Error-transparent evolution: the ability of multi-body interactions to bypass decoherence

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, iii) a single qubit from all errors, is 3-body, 4-body, and 5-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.