Electric dipoles such as Rydberg atoms and polar molecules are among the most promising candidates for building a quantum computer. We propose a protocol that uses long-range dipole-dipole interactions in these systems to quickly implement a generalized controlled-not (CNOT) quantum gate, in which multiple control qubits simultaneously control multiple target qubits (i.e. if all qubits are in state 1, flip all target qubits). Such multiqubit gates can be used to dramatically speed up the implementation of a wide range of quantum algorithms, including the famous Shor’s factoring algorithm. A modification of our protocol can also be used to robustly and quickly prepare metrologically relevant entangled states.
Due to their strong and tunable interactions, Rydberg atoms can be used to realize fast two-qubit entangling gates. We propose a generalization of a generic two-qubit Rydberg-blockade gate to multi-qubit Rydberg-blockade gates which involve both many control qubits and many target qubits simultaneously. This is achieved by using strong microwave fields to dress nearby Rydberg states, leading to asymmetric blockade in which control-target interactions are much stronger than control-control and target-target interactions. The implementation of these multi-qubit gates can drastically simplify both quantum algorithms and state preparation. To illustrate this, we show that a 25-atom GHZ state can be created using only three gates with an error of 7.8%.