High quality QCD axion at gravitational wave observatories

The axion solution to the strong CP problem is delicately sensitive to Peccei-Quinn breaking contributions that are misaligned with respect to QCD instantons. Heavy QCD axion models are appealing because they avoid this so-called quality problem. We show that generic realizations of this framework can be probed by the LIGO-Virgo-KAGRA interferometers, through the stochastic gravitational wave (GW) signal sourced by the long-lived axionic string-domain wall network and by upcoming measurements of the neutron and proton electric dipole moments. Additionally, we provide predictions for searches at future GW observatories, which will further explore the parameter space of heavy QCD axion models.