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
or bit-flip

180° turn around the X-axis


Create a new program in the Quantum Experience using ibmqx4. Drag the X-gate to qubit q(0) on the score, and then apply the measurement tool. If you make a mistake, double-click 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:

Q Experience

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 X-gate, it had the value |0>).

So, the X-gate 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




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?




Glance at the IBM quantum experience user guide at:


Check quiz: Quantum Gates




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
or bit-flip

180° turn around the X-axis

Pauli Y gate

180° turn around the Y-axis

Pauli Z gate
or phase-flip

180° turn around the Z-axis

Hadamard gate

Makes superpositions

Phase gate

Makes complex superpositions: maps X→Y

Opposite Phase gate

maps X→−Y

Controlled-NOT gate

Generates entanglement between two qubits


Phase gate

45° rotation around the Z-axis

Measurement gate

Gives the value of the qubit in the Z-axis (i.e. |0> or |1>)