pretty obvious that the first move MUST be a check, else 1....Qxc2#. 

So, two checks are available - 1. Rh8+ and 1. Rg7+.
1. Rh8+ allows ... Kf7 and he now can escape to e6 or e8 when checked on the second move.  Not only would white not mate in 2, but he would very likely lose the game, since black only needs a 1-move tempo to play Qxc2#

So, 1. Rg7 Kxg7 (forced) 2. Qh7# is the way to go.

Another approach that I looked at was

1.Rc7.  Then, unless black sacrifices his Queen, it is 2.Qh8#

Some variations on that:
1. Rc7  Qd7, 2. Rxd7 any-move, 3.Qh8#
1. Rc7  Qxc2+, 2. Rxc2  Kf7,  3. Rc7+ Ke8  from here there are too many variations, but I think white's queen to a knight material advantage will win.