A Copositive Framework for Analysis of Hybrid Ising-Classical Algorithms

Recent years have seen significant advances in quantum/quantum-inspired technologies capable of approximately searching for the ground state of Ising spin Hamiltonians. The promise of leveraging such technologies to accelerate the solution of difficult optimization problems has spurred an increased interest in exploring methods to integrate Ising problems as part of their solution process, with existing approaches ranging from direct transcription to hybrid quantum-classical approaches rooted in existing optimization algorithms. While it is widely acknowledged that quantum computers should augment classical computers, rather than replace them entirely, comparatively little attention has been directed toward deriving analytical characterizations of their interactions. In this paper, we present a formal analysis of hybrid algorithms in the context of solving mixed-binary quadratic programs (MBQP) via Ising solvers. We show the exactness of a convex copositive reformulation of MBQPs, allowing the resulting reformulation to inherit the straightforward analysis of convex optimization. We propose to solve this reformulation with a hybrid quantum-classical cutting-plane algorithm. Using existing complexity results for convex cutting-plane algorithms, we deduce that the classical portion of this hybrid framework is guaranteed to be polynomial time. This suggests that when applied to NP-hard problems, the complexity of the solution is shifted onto the subroutine handled by the Ising solver

Asymptotically Faster Quantum Distributed Algorithms for Approximate Steiner Trees and Directed Minimum Spanning Trees

The CONGEST and CONGEST-CLIQUE models have been carefully studied to represent situations where the communication bandwidth between processors in a network is severely limited. Messages of only $O(log(n))$ bits of information each may be sent between processors in each round. The quantum versions of these models allow the processors instead to communicate and compute with quantum bits under the same bandwidth limitations. This leads to the following natural research question: What problems can be solved more efficiently in these quantum models than in the classical ones? Building on existing work, we contribute to this question in two ways. Firstly, we present two algorithms in the Quantum CONGEST-CLIQUE model of distributed computation that succeed with high probability; one for producing an approximately optimal Steiner Tree, and one for producing an exact directed minimum spanning tree, each of which uses $\tilde{O}(n^{1/4})$ rounds of communication and $\tilde{O}(n^{9/4})$ messages, where $n$ is the number of nodes in the network. The algorithms thus achieve a lower asymptotic round and message complexity than any known algorithms in the classical CONGEST-CLIQUE model. At a high level, we achieve these results by combining classical algorithmic frameworks with quantum subroutines. An existing framework for using distributed version of Grover's search algorithm to accelerate triangle finding lies at the core of the asymptotic speedup. Secondly, we carefully characterize the constants and logarithmic factors involved in our algorithms as well as related algorithms, otherwise commonly obscured by $\tilde{O}$ notation. The analysis shows that some improvements are needed to render both our and existing related quantum and classical algorithms practical, as their asymptotic speedups only help for very large values of $n$.Comment: 23 pages, 0 figure

QUBO.jl: A Julia Ecosystem for Quadratic Unconstrained Binary Optimization

We present QUBO.jl, an end-to-end Julia package for working with QUBO (Quadratic Unconstrained Binary Optimization) instances. This tool aims to convert a broad range of JuMP problems for straightforward application in many physics and physics-inspired solution methods whose standard optimization form is equivalent to the QUBO. These methods include quantum annealing, quantum gate-circuit optimization algorithms (Quantum Optimization Alternating Ansatz, Variational Quantum Eigensolver), other hardware-accelerated platforms, such as Coherent Ising Machines and Simulated Bifurcation Machines, and more traditional methods such as simulated annealing. Besides working with reformulations, QUBO.jl allows its users to interface with the aforementioned hardware, sending QUBO models in various file formats and retrieving results for subsequent analysis. QUBO.jl was written as a JuMP / MathOptInterface (MOI) layer that automatically maps between the input and output frames, thus providing a smooth modeling experience

Clonal chromosomal mosaicism and loss of chromosome Y in elderly men increase vulnerability for SARS-CoV-2

The pandemic caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2, COVID-19) had an estimated overall case fatality ratio of 1.38% (pre-vaccination), being 53% higher in males and increasing exponentially with age. Among 9578 individuals diagnosed with COVID-19 in the SCOURGE study, we found 133 cases (1.42%) with detectable clonal mosaicism for chromosome alterations (mCA) and 226 males (5.08%) with acquired loss of chromosome Y (LOY). Individuals with clonal mosaic events (mCA and/or LOY) showed a 54% increase in the risk of COVID-19 lethality. LOY is associated with transcriptomic biomarkers of immune dysfunction, pro-coagulation activity and cardiovascular risk. Interferon-induced genes involved in the initial immune response to SARS-CoV-2 are also down-regulated in LOY. Thus, mCA and LOY underlie at least part of the sex-biased severity and mortality of COVID-19 in aging patients. Given its potential therapeutic and prognostic relevance, evaluation of clonal mosaicism should be implemented as biomarker of COVID-19 severity in elderly people. Among 9578 individuals diagnosed with COVID-19 in the SCOURGE study, individuals with clonal mosaic events (clonal mosaicism for chromosome alterations and/or loss of chromosome Y) showed an increased risk of COVID-19 lethality

HamLib: A Library of Hamiltonians for Benchmarking Quantum Algorithms and Hardware

For a considerable time, large datasets containing problem instances have proven valuable for analyzing computer hardware, software, and algorithms. One notable example of the value of large datasets is ImageNet [1], a vast repository of images that has been instrumental in testing numerous deep learning packages. Similarly, in the domain of computational chemistry and materials science, the availability of extensive datasets such as the Protein Data Bank [2], the Materials Project [3], and QM9 [4] has greatly facilitated the evaluation of new algorithms and software approaches, while also promoting standardization within the field. These well-defined datasets and problem instances, in turn, serve as the foundation for creating benchmarking suites like MLPerf [5] and LINPACK [6], [7]. These suites enable fair and rigorous comparisons of different methodologies and solutions, fostering continuous advancements in various areas of computer science and beyond

GWAS and meta-analysis identifies 49 genetic variants underlying critical COVID-19

Data availability: Downloadable summary data are available through the GenOMICC data site (https://genomicc.org/data). Summary statistics are available, but without the 23andMe summary statistics, except for the 10,000 most significant hits, for which full summary statistics are available. The full GWAS summary statistics for the 23andMe discovery dataset will be made available through 23andMe to qualified researchers under an agreement with 23andMe that protects the privacy of the 23andMe participants. For further information and to apply for access to the data, see the 23andMe website (https://research.23andMe.com/dataset-access/). All individual-level genotype and whole-genome sequencing data (for both academic and commercial uses) can be accessed through the UKRI/HDR UK Outbreak Data Analysis Platform (https://odap.ac.uk). A restricted dataset for a subset of GenOMICC participants is also available through the Genomics England data service. Monocyte RNA-seq data are available under the title ‘Monocyte gene expression data’ within the Oxford University Research Archives (https://doi.org/10.5287/ora-ko7q2nq66). Sequencing data will be made freely available to organizations and researchers to conduct research in accordance with the UK Policy Framework for Health and Social Care Research through a data access agreement. Sequencing data have been deposited at the European Genome–Phenome Archive (EGA), which is hosted by the EBI and the CRG, under accession number EGAS00001007111.Extended data figures and tables are available online at https://www.nature.com/articles/s41586-023-06034-3#Sec21 .Supplementary information is available online at https://www.nature.com/articles/s41586-023-06034-3#Sec22 .Code availability: Code to calculate the imputation of P values on the basis of SNPs in linkage disequilibrium is available at GitHub (https://github.com/baillielab/GenOMICC_GWAS).Acknowledgements: We thank the members of the Banco Nacional de ADN and the GRA@CE cohort group; and the research participants and employees of 23andMe for making this work possible. A full list of contributors who have provided data that were collated in the HGI project, including previous iterations, is available online (https://www.covid19hg.org/acknowledgements).Change history: 11 July 2023: A Correction to this paper has been published at: https://doi.org/10.1038/s41586-023-06383-z. -- In the version of this article initially published, the name of Ana Margarita Baldión-Elorza, of the SCOURGE Consortium, appeared incorrectly (as Ana María Baldion) and has now been amended in the HTML and PDF versions of the article.Copyright © The Author(s) 2023, Critical illness in COVID-19 is an extreme and clinically homogeneous disease phenotype that we have previously shown1 to be highly efficient for discovery of genetic associations2. Despite the advanced stage of illness at presentation, we have shown that host genetics in patients who are critically ill with COVID-19 can identify immunomodulatory therapies with strong beneficial effects in this group3. Here we analyse 24,202 cases of COVID-19 with critical illness comprising a combination of microarray genotype and whole-genome sequencing data from cases of critical illness in the international GenOMICC (11,440 cases) study, combined with other studies recruiting hospitalized patients with a strong focus on severe and critical disease: ISARIC4C (676 cases) and the SCOURGE consortium (5,934 cases). To put these results in the context of existing work, we conduct a meta-analysis of the new GenOMICC genome-wide association study (GWAS) results with previously published data. We find 49 genome-wide significant associations, of which 16 have not been reported previously. To investigate the therapeutic implications of these findings, we infer the structural consequences of protein-coding variants, and combine our GWAS results with gene expression data using a monocyte transcriptome-wide association study (TWAS) model, as well as gene and protein expression using Mendelian randomization. We identify potentially druggable targets in multiple systems, including inflammatory signalling (JAK1), monocyte–macrophage activation and endothelial permeability (PDE4A), immunometabolism (SLC2A5 and AK5), and host factors required for viral entry and replication (TMPRSS2 and RAB2A).GenOMICC was funded by Sepsis Research (the Fiona Elizabeth Agnew Trust), the Intensive Care Society, a Wellcome Trust Senior Research Fellowship (to J.K.B., 223164/Z/21/Z), the Department of Health and Social Care (DHSC), Illumina, LifeArc, the Medical Research Council, UKRI, a BBSRC Institute Program Support Grant to the Roslin Institute (BBS/E/D/20002172, BBS/E/D/10002070 and BBS/E/D/30002275) and UKRI grants MC_PC_20004, MC_PC_19025, MC_PC_1905 and MRNO2995X/1. A.D.B. acknowledges funding from the Wellcome PhD training fellowship for clinicians (204979/Z/16/Z), the Edinburgh Clinical Academic Track (ECAT) programme. This research is supported in part by the Data and Connectivity National Core Study, led by Health Data Research UK in partnership with the Office for National Statistics and funded by UK Research and Innovation (grant MC_PC_20029). Laboratory work was funded by a Wellcome Intermediate Clinical Fellowship to B.F. (201488/Z/16/Z). We acknowledge the staff at NHS Digital, Public Health England and the Intensive Care National Audit and Research Centre who provided clinical data on the participants; and the National Institute for Healthcare Research Clinical Research Network (NIHR CRN) and the Chief Scientist’s Office (Scotland), who facilitate recruitment into research studies in NHS hospitals, and to the global ISARIC and InFACT consortia. GenOMICC genotype controls were obtained using UK Biobank Resource under project 788 funded by Roslin Institute Strategic Programme Grants from the BBSRC (BBS/E/D/10002070 and BBS/E/D/30002275) and Health Data Research UK (HDR-9004 and HDR-9003). UK Biobank data were used in the GSMR analyses presented here under project 66982. The UK Biobank was established by the Wellcome Trust medical charity, Medical Research Council, Department of Health, Scottish Government and the Northwest Regional Development Agency. It has also had funding from the Welsh Assembly Government, British Heart Foundation and Diabetes UK. The work of L.K. was supported by an RCUK Innovation Fellowship from the National Productivity Investment Fund (MR/R026408/1). J.Y. is supported by the Westlake Education Foundation. SCOURGE is funded by the Instituto de Salud Carlos III (COV20_00622 to A.C., PI20/00876 to C.F.), European Union (ERDF) ‘A way of making Europe’, Fundación Amancio Ortega, Banco de Santander (to A.C.), Cabildo Insular de Tenerife (CGIEU0000219140 ‘Apuestas científicas del ITER para colaborar en la lucha contra la COVID-19’ to C.F.) and Fundación Canaria Instituto de Investigación Sanitaria de Canarias (PIFIISC20/57 to C.F.). We also acknowledge the contribution of the Centro National de Genotipado (CEGEN) and Centro de Supercomputación de Galicia (CESGA) for funding this project by providing supercomputing infrastructures. A.D.L. is a recipient of fellowships from the National Council for Scientific and Technological Development (CNPq)-Brazil (309173/2019-1 and 201527/2020-0)