Quantum Encoding Framework for Leptophilic Gauge Theories

Abstract: We present a systematic quantum encoding framework for leptophilic extensions of the Standard Model, tailored to quantum simulation applications on near term and future quantum devices. Focusing on anomaly free $U(1)'{\ell}$ gauge theories, we show that the leptonic charge structure admits a natural and scalable representation on qubit registers, where gauge symmetries and anomaly cancellation conditions are enforced directly at the level of quantum states. Within this framework, gauge invariant operators are mapped to unitary quantum circuits, ensuring the preservation of gauge symmetry under quantum evolution. As a proof of principle, we construct explicit circuits that encode scattering processes mediated by a leptophilic gauge boson $Z'{\ell}$. Our results establish a reusable bridge between beyond the Standard Model gauge theories and quantum information science, providing a concrete pathway for simulating leptophilic gauge sectors within emerging quantum computing architectures.