1. Error correction 8 marks Suppose we are using the 3qubit phase-ip code and recovery operaton with error operation 5 : p I> U5 0} U9 933 ngU; U; 8 Ug: Where U9 = R369) and sin2(9/2) = p. (In other words: a U9 operation is applied to each qubite) (a) 2 marks Suppose we start with the encoded state l+>l+)l+), and then the above error DCCUTS. Express the resulting state Us 69 Us 69 U3l+)l+>l+) as a superposition of Ml l)|l>l Mlll )lltl >|l>ll>=|l>l ll M >ll)| Ll )l )ll),| )I )l l (b) 2 marks S lllll, 10\"" that the probability of being in a state that will not be corrected by \"majority voting" in the {H}, l)} basis is in 0(p2). (C) Suppose we measure the stabilizers XXI and XIX. i. ii. 0 . 5 marks each Show t 1at the probability of obtaining +1 and +1 is in 1 7 0(p). \"'hat is the resulting, state of the encoded qubit in this case? What is the resulting state of the encoded qubit after the appropriate correce tion is done? Show t 1st the resulting error probability in this case is in 0(p3). 0 . 5 marks each Show t 1st the probability of obtaining +1 and 1 is in 0(1)). What is the resulting state of the encoded qubit in this case? What is the resulting state of the encoded qubit after the appropriate correc tion is done? Show t 1at the resulting error probability in this case is in 0(p)