N.B. These questions are provided to give you
something concrete to think about to exercise
your understanding of the concepts introduced in lectures.
Which of them you work is your choice, as is collaboration.
Hint: Apply the hybrid argument that we used to show a lower
bound for the search problem.
Show that a quantum error correcting code that is resilient
against both a bit- and a phase-flip on one qubit is also resilient
against any linear error on one qubit. Verify this for the
9-qubit Shor code.
What about linear errors on more qubits?
Hint: Can you express any linear operation on one qubit in
terms of the identity (no error), a bit-flip, a phase-flip, and
a simultaneous bit and phase flip?