IQM Academy - Foundations of Quantum Computing

Bringing quantum into the mix – Hadamard gate

The X gate behaves very similarly to the NOT gate of classical computers. In fact it is sometimes even called the quantum not gate. Not that different from classical computing so far. So, what really makes quantum computers special?

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.
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.)