The Poisson equation has many applications across the broad areas of science and engineering. Most quantum algorithms for the Poisson solver presented so far either suffer from lack of accuracy ...and/or are limited to very small sizes of the problem and thus have no practical usage. In this regard, our previous work (Robson in 2022 IEEE International Conference on Quantum Computing and Engineering (QCE), 2022) showed a proof-of-concept demonstration in advancing quantum Poisson solver algorithm and validated preliminary results for a simple case of
3
×
3
problem. In this work, we delve into comprehensive research details, presenting the results on up to
15
×
15
problems that include step-by-step improvements in Poisson equation solutions, scaling performance, and experimental exploration. In particular, we demonstrate the implementation of eigenvalue amplification by a factor of up to
2
8
, achieving a significant improvement in the accuracy of our quantum Poisson solver and comparing that to the exact solution. Additionally, we present success probability results, highlighting the reliability of our quantum Poisson solver. Moreover, we explore the scaling performance of our algorithm against the circuit depth and width, demonstrating how our approach scales with larger problem sizes and thus further solidifies the practicality of easy adaptation of this algorithm in real-world applications. We also discuss a multilevel strategy for how this algorithm might be further improved to explore much larger problems with greater performance. Finally, through our experiments on the IBM quantum hardware, we conclude that though overall results on the existing NISQ hardware are dominated by the error in the
CNOT
gates, this work opens a path to realizing a multidimensional Poisson solver on near-term quantum hardware.
Abstract
The Eukaryotic Pathogen, Vector and Host Informatics Resource (VEuPathDB, https://veupathdb.org) is a Bioinformatics Resource Center funded by the National Institutes of Health with ...additional funding from the Wellcome Trust. VEuPathDB supports >600 organisms that comprise invertebrate vectors, eukaryotic pathogens (protists and fungi) and relevant free-living or non-pathogenic species or hosts. Since 2004, VEuPathDB has analyzed omics data from the public domain using contemporary bioinformatic workflows, including orthology predictions via OrthoMCL, and integrated the analysis results with analysis tools, visualizations, and advanced search capabilities. The unique data mining platform coupled with >3000 pre-analyzed data sets facilitates the exploration of pertinent omics data in support of hypothesis driven research. Comparisons are easily made across data sets, data types and organisms. A Galaxy workspace offers the opportunity for the analysis of private large-scale datasets and for porting to VEuPathDB for comparisons with integrated data. The MapVEu tool provides a platform for exploration of spatially resolved data such as vector surveillance and insecticide resistance monitoring. To address the growing body of omics data and advances in laboratory techniques, VEuPathDB has added several new data types, searches and features, improved the Galaxy workspace environment, redesigned the MapVEu interface and updated the infrastructure to accommodate these changes.
Graphical Abstract
Graphical Abstract
The Poisson equation has many applications across the broad areas of science and engineering. Most quantum algorithms for the Poisson solver presented so far either suffer from lack of accuracy ...and/or are limited to very small sizes of the problem, and thus have no practical usage. Here we present an advanced quantum algorithm for solving the Poisson equation with high accuracy and dynamically tunable problem size. After converting the Poisson equation to a linear system through the finite difference method, we adopt the HHL algorithm as the basic framework. Particularly, in this work we present an advanced circuit that ensures the accuracy of the solution by implementing non-truncated eigenvalues through eigenvalue amplification, as well as by increasing the accuracy of the controlled rotation angular coefficients, which are the critical factors in the HHL algorithm. Consequently, we are able to drastically reduce the relative error in the solution while achieving higher success probability as the amplification level is increased. We show that our algorithm not only increases the accuracy of the solutions but also composes more practical and scalable circuits by dynamically controlling problem size in NISQ devices. We present both simulated and experimental results and discuss the sources of errors. Finally, we conclude that though overall results on the existing NISQ hardware are dominated by the error in the CNOT gates, this work opens a path to realizing a multidimensional Poisson solver on near-term quantum hardware.
The Poisson equation has many applications across the broad areas of science and engineering. Most quantum algorithms for the Poisson solver presented so far, either suffer from lack of accuracy ...and/or are limited to very small sizes of the problem, and thus have no practical usage. Here we present an advanced quantum algorithm for solving the Poisson equation with high accuracy and dynamically tunable problem size. After converting the Poisson equation to the linear systems through the finite difference method, we adopt the Harrow-Hassidim-Lloyd (HHL) algorithm as the basic framework. Particularly, in this work we present an advanced circuit that ensures the accuracy of the solution by implementing non-truncated eigenvalues through eigenvalue amplification as well as by increasing the accuracy of the controlled rotation angular coefficients, which are the critical factors in the HHL algorithm. We show that our algorithm not only increases the accuracy of the solutions, but also composes more practical and scalable circuits by dynamically controlling problem size in the NISQ devices. We present both simulated and experimental solutions, and conclude that overall results on the quantum hardware are dominated by the error in the CNOT gates.
Introduction: We discuss a case of massive hemoptysis in the setting of a direct-acting oral anticoagulant (DOAC) successfully managed with nebulized tranexamic acid (TXA).
Case Report: Per the ...American College of Cardiology and the American Society of Hematology, it is recommended that significant bleeding associated with a DOAC be treated with either 4-factor prothrombin complex concentrate or andexanet alfa. However, our patient was at high risk for thrombotic complications given a recent pulmonary embolism.
Conclusion: We demonstrate that it is reasonable to trial nebulized TXA given its low cost, ease of administration, and safety profile. Additionally, this report discusses a unique dosing strategy and a previously unreported complication associated with nebulization of undiluted TXA.
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