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

TL;DR

The work addresses the strong-CP problem in QCD, where a topological θ-term induces CP violation but experimental bounds require $|\theta|\lesssim 10^{-10}$. It constructs a qubit-encoded (1+1)D Schwinger model with a θ-term using Jordan–Wigner mappings for fermions and a quantum-link truncation for gauge fields, yielding a Hamiltonian $H_{\text{total}} = H_m + H_{\text{hop}} + H_{\theta} + H_G$ and extending to a dynamical axion via $\theta_{\mathrm{eff}} = \theta + a/f_a$ with $H_a = -\kappa \cos(\theta + a/f_a)$. The axion back-reaction drives $\theta_{\mathrm{eff}}$ to zero, realizing the Peccei–Quinn mechanism in a minimal quantum-simulation setting; the study analyzes both a two-site (3 qubits) and a four-site (7 qubits) model, demonstrating CP-restoring dynamics under axion coupling. This work establishes a practical quantum-platform for probing topological gauge physics, real-time CP-violating dynamics, and dynamical resolution mechanisms in gauge theories on near-term hardware.

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.

Figures (2)

• Figure 1: Vacuum energy of the two sites lattice Schwinger model with and without a dynamical axion. (a) Ground (vacuum) energy $E_0(\theta)$ of the qubit-encoded Schwinger model for three representative parameter regimes. In all cases, the minimum appears at a finite, nonzero value of $\theta$, consistent with the theoretical expectation that a generic $\theta$-term leads to $CP$ violation in strong interactions. (b) Ground (vacuum) energy after coupling the model to a dynamical axion field. The axion back-reaction reshapes the $\theta$-dependent potential, producing a $2\pi$-periodic structure whose global minimum is pinned at $\theta = 0$. This shift from a displaced vacuum in (a) to a $CP$-symmetric vacuum in (b) shows that the axion-Schwinger construction reproduces the dynamical relaxation mechanism central to the Peccei-Quinn solution of the strong $CP$ problem.
• Figure 2: Vacuum energy of the four sites lattice Schwinger model with and without a dynamical axion. Ground-state (vacuum) energy $E_{0}(\theta)$ of the qubit-encoded Schwinger model for three representative parameter regimes, shown using the same conventions as Fig. \ref{['fig1']} for (a) without axion field, and (b) with axion field.