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We observe that multi-body interactions, unlike two-body interactions, can implement any unitary operation on an encoded system in such a way that the evolution is uninterrupted by noise that the encoding is designed to protect against. Such ‘error-transparent’ evolution is distinct from that usually considered in quantum computing, as the latter is merely correctable. We prove that the minimum body-ness required to protect (i) a qubit from a single type of Pauli error, (ii) a target qubit from a controller with such errors and (iii) a single qubit from all errors is three-body, four-body and five-body, respectively. We also discuss applications to computing, coherent feedback control and quantum metrology. Finally, we evaluate the performance of error-transparent evolution for some examples using numerical simulations.