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It has previously been shown that probabilistic quantum logic operations can be performed using linear optical elements, additional photons (ancilla), and post-selection based on the output of single-photon detectors. Here we describe the operation of several quantum logic operations of an elementary nature, including a quantum parity check and a quantum encoder, and we show how they can be combined to implement a controlled-NOT (CNOT) gate. All of these gates can be constructed using polarizing beam splitters that completely transmit one state of polarization and totally reflect the orthogonal state of polarization, which allows a simple explanation of each operation. We also describe a polarizing beam splitter implementation of a CNOT gate that is closely analogous to the quantum teleportation technique previously suggested by Gottesman and Chuang [Nature 402, 390 (1999)]. Finally, our approach has the interesting feature that it makes practical use of a quantum-eraser technique. II. CNOT USING FOUR-PHOTON ENTANGLED STATESAs we mentioned earlier, Gottesman and Chuang showed in a pioneering paper [4] that a CNOT operation could be performed using a modified form of quantum teleportation. Although the required Bell-state measure-

We report a proof-of-principle demonstration of a probabilistic controlled-NOT gate for single photons. Single-photon control and target qubits were mixed with a single ancilla photon in a device constructed using only linear optical elements. The successful operation of the controlled-NOT gate relied on post-selected three-photon interference effects which required the detection of the photons in the output modes.There has been considerable interest in a linear optics approach to quantum computing [1,2], in which probabilistic two-qubit logic operations are implemented using linear optical elements and measurements made on a set of n additional (ancilla) photons. Here we report a proofof-principle demonstration of a probabilistic controlled-NOT (CNOT) gate using a single ancilla photon. Two of the required single-photons were produced using parametric down-conversion [3] while a third photon was obtained from an attenuated laser pulse. The use of only one ancilla photon required that all three photons be detected, in which case the device was known to have correctly performed a CNOT logic operation.Logic operations are inherently nonlinear, so it is somewhat surprising that they can be performed using simple linear optical elements [1,4,5,6,7,8,9,10]. The necessary nonlinearity is obtained by mixing the input photons with n ancilla photons using linear elements, and then measuring the state of the ancilla photons after the interaction. The measurement process is nonlinear [11], since a single-photon detector either records a photon or not, and it projects out the desired logical output state provided that certain results are obtained from the measurements. The results of the operation are known to be correct whenever these specific measurement results are obtained, which occurs with a failure rate that scales as

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Abstract:We show that the quantum Zeno effect can be used to implement several quantum logic gates for photonic qubits, including a gate that is similar to the squareroot of SWAP operation. The operation of these devices depends on the fact that photons can behave as if they were non-interacting fermions instead of bosons in the presence of a strong Zeno effect. These results are discussed within the context of several no-go theorems for non-interacting fermions or bosons.