IQM Workshop

Working with qubits - The Hadamard gate

Exploring the Hadamard gate H

Qubits have some properties that bits don't have. To investigate this in more detail, we will explore the H gate. It gives us a first taste of what makes quantum computers so special. And to really see this, we need to perform multiple measurements.

Explore what effect the Hadamard gate H has on a qubit by trying different input values and taking at least 10 measurements per input value. Then, do the same only a X gate and compare the results.

Hints

Each line represents a qubit. Change the input values by clicking on the numbers at the beginning of a line.
Perform a measurement by clicking on Measure.
Use drag & drop to move, add or remove quantum gates.

My measurements

What best describes your observations?

A

The H gate behaves very similarly to the NOT gate from classical computers (i.e. a 0 turns to a 1, and vice versa).
B

The H gate transforms any input into \(\ket{1}\).
C

With the H gate \(\ket{0}\) and \(\ket{1}\) are measured randomly.

Well done! Measuring the output of a circuit with just one H gate multiple times, will lead to \(\ket{0}\) and \(\ket{1}\) being measured randomly. If we do more repetitions, we will see them in approximately 50% of cases each.

Not quite! Measuring the output of a circuit with just one H gate multiple times, will lead to \(\ket{0}\) and \(\ket{1}\) being measured in approximately 50% of cases each.

Take it further ...

To take this further, explore the behavior of two H gates and compare it with two X gates. What are your observations? (You will be able to find the answer on the upcoming pages.)