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We consider a multi-qubit system of atoms or ions with two computationalground states and an interacting excited state in the so-called blockaderegime, such that only one qubit can be excited at any one time. Examples ofsuch systems are rare-earth-ion-doped crystals and neutral atoms trapped intweezer arrays. We present a simple laser excitation protocol that yields acomplex phase factor on any desired multi-qubit product state, and which can beused to implement multi-qubit gates such as the n-bit Toffoli gates. Theoperation is performed using only two pulses, where each pulse simultaneouslyaddress all qubits. By the use of complex hyperbolic secant pulses our schemeis robust and permits complete transfers to and from the excited states despitethe variability of interaction parameters. A detailed analysis of themulti-qubit gate performance is provided.

Optical multi-qubit gate operations on an excitation blockaded atomic quantum register