Introduction to Quantum Computing 
Quantum gates
In this lesson, you will use a single qubit with Pauli X, Y and Z gates.
1) Quantum Gates – the Pauli X gate
You have used some of the programming instructions, or gates, in the quantum computer composer. Last time you only used the measurement tool, and found a single qubit started in the 0> state had a 100% chance of registering zero when no other operations were performed.
This time we are going to try the effect of a few other gates. Let’s start off with the Pauli X gate.
Gate icon 
Gate name 
What it does 
Bloch sphere representation 
Pauli X
gate 
180° turn around the Xaxis 
Create a new program in the Quantum Experience using ibmqx4. Drag the Xgate to qubit q(0) on the score, and then apply the measurement tool. If you make a mistake, doubleclick on the gate to delete it, or drag it to the top left (a delete bin will appear). This is how your program should look: 
Run the program by clicking on the ‘Simulate’ button, and it will be run 100 times. Look at the output.
This time, there is 100% chance that qubit q(0) has the value 1>. (Last time, without the Xgate, it had the value 0>).
So, the Xgate can flip the value of our qubit, from 0> to 1>.
2) Other Pauli gates
Now it is your turn. Find the effect of using the Pauli Y and Z gates.
This is what you should see.
= = 1
==0
Now you can experiment. Please use any combination of X, Y and Z gates to see if you can make the qubit have any value other than 0> or 1>.
When you have tried several combinations, add just one more gate to some of your trials. Does this help?
Homework
Glance at the IBM quantum experience user guide at:
https://www.qiskit.org/ibmqxuserguides/fulluserguide/introduction.html
Appendix
Here is a short description of the most popular quantum gates with a Bloch sphere illustrating their action. Most illustrations are done on a qubit in the 0> state, but the twists and turns would apply on a qubit in any other state.
Gate icon 
Gate name 
What it does 
Bloch sphere representation 
Identity gate 
Performs an idle operation on the qubit for one unit of time 
No change 

Pauli X
gate 
180° turn around the Xaxis 

Pauli Y gate 
180° turn around the Yaxis 

Pauli Z
gate 
180° turn around the Zaxis 

Hadamard gate 
Makes superpositions 


Phase gate 
Makes complex superpositions: maps X→Y 

Opposite Phase gate 
maps X→−Y 

ControlledNOT gate 
Generates entanglement between two qubits 
←→ 

Phase gate 
45° rotation around the Zaxis 

Measurement gate 
Gives the value of the qubit in the Zaxis (i.e. 0> or 1>) 