11.5 Error correction for physical qubits

In section 2.1 and section 6.4, we looked at some basic ideas around classical repetition codes. If you want to send information, transmit multiple copies of it. If enough copies get through unscathed, the recipient can determine what you sent. error correction$quantum error correction$repetition code

For the quantum situation, the No-Cloning Theorem (section 9.3.4) says that we can’t copy the state of a qubit, so traditional repetition is not available. No-Cloning Theorem QEC

We can do entanglement, and it turns out that this is powerful enough when combined with aspects of traditional error correction to give us quantum error correction, or QEC.

How can we go from |ψ⟩ = a|0⟩ + b|1⟩ to a|000⟩ + b|111⟩? As you start thinking about such questions, there are two good starting points: “Would applying an H change the situation into something I know how...