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We investigate the accuracy of weak lensing simulations by comparing the results of five independently developed lensing simulation codes run on the same input N-body simulation. Our comparison focuses on the lensing convergence maps produced by the codes, and in particular on the corresponding PDFs, power spectra, and peak counts. We find that the convergence power spectra of the lensing codes agree to ≤ 2 per cent out to scales ℓ ≈ 4000. For lensing peak counts, the agreement is better than 5 per cent for peaks with signal-to-noise ≤ 6. We also discuss the systematic errors due to the Born approximation, line-of-sight discretization, particle noise, and smoothing. The lensing codes tested deal in markedly different ways with these effects, but they none-the-less display a satisfactory level of agreement. Our results thus suggest that systematic errors due to the operation of existing lensing codes should be small. Moreover their impact on the convergence power spectra for a lensing simulation can be predicted given its numerical details, which may then serve as a validation test. ; The simulations and some of the analyses in this work used the DiRAC facility, managed by the Institute for Computational Cosmology, Durham University on behalf of the STFC DiRAC HPC Facility (www.dirac.ac.uk). The equipment was funded by BEIS via STFC capital grants ST/K00042X/1, ST/P002293/1, ST/R002371/1, and ST/S002502/1, Durham University, and STFC operation grant ST/R000832/1. DiRAC is part of the UK National e-Infrastructure. We thank Peter Schneider for useful comments. SH acknowledges support by the DFG cluster of excellence 'Origin and Structure of the Universe' (www.universe-cluster.de). AB acknowledges support from the starting grant (ERC-2015-STG 678652) 'GrInflaGal' of the European Research Council. GF acknowledges support from the CNES postdoctoral fellowship and support by the UK STFC grant ST/P000525/1 as well as by the European Research Council under the European Union's Seventh Framework Programme (FP/2007-2013) ERC Grant Agreement No. [616170]. PF acknowledges support from MINECO through grant ESP2017-89838-C3-1-R, the European Union H2020-COMPET-2017 grant Enabling Weak Lensing Cosmology, and Generalitat de Catalunya through grant 2017-SGR-885. CG acknowledges the grants ASI n.I/023/12/0, ASI-INAF n. 2018-23-HH.0, and PRIN MIUR 2015 Cosmology and Fundamental Physics: illuminating the Dark Universe with Euclid'. MC carried out part of this work while supported by a grant of the EU-ESF, the Autonomous Region of the Aosta Valley, and the Italian Ministry of Labour and Social Policy (CUP B36G15002310006), and by a 2019 'Research and Education' grant from Fondazione CRT. The OAVdA is managed by the Fondazione Clément Fillietroz-ONLUS, which is supported by the Regional Government of the Aosta Valley, the Town Municipality of Nus, and the 'Unité des Communes valdôtaines Mont-Émilius'. CTD is funded by a Science and Technology Facilities Council (STFC) PhD studentship through grant ST/R504725/1. BL is supported by an ERC Starting Grant, ERC-StG-PUNCA-716532, and is additionally supported by the STFC Consolidated Grants (ST/P000541/1).

Funding Information: The CMB-S4 collaboration ( https://cmb-s4.org/ ) is working to plan, construct, and operate a next-generation, multisite CMB experiment in the 2020s. The collaboration is led by an elected Governing Board, Spokespeople, Committee Chairs, and Executive Team. Funding for the CMB-S4 Integrated Project Office is provided by the Department of Energy's Office of Science (project level CD-0) and by the National Science Foundation through the Mid-Scale Research Infrastructure-R1 award OPP-1935892. This research used resources of Argonne National Laboratory, a U.S. Department of Energy (DOE) Office of Science User Facility operated under Contract No. DE-AC02-06CH11357. This document was prepared by the CMB-S4 collaboration using the resources of the Fermi National Accelerator Laboratory (Fermilab), a U.S. Department of Energy, Office of Science, HEP User Facility. Fermilab is managed by Fermi Research Alliance, LLC (FRA), acting under Contract No. DE-AC02-07CH11359. Work at Lawrence Berkeley National Laboratory was supported by the Office of Science, Office of Basic Energy Sciences, of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. Work at SLAC National Accelerator Laboratory is supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Contract No. DE-AC02-76SF00515. This research used resources of the National Energy Research Scientific Computing Center, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. In the United States, work on CMB-S4 by individual investigators has been supported by the National Science Foundation (awards 1248097, 1255358, 1815887, 1835865, 1852617, 2009469), the Department of Energy (awards DE-SC0009919, DE-SC0009946, DE-SC0010129, DE-SC0011784), and the National Aeronautics and Space Administration (award ATP-80NSSC20K0518). In Australia, the Melbourne authors acknowledge support from an Australian Research Council Future Fellowship (FT150100074). In Canada, R.H. is supported by the Discovery Grants program from NSERC, and acknowledges funding from CIFAR, the Sloan Foundation, and the Dunlap family. In Italy, C.B. acknowledges support under the ASI COSMOS and INFN INDARK programs. In the Netherlands, D.M. acknowledges NWO VIDI award number 639.042.730. In Switzerland, J.C. is supported by an SNSF Eccellenza Professorial Fellowship (No. 186879). In the United Kingdom, A.L., G.F., and J.C. are supported by the European Research Council under the European Union's Seventh Framework Programme (FP/2007-2013)/ERC grant Agreement No. [616170]. A.L. also acknowledges STFC award ST/P000525/1. S.M. is supported by the research program Innovational Research Incentives Scheme (Vernieuwingsimpuls), which is financed by the Netherlands Organization for Scientific Research through the NWO VIDI grant No. 639.042.612-Nissanke and the Labex ILP (reference ANR-10-LABX-63) part of the Idex SUPER, received financial state aid managed by the Agence Nationale de la Recherche,as part of the program Investissements d'avenir under the reference ANR-11-IDEX-0004-02. Some computations in this paper were run on the Odyssey cluster, supported by the FAS Science Division Research Computing Group at Harvard University. Publisher Copyright: © 2022. The Author(s). Published by the American Astronomical Society. ; CMB-S4-the next-generation ground-based cosmic microwave background (CMB) experiment-is set to significantly advance the sensitivity of CMB measurements and enhance our understanding of the origin and evolution of the universe. Among the science cases pursued with CMB-S4, the quest for detecting primordial gravitational waves is a central driver of the experimental design. This work details the development of a forecasting framework that includes a power-spectrum-based semianalytic projection tool, targeted explicitly toward optimizing constraints on the tensor-to-scalar ratio, r, in the presence of Galactic foregrounds and gravitational lensing of the CMB. This framework is unique in its direct use of information from the achieved performance of current Stage 2-3 CMB experiments to robustly forecast the science reach of upcoming CMB-polarization endeavors. The methodology allows for rapid iteration over experimental configurations and offers a flexible way to optimize the design of future experiments, given a desired scientific goal. To form a closed-loop process, we couple this semianalytic tool with map-based validation studies, which allow for the injection of additional complexity and verification of our forecasts with several independent analysis methods. We document multiple rounds of forecasts for CMB-S4 using this process and the resulting establishment of the current reference design of the primordial gravitational-wave component of the Stage-4 experiment, optimized to achieve our science goals of detecting primordial gravitational waves for r > 0.003 at greater than 5 sigma, or in the absence of a detection, of reaching an upper limit of r < 0.001 at 95% CL. ; Peer reviewed