Sorry to contradict, but jwenting's answer is totally wrong. I'm shocked to see that it collected so many upvotes. And the picture shows a condensation collar, which is quite unrelated since it is caused by the displacement effect of a relatively blunt rocket near Mach 1 in humid air.
The "boundary layer" at the nose of an aircraft is very thin. What he probably means is a detached shock, but this happens only on a blunt nose and produces too much drag for supersonic aircraft. A detached shock can be found on the nose of the Space Shuttle, and it was selected to keep temperatures there manageable in hypersonic flow. Mach 2.3 aircraft are better off with a pointed nose which produces an attached shock.
But the length of the pitot tube hasn't anything to do with it. The length is not needed for supersonic flight, but for subsonic flight at high angles of attack. Due to the high wing sweep, a high angle of attack capability just happens to coincide with supersonic configurations.
In subsonic flow the air ahead of the aircraft is influenced by the aircraft's pressure field, and at high angles of attack and high wing loadings this reaches out quite a bit. The pitot tube can only measure total pressure when it points into the flow direction. Ahead of the aircraft, the local flow angle increases the closer you are to the aircraft, and this increases measurement errors, because now the pitot tube sits at an oblique angle to the airflow. A longer pitot tube reaches farther out into still relatively undisturbed flow, so less compensation is needed to arrive at good values for total and static pressure. In early flight test, the pitot tube is much longer again, because the compensation factors are not yet established.