We propose a strategy for engineering multiqubit quantum gates. As a first step, it employs an eigengate to map states in the computational basis to eigenstates of a suitable many-body Hamiltonian. The second step employs resonant driving to enforce a transition between a single pair of eigenstates, leaving all others unchanged. The procedure is completed by mapping back to the computational basis. We demonstrate the strategy for the case of a linear array with an even number N of qubits, with specific XX+YY couplings between nearest neighbors. For this so-called Krawtchouk chain, a two-body driving term leads to the iSWAP_N gate, which we numerically test for N = 4 and 6.

Physical Review A: Atomic, Molecular and Optical Physics
Algorithms and Complexity

Groenland, K., & Schoutens, K. (2018). Many-body strategies for multiqubit gates: Quantum control through Krawtchouk-chain dynamics. Physical Review A: Atomic, Molecular and Optical Physics, 97(4). doi:10.1103/PhysRevA.97.042321