Nowadays, various physical systems aiming at universal quantum computation are developing toward increasing the number of controllable qubits and realizing large-scale quantum computation [1–8]. By virtue of the unique advantages of photons, such as fast traveling speed, long coherence time, simple single-qubit operation, and multiple degrees of freedom, the photonic system is considered as one of the most important and possible solutions . Quantum logic gates are the building blocks of quantum circuits to construct universal quantum computers. Both destructive probabilistic two-qubit controlled-NOT (CNOT) gates [10,11] and non-destructive heralded CNOT gates [12–15] as well as three-qubit Toffoli gates [16–19] and Fredkin gates [20,21] based on bulk optical elements have been demonstrated.
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