity on the RB fitting procedure. Close to published versio

Contextuality under weak assumptions

The presence of contextuality in quantum theory was first highlighted by Bell, Kochen and Specker, who discovered that for quantum systems of three or more dimensions, measurements could not be viewed as deterministically revealing pre-existing properties of the system. More precisely, no model can assign deterministic outcomes to the projectors of a quantum measurement in a way that depends only on the projector and not the context (the full set of projectors) in which it appeared, despite the fact that the Born rule probabilities associated with projectors are independent of the context. A more general, operational definition of contextuality introduced by Spekkens, which we will term "probabilistic contextuality", drops the assumption of determinism and allows for operations other than measurements to be considered contextual. Even two-dimensional quantum mechanics can be shown to be contextual under this generalised notion. Probabilistic noncontextuality represents the postulate that elements of an operational theory that cannot be distinguished from each other based on the statistics of arbitrarily many repeated experiments (they give rise to the same operational probabilities) are ontologically identical. In this paper, we introduce a framework that enables us to distinguish between different noncontextuality assumptions in terms of the relationships between the ontological representations of objects in the theory given a certain relation between their operational representations. This framework can be used to motivate and define a "possibilistic" analogue, encapsulating the idea that elements of an operational theory that cannot be unambiguously distinguished operationally can also not be unambiguously distinguished ontologically. We then prove that possibilistic noncontextuality is equivalent to an alternative notion of noncontextuality proposed by Hardy. Finally, we demonstrate that these weaker noncontextuality assumptions are sufficient to prove alternative versions of known "no-go" theorems that constrain ψ-epistemic models for quantum mechanics

First instar larvae of endemic Australian Miltogramminae (Diptera: Sarcophagidae)

The first instar larva of a species of the Australian endemic genus Aenigmetopia Malloch is described for the first time, along with the first instar larvae of three other Australian species representing the genera Amobia Robineau-Desvoidy and Protomiltogramma Townsend. Larval morphology was analysed using a combination of light microscopy, confocal laser scanning microscopy and scanning electron microscopy. The following morphological structures are documented: pseudocephalon, antennal complex, maxillary palpus, facial mask, modifications of thoracic and abdominal segments, anal region, spiracular field, posterior spiracles and details of the cephaloskeleton. Substantial morphological differences are observed between the three genera, most notably in the labrum and mouthhooks of the cephaloskeleton, sensory organs of the pseudocephalon, spinulation, sculpture of the integument and form of the spiracular field. The first instar larval morphology of Aenigmetopia amissa Johnston, Wallman, Szpila & Pape corroborates the close phylogenetic affinity of Aenigmetopia Malloch with Metopia Meigen, inferred from recent molecular analysis. The larval morphology of Amobia auriceps (Baranov), Protomiltogramma cincta Townsend and Protomiltogramma plebeia Malloch is mostly congruent with the morphology of Palaearctic representatives of both genera

Revisiting consistency conditions for quantum states of systems on closed timelike curves: an epistemic perspective

There has been considerable recent interest in the consequences of closed timelike curves (CTCs) for the dynamics of quantum mechanical systems. A vast majority of research into this area makes use of the dynamical equations developed by Deutsch, which were developed from a consistency condition that assumes that mixed quantum states uniquely describe the physical state of a system. We criticise this choice of consistency condition from an epistemic perspective, i.e., a perspective in which the quantum state represents a state of knowledge about a system. We demonstrate that directly applying Deutsch's condition when mixed states are treated as representing an observer's knowledge of a system can conceal time travel paradoxes from the observer, rather than resolving them. To shed further light on the appropriate dynamics for quantum systems traversing CTCs, we make use of a toy epistemic theory with a strictly classical ontology due to Spekkens and show that, in contrast to the results of Deutsch, many of the traditional paradoxical effects of time travel are present.Comment: 10 pages, 6 figures, comments welcome; v2 added references and clarified some points; v3 published versio

The prognosis for individuals on disability retirement An 18-year mortality follow-up study of 6887 men and women sampled from the general population

BACKGROUND: Several studies have shown a markedly higher mortality rate among disability pensioners than among non-retired. Since most disability pensions are granted because of non-fatal diseases the reason for the increased mortality therefore remains largely unknown. The aim of this study was to evaluate potential explanatory factors. METHODS: Data from five longitudinal cohort studies in Sweden, including 6,887 men and women less than 65 years old at baseline were linked to disability pension data, hospital admission data, and mortality data from 1971 until 2001. Mortality odds ratios were analyzed with Poisson regression and Cox's proportional hazards regression models. RESULTS: 1,683 (24.4%) subjects had a disability pension at baseline or received one during follow up. 525 (7.6%) subjects died during follow up. The subjects on disability pension had a higher mortality rate than the non-retired, the hazards ratio (HR) being 2.78 (95%CI 2.08–3.71) among women and 3.43 (95%CI 2.61–4.51) among men. HR was highest among individuals granted a disability pension at young ages (HR >7), and declined parallel to age at which the disability pension was granted. The higher mortality rate among the retired subjects was not explained by disability pension cause or underlying disease or differences in age, marital status, educational level, smoking habits or drug abuse. There was no significant association between reason for disability pension and cause of death. CONCLUSION: Subjects with a disability pension had increased mortality rates as compared with non-retired subjects, only modestly affected by adjustments for psycho-socio-economic factors, underlying disease, etcetera. It is unlikely that these factors were the causes of the unfavorable outcome. Other factors must be at work

Sick-leave track record and other potential predictors of a disability pension. A population based study of 8,218 men and women followed for 16 years

<p>Abstract</p> <p>Background</p> <p>A number of previous studies have investigated various predictors for being granted a disability pension. The aim of this study was to test the efficacy of sick-leave track record as a predictor of being granted a disability pension in a large dataset based on subjects sampled from the general population and followed for a long time.</p> <p>Methods</p> <p>Data from five ongoing population-based Swedish studies was used, supplemented with data on all compensated sick leave periods, disability pensions granted, and vital status, obtained from official registers. The data set included 8,218 men and women followed for 16 years, generated 109,369 person years of observation and 97,160 sickness spells. Various measures of days of sick leave during follow up were used as independent variables and disability pension grant was used as outcome.</p> <p>Results</p> <p>There was a strong relationship between individual sickness spell duration and annual cumulative days of sick leave on the one hand and being granted a disability pension on the other, among both men and women, after adjustment for the effects of marital status, education, household size, smoking habits, geographical area and calendar time period, a proxy for position in the business cycle. The interval between sickness spells showed a corresponding inverse relationship. Of all the variables studied, the number of days of sick leave per year was the most powerful predictor of a disability pension. For both men and women 245 annual sick leave days were needed to reach a 50% probability of transition to disability. The independent variables, taken together, explained 96% of the variation in disability pension grantings.</p> <p>Conclusion</p> <p>The sick-leave track record was the most important predictor of the probability of being granted a disability pension in this study, even when the influences of other variables affecting the outcome were taken into account.</p