  Noise causes severe difficulties in implementing quantum computing and
quantum cryptography. Several schemes have been suggested to reduce this
problem, mainly focusing on quantum computation. Motivated by quantum
cryptography, we suggest a coding which uses $N$ quantum bits ($N=n^2$) to
encode one quantum bit, and reduces the error exponentially with $n$. Our
result suggests the possibility of distributing a secure key over very long
distances, and maintaining quantum states for very long times. It also provides
a new quantum privacy amplification against a strong adversary.
