Abstract
Quantum Chromodynamics (QCD) admits a topological θ term that violates charge-parity (CP) symmetry, yet experiments indicate that θ 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 θ=0 and 2π, consistent with the continuum QCD expectations within the accessible regime. Upon coupling to a dynamical axion field, the system relaxes to θ_ 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.