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 = =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: 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 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>) 