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

Abstract

We propose a strategy for engineering multi-qubit 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 2-body driving term leads to the iSWAP${}_N$ gate, which we numerically test for N = 4 and 6.

10 pages, 3 figures

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• Quantum gates by resonantly driving many-body eigenstates, with a focus on Polychronakos' model