Enter these on the designated password screen from the Main Menu:

The game starts with Q*Bert at rank 1. This is indicated by the number on the cube that Q*Bert stands on at the main menu.

To reach rank 2, get over 60,000 points.
To reach rank 3, get over 100,000 points.

You can only change the color of the numbered cubes during game play if your rank equals or exceeds it.