Universal quantum multi-qubit entangling gates with auxiliary spaces

TL;DR

This paper presents a new quantum circuit design for universal multi-qubit entangling gates, including CNOT and Toffoli gates, using auxiliary spaces and linear optics, achieving higher success probabilities without extra photons.

Contribution

It introduces a novel quantum circuit approach utilizing auxiliary states for implementing multi-qubit gates with improved efficiency and success rates.

Findings

Designed optical schemes for CNOT and Toffoli gates with higher success probability

No additional auxiliary photons required in the proposed optical implementations

Extended the method to general n-control-qubit Toffoli gates

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 (2n-1) qubit-qudit gates and (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.