  Proton transfer is ubiquitous in many fundamental chemical and biological
processes, and the ability to modulate and control the proton transfer rate
would have a major impact on numerous quantum technological advances. One
possibility to modulate the reaction rate of proton transfer processes is given
by exploiting the strong light-matter coupling of chemical systems inside
optical or nanoplasmonic cavities. In this work, we investigate the proton
transfer reactions in the prototype malonaldehyde and Z-3-amino-propenal
(aminopropenal) molecules using different quantum electrodynamics methods, in
particular quantum electrodynamics coupled cluster theory (QED-CC) and quantum
electrodynamical density functional theory (QEDFT). Depending on the cavity
mode polarization direction, we show that the optical cavity can increase the
reaction energy barrier by 10--20$\%$ or decrease the reaction barrier by
$\sim$5$\%$. By using first principles methods, this work establishes strong
light-matter coupling as a viable and practical route to alter and catalyze
proton transfer reactions.
