We can already make basic quantum computers. However, these quantum computers are subject to errors due to the nature of qubits. When these errors become too large, our computer might not be calculating the thing we wanted, but something completely different!
We can detect and correct these errors using quantum error correction. But as we saw earlier, we cannot clone quantum information, and so quantum error correction has to work differently from its classical counterparts.
Now let’s see some quantum error correction schemes in a bit more detail.
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?