Quantum simulation of strong charge-parity violation and Peccei-Quinn mechanism
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Abstract
Quantum Chromodynamics (QCD) admits a topological $\barθ$ term that violates charge-parity ($CP$) symmetry, yet experiments indicate that $\barθ$ 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 $\barθ=0$ and $2π$, consistent with the continuum QCD expectations within the accessible regime. Upon coupling to a dynamical axion field, the system relaxes to $θ_{\rm eff}=0$, 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.