Quantum simulation of strong Charge-Parity violation and Peccei-Quinn mechanism

Abstract: Quantum Chromodynamics (QCD) admits a topological θ-term that violates Charge-Parity (CP) symmetry, yet experimental indicate that θ is nearly zero. To investigate this discrepancy in a controlled setting, we derive the Hamiltonian representation of the QCD Lagrangian and construct its (1+1)-dimensional Schwinger-model analogue. By encoding fermionic and gauge degrees of freedom into qubits using the Jordan-Wigner and quantum-link schemes, we obtain a compact Pauli Hamiltonian that retains the relevant topological vacuum structure. Ground states are prepared using a feedback-based quantum optimization protocol, enabling numerical evaluation of the vacuum energy E0(θ) on a few-qubit simulator. Our results show a displaced vacuum at nonzero θin agreement with strong-interaction expectations, and demonstrate that introducing a dynamical axion field drives the system toward θ= 0, thereby realizing the Peccei-Quinn mechanism within a minimal quantum simulation. These results illustrate how quantum hardware can examine symmetry violation and its dynamical resolution in gauge theories.