Kerr media, or mediums displaying the optical Kerr effect, are used in some optical quantum computers - on Chuang and Nielsen's Quantum Computing and Quantum Information, pgs. 289 - 290, it says,
Nonlinear optics provides one final useful component for this exercise: a material whose index of refraction $n$ is proportional to the total intensity $I$ of light going through it:
$$n(I) = n+n_2I$$
This is known as the optical Kerr effect [...]
Examining the Wikipedia article for the Kerr effect mentions three (!) different Kerr effects: the magneto-optic, electro-optic, and just plain old optical Kerr effect. Since the phrasing and equations match, I assume the book means the optical Kerr effect (also known as the AC Kerr effect).
The major difference between the optical/AC Kerr effect and the electro-optic/DC Kerr effect is for the DC version to work, one must manually apply the electric field to the medium, whereas for the AC version, the light going through produces the effect itself. So far, so good.
Now, the problem in my understanding arises when considering the term "intensity" ($I$) and what it means. When talking about optical quantum computers, we're talking about single photons, meaning the only way to vary the energy of the photon is by varying the wavelength (though this is a very small difference in energy).
Reading some papers, it talks about the light being of higher intensity to cause a larger Kerr effect...but it's a single photon. How can you vary intensity here, in a way large enough to really change the effect's significance?