Description

CS 518, Spring 2024

Read class notes and chapter 3 P Lala (X, H, Y, Z gates).
1. a) What is X gate? Write circuit representation and matrix representation of X gate. Show the intermediatory and final output of a circuit when 3 X gates are in series (use both circuit and matrix representation of X gate)
b) If a qubit goes through a circuit of 2 X gate connected in series, what is the output of the circuit (show output at each stage)?
2. a) What is Hadamard gate?
b) Write expression for mapping input |m> by a Hadamard gate (use class notes)
c) Write circuit and matrix representation of H gate.
d) Show the intermediatory and final output of a circuit when 3 H gates are in series (use both circuit and matrix representation of H gate) when initial input is a |0>.
e) Show the intermediatory and final output of a circuit when 3 H gates are in series (use both circuit and matrix representation of H gate) when initial input is a qubit.

3. Show the output of a circuit of X gate and H gate connected in series when the input is |1>. Show the output of each stage of the circuit.