Quantum simulation of strong charge-parity violation and Peccei-Quinn mechanism

Quantum Chromodynamics (QCD) admits a topological $\bar{\theta}$ term that violates charge-parity ($CP$) symmetry, yet experiments indicate that $\bar{\theta}$ is extremely small. To investigate this problem in a controlled setting, we derive a Hamiltonian formulation of QCD through a $(1+1)$-dimensional Schwinger-model analogue. Fermionic and gauge degrees of freedom are encoded into qubits using Jordan-Wigner and quantum-link mappings, yielding a compact Pauli Hamiltonian that preserves the essential topological vacuum structure. Ground states are prepared using a feedback-based quantum optimization protocol, providing access to the vacuum energy on few-qubit simulators. We observe vacuum minima at $\bar{\theta}=0$ and $2\pi$, consistent with the continuum QCD expectations within the accessible regime. Upon coupling to a dynamical axion field, the system relaxes to $\theta_{\rm eff}=0$, realizing the Peccei-Quinn mechanism within a minimal quantum simulation. These results demonstrate how quantum simulation can probe $CP$ violation and its dynamical resolution in gauge theories.