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We present a minimal encoding of a single-site interacting boson–fermion system on a quantum computer, with the aim of computing the ground state and low-lying excited states to investigate signatures of spontaneous supersymmetry breaking. Within the framework of quantum variational methods, specifically the Adaptive-VQE approach, we construct variational ansätze that scale efficiently with bosonic levels. We further highlight the underlying computational costs of the method and invite brainstorming on alternative approaches, particularly in the context of multi-site boson–fermion systems with richer dynamics, such as the Wess–Zumino model.