This is a topic I became interested in because my third son, now three years old has been reading since he was two years old.
First we need a definition: What does it mean to say that a child can read? It means that you can give them a book or paper, which they haven't seen before, with no pictures or visual clues to what the words say, and they can read five words in that book or on the page. This definition is from a book entitled "Exceptionally gifted children" by Miraca Gross.
Particularly typical of exceptionally gifted children is not only do they read from an early age but they learn to read by themselves without being taught. In the case of my son, he learned from public television shows but I think that does not count as being taught because the important point is that he was not made to read by a parent obsessed with making the child read at an early age. This is certainly not the case with my youngest because this is my third child and both of his two older brothers learned to read at the usual age in first grade.
The study of this kind of exceptionally gifted children show that they typically have IQs of 170+. I know that my son has a good visual memory but not anything like a photographic memory. He has a particularly good aptitude for recognizing and identifying shapes. He has not only learned the english alphabet, numbers, and geometric shapes (like square, oval, crecent) but has also learned the Japanese alphabet (Hiragana) of 46 letters, which is better than his considerably older brothers. His early reading at the age of two was just remembering whole words including those which he could read on signs everywhere, but now he actually sounds out words he hasn't read before.
Here is an example of the most recent paper with words which I have used to measure his reading ability (with the results). On this one I was intentionally thinking up longer words which I knew that he would understand the meaning of, some of which were words I knew he could read already (last marked with *).
COMPUTER............read instantly
PAPER...................read instantly
TELEPHONE............read instantly
KITCHEN................read instantly
CHOCOLATE...........read instantly
LIBRARY ..............*read instantly
ALPHABET..............read instantly
OUTSIDE................read instantly
LIVING ROOM.........couldn't read
CIRCLE..................would not read possibly due to lost confidence
SENTENCE..............couldn't read
CHURCH.................would not read possibly due to lost confidence
GROCERY STORE....was determined to read but did not read without assistance
SCHOOL...............*read after some hesitation definitely due to lost confidence
PARKING..............*struggled with this, used to reading "no parking" signs
JAPANESE..............tried to sound this out but did not click
MORNING...............tried to sound this out but could not read
DANCING...............successfully sounded this out to figure out what it said
GRASSHOPPER......*read instantly
READING..............*read instantly
WORKING..............this one he figured out by sounding out the letters