Grover's search with faults on some marked elements

Grover's algorithm is a quantum query algorithm solving the unstructured search problem of size $N$ using $O(\sqrt{N})$ queries. It provides a significant speed-up over any classical algorithm \cite{Gro96}. The running time of the algorithm, however, is very sensitive to errors in queries. It is known that if query may fail (report all marked elements as unmarked) the algorithm needs $\Omega(N)$ queries to find a marked element \cite{RS08}. \cite{AB+13} have proved the same result for the model where each marked element has its own probability to be reported as unmarked. We study the behavior of Grover's algorithm in the model where the search space contains both faulty and non-faulty marked elements. We show that in this setting it is indeed possible to find one of non-faulty marked items in $O(\sqrt{N})$ queries. We also analyze the limiting behavior of the algorithm for a large number of steps and show the existence and the structure of limiting state $\rho_{lim}$.Comment: 17 pages, 6 figure

Light scattering and phase behavior of Lysozyme-PEG mixtures

Measurements of liquid-liquid phase transition temperatures (cloud points) of mixtures of a protein (lysozyme) and a polymer, poly(ethylene glycol) (PEG) show that the addition of low molecular weight PEG stabilizes the mixture whereas high molecular weight PEG was destabilizing. We demonstrate that this behavior is inconsistent with an entropic depletion interaction between lysozyme and PEG and suggest that an energetic attraction between lysozyme and PEG is responsible. In order to independently characterize the lysozyme/PEG interactions, light scattering experiments on the same mixtures were performed to measure second and third virial coefficients. These measurements indicate that PEG induces repulsion between lysozyme molecules, contrary to the depletion prediction. Furthermore, it is shown that third virial terms must be included in the mixture's free energy in order to qualitatively capture our cloud point and light scattering data. The light scattering results were consistent with the cloud point measurements and indicate that attractions do exist between lysozyme and PEG.Comment: 5 pages, 2 figures, 1 tabl

SMEI observations of previously unseen pulsation frequencies in γ Doradus

Aims. As g-mode pulsators, gamma-Doradus-class stars may naïvely be expected to show a large number of modes. Taking advantage of the long photometric time-series generated by the solar mass ejection imager (SMEI) instrument, we have studied the star gamma Doradus to determine whether any other modes than the three already known are present at observable amplitude. Methods. High-precision photometric data from SMEI taken between April 2003 and March 2006 were subjected to periodogram analysis with the PERIOD04 package. Results. We confidently determine three additional frequencies at 1.39, 1.87, and 2.743 d−1. These are above and beyond the known frequencies of 1.320, 1.364, and 1.47 d−1. Conclusions. Two of the new frequencies, at 1.39 and 1.87 d−1, are speculated to be additional modes of oscillation, with the third frequency at 2.743−1 a possible combination frequency

State-space distribution and dynamical flow for closed and open quantum systems

We present a general formalism for studying the effects of dynamical heterogeneity in open quantum systems. We develop this formalism in the state space of density operators, on which ensembles of quantum states can be conveniently represented by probability distributions. We describe how this representation reduces ambiguity in the definition of quantum ensembles by providing the ability to explicitly separate classical and quantum sources of probabilistic uncertainty. We then derive explicit equations of motion for state space distributions of both open and closed quantum systems and demonstrate that resulting dynamics take a fluid mechanical form analogous to a classical probability fluid on Hamiltonian phase space, thus enabling a straightforward quantum generalization of Liouville's theorem. We illustrate the utility of our formalism by analyzing the dynamics of an open two-level system using the state-space formalism that are shown to be consistent with the derived analytical results

Approximating Fractional Time Quantum Evolution

An algorithm is presented for approximating arbitrary powers of a black box unitary operation, $\mathcal{U}^t$, where $t$ is a real number, and $\mathcal{U}$ is a black box implementing an unknown unitary. The complexity of this algorithm is calculated in terms of the number of calls to the black box, the errors in the approximation, and a certain `gap' parameter. For general $\mathcal{U}$ and large $t$, one should apply $\mathcal{U}$ a total of $\lfloor t \rfloor$ times followed by our procedure for approximating the fractional power $\mathcal{U}^{t-\lfloor t \rfloor}$. An example is also given where for large integers $t$ this method is more efficient than direct application of $t$ copies of $\mathcal{U}$. Further applications and related algorithms are also discussed.Comment: 13 pages, 2 figure

Impact of COVID-19 pandemic on chronic pain management: Looking for the best way to deliver care

Although pain treatment has been described as a fundamental human right, the Coronavirus disease 2019 (COVID-19) pandemic forced healthcare systems worldwide to redistribute healthcare resources toward intensive care units and other COVID-19 dedicated sites. As most chronic pain services were subsequently deemed non-urgent, all outpatient and elective interventional procedures have been reduced or interrupted during the COVID-19 pandemic in order to reduce the risk of viral spread. The shutdown of pain services jointly to the home lockdown imposed by governments has affected chronic pain management worldwide with additional impact on patients' psychological health. Therefore, the aim of this review is to analyze the impact of COVID-19 pandemic on chronic pain treatment and to address what types of strategies can be implemented or supported in order to overcome imposed limitations in delivery of chronic pain patient care

The use of positive end expiratory pressure in patients affected by COVID-19: Time to reconsider the relation between morphology and physiology

Coronavirus disease 2019 (COVID-19) is a new disease with different phases that can be catastrophic for subpopulations of patients with cardiovascular and pulmonary disease states at baseline. Appreciation for these different phases and treatment modalities, including manipulation of ventilatory settings and therapeutics, has made it a less lethal disease than when it emerged earlier this year. Different aspects of the disease are still largely unknown. However, laboratory investigation and clinical course of the COVID-19 show that this new disease is not a typical acute respiratory distress syndrome process, especially during the first phase. For this reason, the best strategy to be applied is to treat differently the single phases and to support the single functions of the failing organs as they appear