The influence of quantum effects on the processes of initiation of combustion and detonation of hydrogen and acetylene near the low-temperature limits at elevated pressures is analyzed. A theoretical consideration which allows quantification of the quantum corrections to the rate constants of endothermic reactions associated with an increase in the high-energy tail of the equilibrium momentum distribution function at high pressures is presented. This quantum effect is caused by a manifestation of the principle of uncertainty for the energy of the colliding particles at a high frequency of collisions. It is shown that significant deviations of experimentally observed ignition and detonation delay time from the predictions of kinetic calculations are quite well described by the proposed quantum corrections. This general mechanism should be considered in the safety problem with emergency emissions of hydrogen at nuclear power stations, as well as problems of the safe production and storage of hydrogen and acetylene, which have a fundamental importance for industry and power engineering.