According to wikipedia, the Tianhe-I is the fastest supercomputer in the world. It can perform operations at approximately 2.566 PetaFLOPS.

How many hashes per second could this beast create?

"It is now equipped with 14,336 Xeon X5670 processors and 7,168 Nvidia Tesla M2050 general purpose GPUs"

You can look up the performance of those processors here:

https://en.bitcoin.it/wiki/Mining_hardware_comparison

M2050: 100 Mhash/s
X5630: 8 Mhash/s  (let's just guesstimate that the X5670 can do 10 Mhash/s)

So, Tianhe-1A can do approx. 0.72 Thash/s with GPUs alone, and approx. 0.86 Thash/s with GPU+CPU.

Not enough to do a double spending attack!