Universal Quantum Multi‐Qubit Entangling Gates with Auxiliary Spaces. Issue 5 (18th March 2022) - Liu, Wen‐Qiang; Wei, Hai‐Rui; Kwek, Leong‐Chuan
Abstract: Universal quantum entangling gates are a crucial building block in the large‐scale quantum computation and quantum communication, and it is an important task to find simple ways to implement them. Here an effective quantum circuit for the implementation of a controlled‐NOT (CNOT) gate is constructed by introducing a non‐computational quantum state in the auxiliary space. Furthermore, the method is extended to the construction of a general n ‐control‐qubit Toffoli gate with ( 2 n − 1 ) (2n-1) qubit–qudit gates and ( 2 n − 2 ) (2n-2) single‐qudit gates. Based on the presented quantum circuits, the polarization CNOT and Toffoli gates with linear optics are designed by operating on the spatial‐mode degree of freedom of photons. The proposed optical schemes can be achieved with a higher success probability and no extra auxiliary photons are needed. Abstract : Effective quantum circuits for a controlled‐NOT (CNOT) gate and an n ‐control‐qubit Toffoli gate are constructed assisted by the auxiliary spaces. Moreover, the post‐selected CNOT and Toffoli gates with linear optics are designed by operating on the spatial‐mode degree of freedom of photons. The proposed optical schemes can be achieved with a higher success probability and extra auxiliary photons are not required.