On the Universality and Membership problems for quantum gates

Mattioli, Lorenzo; Sawicki, Adam

doi:10.48550/arxiv.2110.04210

Cited by 1 publication

(1 citation statement)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[54] The Toffoli (controlled-controlled-NOT) gate, a three-qubit conditional operation, is one of the most popular universal multi-qubit quantum gates. [55][56][57] It is also an essential component in complex quantum algorithms, [2][3][4][5][6] quantum error correction, [58,59] and quantum fault tolerance. [60,61] In 1995, Barenco et al [1] proposed a concrete construction of a three-qubit Toffoli gate with five two-qubit entangled gates.…”

Section: Introductionmentioning

confidence: 99%

Universal Quantum Multi‐Qubit Entangling Gates with Auxiliary Spaces

2022

View full text Add to dashboard Cite

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 false(2n−1false)$(2n-1)$ qubit–qudit gates and false(2n−2false)$(2n-2)$ 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.

show abstract