Optimal synthesis of the Fredkin gate in a multilevel system

• URL: http://arxiv.org/abs/2004.03134v1
• Date: Tue, 7 Apr 2020 05:36:34 GMT
• Title: Optimal synthesis of the Fredkin gate in a multilevel system
• Authors: Wen-Qiang Liu and Hai-Rui Wei
• Abstract summary: optimal cost of a three-qubit Fredkin gate is 5 two-qubit entangling gates, and the overhead climbs to 8 when restricted to controlled-not (CNOT) gates. We reduce the cost of a three-qubit Fredkin gate from 8 CNOTs to 5 nearest-neighbor CNOTs. The cost of a nondeterministic three-qubit Fredkin gate is further reduced to 4 nearest-neighbor CNOTs, and the success of such a gate is heralded by a single-photon detector.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The optimal cost of a three-qubit Fredkin gate is 5 two-qubit entangling gates, and the overhead climbs to 8 when restricted to controlled-not (CNOT) gates. By harnessing higher-dimensional Hilbert spaces, we reduce the cost of a three-qubit Fredkin gate from 8 CNOTs to 5 nearest-neighbor CNOTs. We also present construction of an n-control-qubit Fredkin gate with 2n+3 CNOTs and 2n single-qudit operations. Finally, we design deterministic and nondeterministic three-qubit Fredkin gates in photonic architectures. The cost of a nondeterministic three-qubit Fredkin gate is further reduced to 4 nearest-neighbor CNOTs, and the success of such a gate is heralded by a single-photon detector. Our insights bridge the gap between the theoretical lower bound and the current best result for the n-qubit quantum computation.

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