The Compact Linear Collider (CLIC) is an attractive option for a future multi-TeV linear electron-positron collider, offering the potential for a rich precision physics programme, combined with sensitivity to a wide range of new phenomena. The physics reach of CLIC has been studied in the context of three distinct centre-of-mass energies, √s=350 GeV, 1.4 TeV and 3.0 TeV. This staged scenario provides an excellent environment for precise studies of the properties of the 126 GeV Higgs boson. Operation at √s=350 GeV allows, on the one hand, for a determination of the couplings and width of the Higgs boson in a model-independent manner through the study of the Higgsstrahlung process, and on the other hand, for a study of Higgs bosons produced in W+W- fusion for the most common Higgs decay modes. Operation at higher centre-of-mass energies, √s=1.4 TeV and 3 TeV, provides high statistics W+W- fusion samples allowing for high precision measurements of many Higgs couplings and a study of rare Higgs decay modes, Higgs boson samples produced in ZZ fusion, and the potential to study the top Yukawa coupling as well as the Higgs boson self-coupling. We explore the potential of the CLIC Higgs physics programme based on full simulation studies of a wide range of final states. The evolution of the physics sensitivity as a function of the centre-of-mass energy is presented in terms of combined fits to all measurements and their respective statistical uncertainty.
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