Question

please write a detailed solution to each part of this problem you may refer to some of hints given below

Short Problem 2 Let's explore some quantum logic gate identities a) What is the single gate that is equivalent to the following three single qubit gates? b) Show that the SWAP operator, that exchanges the state of two qubits, can be created with 3 CNOT gates. Give the rail diagram that puts this into effect. la) b) la) Rail diagram notatio Single qubit unitaries (quantum logic gates), U, appear as Time proceeds left to right (note that multiplication of operators is right to left): lu(to)) The control not (CNOT) gate is written in a couple of different ways. Here we will use the following (more basic) notation that extends to any other control gate, la) lb) where the small solid dot indicates the control qubit (a)) here and acts on the target qubit with the gate indicate if the control is in the 1 state.

Answer 1

0 2 lb) 1 a〉 WAP 1 0 0 CNo T o O 0 1 皿ㄐ〇

(A0) SHAP) (SCNOT adtes