Abstract: A controller of a quantum system causes a geometric phase gate to be performed on two or more qubits by causing two or more qubits of the quantum system to experience a (near field and/or non-radiating) magnetic field gradient; and, responsive to determining that a gate time period has elapsed since the two or more qubits of the quantum system started to experience the magnetic field gradient, causing the two or more qubits to no longer experience the magnetic field gradient. The entanglement of the two or more qubits corresponding to the performance of the gate is enacted, mediated, and/or caused by the magnetic field gradient.

Abstract: A trapped-ion quantum logic gate and a method of operating the trapped-ion quantum logic gate are provided. The trapped-ion quantum logic gate includes at least one ion having two internal states and forming a qubit having a qubit transition frequency ?0, a magnetic field gradient, and two microwave fields. Each of the two microwave fields has a respective frequency that is detuned from the qubit transition frequency ?0 by frequency difference ?. The at least one ion has a Rabi frequency ?? due to the two microwave fields and a Rabi frequency ?g due to the magnetic field gradient. The method includes applying the magnetic field gradient and the two microwave fields to the at least one ion such that a quantity ?g/? is in a range between zero and 5×10?2.

Abstract: A trapped-ion quantum logic gate and a method of operating the trapped-ion quantum logic gate are provided. The trapped-ion quantum logic gate includes at least one ion having two internal states and forming a qubit having a qubit transition frequency ?0, a magnetic field gradient, and two microwave fields. Each of the two microwave fields has a respective frequency that is detuned from the qubit transition frequency ?0 by frequency difference ?. The at least one ion has a Rabi frequency ?? due to the two microwave fields and a Rabi frequency ?g due to the magnetic field gradient. The method includes applying the magnetic field gradient and the two microwave fields to the at least one ion such that a quantity ?g/? is in a range between zero and 5×10?2.