11.5 Error correction

In section 2.1

For the quantum situation, the No-Cloning Theorem (subsection 9.3.3

What we can do is 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 to handle,’’ and ‘‘how might a CNOT and entanglement affect things?’’

Since I already let on that entanglement is part of the solution, note that a simple

takes |ψ⟩|0⟩|0⟩ to a |000⟩ + b |111⟩. Each CNOT changes the |0⟩ in q₁ and q₂ to |1⟩ if the amplitude b...