Linear optics quantum Toffoli and Fredkin gates

Abstract

We design linear optics multiqubit quantum logic gates. We assume the traditional encoding of a qubit onto state of a single photon in two modes (e.g. spatial or polarization). We suggest schemes allowing direct probabilistic realization of the fundamental Toffoli and Fredkin gates without resorting to a sequence of single- and two-qubit gates. This yields more compact schemes and potentially reduces the number of ancilla photons. The proposed setups involve passive linear optics, sources of auxiliary single photons or maximally entangled pairs of photons, and single-photon detectors. In particular, we propose an interferometric implementation of the Toffoli gate in the coincidence basis, which does not require any ancilla photons and is experimentally feasible with current technology.

8 pages, 4 figures, RevTeX4

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• Protocol for secure quantum machine learning at a distant place
• A simple trapped-ion architecture for high-fidelity Toffoli gates
• Addendum to "Single photon logic gates using minimum resources"
• Experimental Demonstration of a Quantum Controlled-SWAP Gate with Multiple Degrees of Freedom of a Single Photon
• Implementations of more general solid-state (SWAP)${}^{1/m}$ and controlled-(swap)${}^{1/m}$ gates
• One-step implementation of the genuine Fredkin gate in high-$Q$ coupled three-cavity arrays
• Efficient Fusion of Photonic W-states with Nonunitary Partial-swap Gates
• Application of the Diamond Gate in Quantum Fourier Transformations and Quantum Machine Learning
• Resource Reduction in Multiplexed High-Dimensional Quantum Reed-Solomon Codes
• On the symmetry of the seminal Horodecki state
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