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We put forward a strategy to encode a quantum operation into the unmodulateddynamics of a quantum network without the need of external control pulses,measurements or active feedback. Our optimization scheme, inspired bysupervised machine learning, consists in engineering the pairwise couplingsbetween the network qubits so that the target quantum operation is encoded inthe natural reduced dynamics of a network section. The efficacy of the proposedscheme is demonstrated by the finding of uncontrolled four-qubit networks thatimplement either the Toffoli gate, the Fredkin gate, or remote logicoperations. The proposed Toffoli gate is stable against imperfections, has ahigh-fidelity for fault tolerant quantum computation, and is fast, being basedon the non-equilibrium dynamics.

Quantum gate learning in engineered qubit networks: Toffoli gate with always-on interactions