This door opens synchronously when you walk across the carpet. No need to press buttons, flip switches or traipse across pressure plates.

The secret lies under the carpet: underneath are two redstone ore blocks.
Anyone who has ever dismantled redtone ore blocks has certainly noticed that the block glows dimly when dismantled.
This glow is detected at the door by Block Update Detectors (BUD), which then ensure that the door opens.

Instructions:

First you have to build the BUDs (with sticky pistons):

After that you need to mirror the design and build 2 blocks away:

The redstone ore blocks are then placed between the two pistons.
Next you have to mirror the two finished BUDs again, so that the door is also usable from the other side:

At the place where you see the yellow block in the picture above, you now place a sticky piston pointing downwards. This is activated by all four BUDs without the BUDs activating each other.
A block is placed on the sticky piston pointing downwards, and a Redstone flare with a repeater is now placed one below, which passes the signal through the block when the sticky piston extends:

Laterally from the place where the sticky piston from above pushes the block you lead Redstone outwards as shown in the picture. On the blocks again sticky pistons come, which point upwards, on it slime blocks (in the front of the picture: 2 slime blocks, in the back of the picture: 2 slime blocks) and kettles with water in it (no matter how much):

Now you only have to place two comparators on immovable objects, as shown in the picture.

Ankerkung:
-All blocks that somehow sit next to slime blocks, even if a piston must extend, must be immovable blocks. Here is a list: http://www.planetminecraft.com/blog/what-a-slimeblock-doesnt-stick-to/
-When the door is open at rest, it's best to put a Redstonedust on one piston of the BUDs.