Randomized benchmarking of single and multi-qubit control in liquid-state NMR quantum information processing

Being able to quantify the level of coherent control in a proposed device implementing a quantum information processor (QIP) is an important task for both comparing different devices and assessing a device's prospects with regards to achieving fault-tolerant quantum control. We implement in a liquid-state nuclear magnetic resonance QIP the randomized benchmarking protocol presented by Knill et al (PRA 77: 012307 (2008)). We report an error per randomized $\frac{\pi}{2}$ pulse of $1.3 \pm 0.1 \times 10^{-4}$ with a single qubit QIP and show an experimentally relevant error model where the randomized benchmarking gives a signature fidelity decay which is not possible to interpret as a single error per gate. We explore and experimentally investigate multi-qubit extensions of this protocol and report an average error rate for one and two qubit gates of $4.7 \pm 0.3 \times 10^{-3}$ for a three qubit QIP. We estimate that these error rates are still not decoherence limited and thus can be improved with modifications to the control hardware and software.Comment: 10 pages, 6 figures, submitted versio

The Importance of Statistical Theory in Outlier Detection

We explore the performance of the outlier-sum statistic (Tibshirani and Hastie, Biostatistics 2007 8:2--8), a proposed method for identifying genes for which only a subset of a group of samples or patients exhibits differential expression levels. Our discussion focuses on this method as an example of how inattention to standard statistical theory can lead to approaches that exhibit some serious drawbacks. In contrast to the results presented by those authors, when comparing this method to several variations of the $t$-test, we find that the proposed method offers little benefit even in the most idealized scenarios, and suffers from a number of limitations including difficulty of calibration, high false positive rates owing to its asymmetric treatment of groups, poor power or discriminatory ability under many alternatives, and poorly defined application to one-sample settings. Further issues in the Tibshirani and Hastie paper concern the presentation and accuracy of their simulation results; we were unable to reproduce their findings, and we discuss several undesirable and implausible aspects of their results

Genes, geología y biodiversidad: diversidad de la fauna y flora de la isla de Gran Canaria

High levels of floral and faunal diversity in the Canary Islands have attracted much attention to the archipelago for both evolutionary and ecological study. Among the processes that have influenced the development of this diversity, the volcanic history of each individual island must have played a pivotal role. The central island of Gran Canaria has a long geological history of approximately 15 million years that was interrupted by violent volcanism between 5.5 and 3 million years ago. Volcanic activity is thought to have been so great as to have made all plant and animal life virtually extinct, with survival being limited to some coastal species. The implication from this is that the higher altitude laurel forest and pine woods environments must have been re–established following the dramatic volcanic period. This paper reviews the evidence for this using recent molecular phylogenetic data for a number of plant and animal groups on the island of Gran Canaria, and concludes that there is general support for the hypotheses that the forest environments of Gran Canaria post–date the Roque Nublo eruptive period.La extensa diversidad de la flora y fauna de las Islas Canarias ha convertido el archipiélago en un centro de especial interés para los estudios sobre evolución y ecología. De entre los procesos que han influido en el desarrollo de esta diversidad, cabe destacar el importante papel que ha desempeñado la historia volcánica de cada una de las islas. La isla principal del archipiélago, Gran Canaria, tiene una larga historia geológica de aproximadamente unos 15 millones de años, que fue interrumpida por un violento volcanismo que tuvo lugar hace entre 5,5 y 3 millones de años. Se considera que la actividad volcánica fue de tal magnitud, que prácticamente extinguió toda la vida vegetal y animal de las islas, a excepción de unas pocas especies costeras que lograron sobrevivir. De ello puede deducirse que los entornos de mayor altitud, como los bosques de laureles y pinos, seguramente se reestablecieron tras el dramático período volcánico antes mencionado. En este trabajo, se revisa la evidencia de ello mediante el análisis de datos filogénicos moleculares recientes de una serie de grupos de plantas y animales de la isla de Gran Canaria, y se demuestra la validez general de la hipótesis que sostiene que los entornos forestales de Gran Canaria son posteriores al ciclo eruptivo de Roque Nublo

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Exploring the Benefits of Adaptive Sequential Designs in Time-to-Event Endpoint Settings

Sequential analysis is frequently employed to address ethical and financial issues in clinical trials. Sequential analysis may be performed using standard group sequential designs, or, more recently, with adaptive designs that use estimates of treatment effect to modify the maximal statistical information to be collected. In the general setting in which statistical information and clinical trial costs are functions of the number of subjects used, it has yet to be established whether there is any major efficiency advantage to adaptive designs over traditional group sequential designs. In survival analysis, however, statistical information (and hence efficiency) is most closely related to the observed number of events, while trial costs still depend on the number of patients accrued. As the number of subjects may dominate the cost of a trial, an adaptive design that specifies a reduced maximal possible sample size when an extreme treatment effect has been observed may allow early termination of accrual and therefore a more costefficient trial. We investigate and compare the tradeoffs between efficiency (as measured by average number of observed events required), power, and cost (a function of the number of subjects accrued and length of observation) for standard group sequential methods and an adaptive design that allows for early termination of accrual. We find that when certain trial design parameters are constrained, an adaptive approach to terminating subject accrual may improve upon the cost efficiency of a group sequential clinical trial investigating time-to-event endpoints. However, when the spectrum of group sequential designs considered is broadened, the advantage of the adaptive designs is less clear

Interpreting quantum nonlocality as platonic information

The "hidden variables" or "guiding equation" explanation for the measurement of quantum nonlocality (entanglement) effects can be interpreted as instantiation of Platonic information. Because these Bohm-deBroglie principles are already external to the material objects that they theoretically affect, interpreting them as Platonic is feasible. Taking an approach partially suggested by Quantum Information Theory which views quantum phenomena as sometimes observable-measurable information, this thesis defines hidden variables/guiding equation as information. This approach enables us to bridge the divide between the abstract Platonic realm and the physical world. The unobservable quantum wavefunction collapse is interpreted as Platonic instantiation. At each interaction, the wave function for a quantum system collapses. Instantly, Platonic information is instantiated in the system

Raising a Coconspirator: A Letter to My Daughter

In this letter to her daughter, the author utilizes a journey map to anticipate some of the decisions and actions she will have to make and take in order to raise her as an antiracist co-conspirator. As a white parent to a white child, the author explores necessary moves towards racial literacy, rethinking obedience, and revisiting concepts of independence. She explores the way in which her parenting must be envisioned differently given this current COVID moment amidst the movement for Black lives