What components are needed to realize a photonic CNOT gate?

Contrary to DaftWullie's answer, it is possible to implement a CNOT gate in a photonic system with 100% efficiency.

However, there are caveats to this - it depends on what's used as the qubits (or, as this is a photonic system, potentially qudits) in the system.

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KLM: A photon as a qubit

The first thing that most people think of in terms of photonic qubits is polarisation. In this case, postselection (/heralding) is generally required. This was theoretical shown to be possible by Knill, Laflamme and Milburn (KLM) in 2001. Within a couple of years, the first probabilistic photonic CNOT gate was shown by O'Brien et. al. (arXiv version) in an equivalent scheme, as shown in figure 1.

Figure 1: Circuit diagram of probabilistic 2-photon CNOT gate. Each photon (control and target) is encoded from polarisation to spatial modes. After postselecting on a single photon in $C_{text{out}}$ and a single photon in $T_{text{out}}$, when the control photon, $C$, is in spatial mode $C_0$, the identity operation is performed on the target photon, $T$, while when $C$ is in $C_1$, the NOT (X) operation is performed on $T$ which has a probability of success of 1/9. Uses beamsplitters. Image taken from Figure 1a of O'Brien et. al.

One variation of this is to use a nonlinear phase shift to make a deterministic version of this.

While the above may not sound overly great for the prospects of optical quantum computing, encoding a qubit as polarisation/2 spatial modes of a photon is far from the only way to perform optical quantum computing.

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Reck: Many modes makes... Many dimensions

One other such method was proposed before KLM by Reck et. al. (shown in figure 2) and has since been improved upon by Clements et. al. In this a single photon is encoded in some number, $d$, of spatial modes. This is equivalent to a $log_2 d$ qubit system and can be used to implement any unitary. For a 2-qubit system, this is equivalent to having 4 spatial modes labelled $left|00right>, left|01right>, left|10right>$ and $left|11right>$ and a CNOT operation is equivalent to swapping the bottom 2 $left(left|10right> text{ and } left|11right>right)$ modes.

Figure 2: Image of a 6-mode Reck scheme chip, which can be used to implement a deterministic 'CNOT' gate. Uses phase shifters and beam splitters to build up a unitary evolution over the modes of the system. Image taken from Figure 1 of Carolan et. al.

Of course, it's not quite that simple and, due to requiring an exponential number of modes, the Reck scheme isn't generally considered to be overly scalable.

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That leaves us with the (final) two options¹: nonlinear optics (continuous variable) and measurement based quantum computing

Continuous variable: Just keep squeezing

As detailed in my answer here, continuous variable QC also offers a universal gateset which can be used to make arbitrary unitaries, in theory at least. Unfortunately, as more squeezing is still required, an experimental realisation of this is yet to occur.

And now for something completely different: Measurement based

Another scheme that hasn't been experimentally achieved, yet shows potential, is measurement based QC. Instead of performing CNOT gates during unitary evolution that defines a circuit, the entangling operations occur as part of the state preparation of the system. As per Ewert and Loock (arXiv version) the current idea of doing this involves generating small clusters of entangled photons, then entangling these into larger clusters using fusion gates, as shown in figure 3.

Figure 3: Diagram of a 75% efficient fusion gate. Inputting the state $left|Upsilon_1right> = frac{1}{sqrt 2}left(left|20right> + left|02right>right)$ allows for the detection of higher dimensional states. These can then be cascaded to detect larger and larger cluster states. The probabilistic measurement is equivalent to an entangling operation, similar to a CNOT gate. Image taken from Figure 1 of Ewert and Loock.

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^{1 Although there are a number of variations of the different schemes used and work is constantly being done to improve upon them}