Since we cannot clone quantum information, quantum error correction cannot be done by simply storing the same state multiple times. An example of a quantum error-correcting code is the Shor 9-qubit code. Can you figure out why this does not violate the no-cloning theorem?
Shor 9-qubit code, or similar quantum error correction schemes, do not violate the no-cloning theorem because they never copy quantum states. By this, we mean that you will never encounter a process like the following:
| Q> → |Q>|Q>
These algorithms only use Hadamards and CNOT gates to form a superposition of physical qubits.