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We propose a strategy for engineering multi-qubit quantum gates. As a firststep, it employs an eigengate to map states in the computational basis toeigenstates of a suitable many-body Hamiltonian. The second step employsresonant driving to enforce a transition between a single pair of eigenstates,leaving all others unchanged. The procedure is completed by mapping back to thecomputational basis. We demonstrate the strategy for the case of a linear arraywith an even number N of qubits, with specific XX+YY couplings between nearestneighbors. For this so-called Krawtchouk chain, a 2-body driving term leads tothe iSWAP$_N$ gate, which we numerically test for N = 4 and 6.

Many-body strategies for multi-qubit gates - quantum control through Krawtchouk chain dynamics