Quantum Encoding Framework for Leptophilic Gauge Theories

TL;DR

This paper develops a quantum encoding framework for leptophilic gauge theories, enabling efficient simulation of these models on quantum computers by directly representing gauge symmetries and anomaly conditions.

Contribution

It introduces a scalable quantum encoding scheme for anomaly-free leptophilic gauge theories, mapping gauge invariants to quantum circuits for simulation purposes.

Findings

Quantum encoding preserves gauge invariance during simulation.

Constructed explicit circuits for leptophilic gauge boson interactions.

Framework bridges beyond Standard Model theories with quantum computing.

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.