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The complete 10-year survey from the Large Synoptic Survey Telescope (LSST)will image $\sim$ 20,000 square degrees of sky in six filter bands every fewnights, bringing the final survey depth to $r\sim27.5$, with over 4 billionwell measured galaxies. To take full advantage of this unprecedentedstatistical power, the systematic errors associated with weak lensingmeasurements need to be controlled to a level similar to the statisticalerrors.  This work is the first attempt to quantitatively estimate the absolute leveland statistical properties of the systematic errors on weak lensing shearmeasurements due to the most important physical effects in the LSST system viahigh fidelity ray-tracing simulations. We identify and isolate the differentsources of algorithm-independent, \textit{additive} systematic errors on shearmeasurements for LSST and predict their impact on the final cosmic shearmeasurements using conventional weak lensing analysis techniques. We find thatthe main source of the errors comes from an inability to adequatelycharacterise the atmospheric point spread function (PSF) due to its highfrequency spatial variation on angular scales smaller than $\sim10'$ in thesingle short exposures, which propagates into a spurious shear correlationfunction at the $10^{-4}$--$10^{-3}$ level on these scales. With the largemulti-epoch dataset that will be acquired by LSST, the stochastic errorsaverage out, bringing the final spurious shear correlation function to a levelvery close to the statistical errors. Our results imply that the cosmologicalconstraints from LSST will not be severely limited by thesealgorithm-independent, additive systematic effects.

Spurious Shear in Weak Lensing with LSST