IQM Academy - Foundations of Quantum Computing

More qubits, more fun

Of course, a quantum computer with only one qubit cannot perform intricate, practical computations. What we need is more qubits. The concept of superposition also applies to multiple qubits. Let's find out how!

A circuit with two qubits

Below you find a circuit with two qubits. A superposition between how many states can you create?

My measurements

A superposition between how many states can we form with two qubits?

A

1
B

2
C

3
D

4

That's right! There are four: \(\ket{00}\), \(\ket{01}\), \(\ket{10}\) and \(\ket{11}\). To obtain these measurements apply an H gate to the first and second qubit and perform several measurements.

Not quite. Actually, there are four: \(\ket{00}\), \(\ket{01}\), \(\ket{10}\) and \(\ket{11}\). To obtain these measurements apply an H gate to the first and second qubit and perform several measurements.

Gates, again

We also need a gate that works with two qubits.

Below you will find a gate that works with two qubits. Measure the circuit multiple times with different input values to explore the effect of the gate.

My measurements

Based on your observation, which answer describes the effect of the gate best?

A

If the first qubit is in state \(\ket{1}\), the second qubit toggles. If the first qubit is in state \(\ket{0}\) nothing happens.
B

If the first qubit is in state \(\ket{1}\), the second qubit will be measured based on the initial state of the second qubit. If the first qubit is in state \(\ket{0}\) the second qubit will be measured as \(\ket{0}\).
C

If the second qubit is in state \(\ket{1}\), the first qubit toggles. If the second qubit is in state \(\ket{0}\) nothing happens.

That's right! If the so-called control qubit (in the example the upper qubit) is in state \(\ket{1}\), the state of the target qubit (in the example the lower qubit) is changed, i.e. \(\ket{0}\) becomes \(\ket{1}\) and \(\ket{1}\) becomes \(\ket{0}\). If the control qubit is in state 0, nothing happens to the target qubit. That's why this gate is also called the Controlled NOT (CNOT) gate.

Not quite! If the so-called control qubit (in the example the upper qubit) is in state \(\ket{1}\), the state of the target qubit (in the example the lower qubit) is changed, i.e. \(\ket{0}\) becomes \(\ket{1}\) and \(\ket{1}\) becomes \(\ket{0}\). If the control qubit is in state 0, nothing happens to the target qubit. That's why this gate is also called the Controlled NOT (CNOT) gate.