Multiple-qubit controlled unitary quantum gate for Rydberg atoms using shortcut to adiabaticity and optimized geometric quantum operations

Multiple-qubit quantum logic gates are an important element in the implementation of quantum computers. The direct construction of multiple-qubit quantum logic gates in an efficient way has important values compared to the construction of multiple-qubit gates using a series of two-qubit and single-qubit gates. We propose a scheme to construct a multiple-qubit CkU gate (k denotes the number of control qubits and U means the arbitrary universal operation performed on the target qubit) in a neutral atom platform through the Rydberg blockade effect by successively exciting them to Rydberg states. This scheme takes advantage of the shortcut to adiabaticity of inverse engineering, geometric quantum operations, as well as optimized control theory. The geometric quantum computation considered in this manuscript guarantees the robustness to operational errors. Meanwhile, inverse engineering-based shortcut to adiabaticity provides a further advantage in terms of the speed of the system evolution compared to adiabatic processes. An additional feature of our multiple-qubit quantum logic gate is that arbitrary operation on the target atom can be realized by adjusting the amplitude and phase of the laser fields. Numerical simulation of the master equation based on the full Hamiltonian demonstrates the high fidelity of the proposed scheme and its robustness to operational errors and spontaneous emission.

Automated summary

The proposed scheme for constructing multiple-qubit quantum logic gates in a neutral atom platform takes advantage of inverse engineering's shortcut to adiabaticity, geometric quantum operations, and optimized control theory. Geometric quantum computation ensures robustness to operational errors, while inverse engineering-based shortcut to adiabaticity speeds up the system evolution compared to adiabatic processes. Additionally, the ability to adjust the amplitude and phase of the laser fields allows for arbitrary operations on the target atom.