This dissertation presents a search for long-lived particles using delayed photons in proton-proton collisions at sqrt(s) = 13 TeV recorded by the Compact Muon Solenoid (CMS) experiment at the CERN Large Hadron Collider in 2017, corresponding to an integrated luminosity of 41.5 fb^-1. This analysis includes a number of unique components that will be discussed: a dedicated signal trigger, out-of-time photon reconstruction and identification, and a detector time resolution measurement. The results of this search include the combination of a related analysis using data collected in 2016 also at sqrt(s) = 13 TeV, corresponding to a combined integrated luminosity of 77.4 fb^-1. The combined results are interpreted in the context of supersymmetry with gauge-mediated supersymmetry breaking, where the neutralino is long-lived and decays to a photon and a gravitino. Limits are presented as a function of the neutralino proper decay length and mass. For neutralino proper decay lengths of 10^1, 10^2, 10^3, and 10^4 cm, masses up to 320, 525, 360, and 215 GeV are excluded at 95% confidence level, respectively. Additionally, a discussion on a high-performance computing upgrade to CMS, known as mkFit, will be presented. mkFit is an on-going effort to exploit highly parallel computer architectures in vectorizing and parallelizing combinatorial Kalman filter charged particle track reconstruction algorithms. The current physics and computational performance of this project will be discussed.