Many-body strategies for multiqubit gates: Quantum control through Krawtchouk-chain dynamics

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.