  We investigate the possibilities and limitations of passive Hamiltonian
protection of a quantum memory against depolarizing noise. Without protection,
the lifetime of a single qubit is independent of N, the number of qubits
composing the memory. In the presence of a protecting Hamiltonian, the lifetime
increases at most logarithmically with N. We construct an explicit
time-independent Hamiltonian which saturates this bound, exploiting the noise
itself to achieve the protection.
