Optical multiqubit gate operations on an excitation-blockaded atomic quantum register

We consider a multiqubit system of atoms or ions with two computational ground states and an interacting excited state in the so-called blockade regime, such that only one qubit can be excited at any one time. Examples of such systems are rare-earth-ion-doped crystals and neutral atoms trapped in tweezer arrays. We present a simple laser excitation protocol that yields a complex phase factor on any desired multiqubit product state, and which can be used to implement multiqubit gates such as the n-bit Toffoli gates. The operation is performed using only two pulses, where each pulse simultaneously address all qubits involved in the operation. By relying on the well-established complex hyperbolic secant pulse shape, our scheme is also robust and permits complete transfers to and from the excited states despite variations in Rabi frequencies and transition frequencies. A detailed analysis of the multiqubit gate performance is provided.