The simulation of systems of interacting fermions is one of the most anticipated applications of quantum computers. The most interesting simulations will require a fault-tolerant quantum computer, and building such a device remains a long-term goal. However, the capabilities of existing noisy quantum processors have steadily improved, sparking an interest in running simulations that, while not necessarily classically intractable, may serve as device benchmarks and help elucidate the challenges to achieving practical applications on near-term devices. Systems of non-interacting fermions are ideally suited to serve these purposes. While they display rich physics and generate highly entangled states when simulated on a quantum processor, their classical tractability enables experimental results to be verified even at large system sizes that would typically defy classical simulation. In this work, we use a noisy superconducting quantum processor to prepare Majorana zero modes (MZMs) as eigenstates of the Kitaev chain Hamiltonian, a model of non-interacting fermions. Our work builds on previous experiments with non-interacting fermionic systems. Previous work demonstrated error mitigation techniques applicable to the special case of Slater determinants. Here, we show how to extend these techniques to the case of general fermionic Gaussian states, and demonstrate them by preparing MZMs on systems of up to seven qubits.