Optimal synthesis of the Fredkin gate in a multilevel system

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.

12 page, 5 figures

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Cited by in corpus (7)

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• Kerr-effect-based quantum logical gates in decoherence-free subspace
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• Randomised benchmarking for universal qudit gates
• Hardware-Efficient Quantum Random Access Memory Design with a Native Gate Set on Superconducting Platforms
• Deterministic linear-optical computing with symmetry-based qubits
• Synthesis and upper bound of Schmidt rank of the bipartite controlled-unitary gates