Efficient entanglement operator for a multi-qubit system

In liquid-state NMR quantum computation, a selective entanglement operator between qubits 2 and 3 of a three-qubit molecule is conventionally realized by applying a pair of short π-pulses to qubit 1. This method, called refocusing, is well suited for heteronuclear molecules. When the molecule is homonuclear, however, the π-pulses applied to qubit 1 often induce unwanted z-rotations on qubits 2 and 3, even if the z-components of qubits 2 and 3 are left unchanged. This phenomenon is known as the transient Bloch-Siegert effect, and compensation thereof is required for precise gate operation. We propose an alternative refocusing method, in which a weak square pulse is applied to qubit 1. This technique has the advantage of curbing the Bloch-Siegert effect, making it suitable for both hetero- and homonuclear molecules.