Sec 1.4 Updates

[nonhermitian]

between initialising the qubits and measuring them, the operations are always reversible! As a result, all the gates we can use in a quantum circuit are reversible too.

This is reversed. the circuits are reversible because the gates are reversible (unitary).

These reversible gates can be represented as matrices, or thought of as rotations around the Bloch sphere.

This is and "and" not "or" statement.

You should be familiar with the Pauli matrices from the linear algebra section. If any of the maths here is new to you, you should use the linear algebra section to bring yourself up to speed.

This looks like it should be in a box rather than inline in the intro text.

We can think of this as a rotation by 𝜋 radians around the x-axis of the Bloch sphere.

It would be nice to show this visually.

Using only the Pauli-gates it is impossible to move our initialised qubit to any state other than |0⟩ or |1⟩, i.e. we cannot achieve superposition

Should mention that the poles correspond to classical states, and thus moving elsewhere on the Bloch sphere is necessary for interesting computation.

3. The Hadamard Gate

Important to mention that H is a fundamentally quantum gate. Takes one off the poles of the Bloch sphere.

4. Digression: Measuring in Different Bases

This should not be a digression. Measuring in different bases is of fundamental importance.

Before, we saw you could create an X-gate by sandwiching our Z-gate between two H-gates:

I do not see where this was covered before?

[quantumjim]

This should not be a digression. Measuring in different bases is of fundamental importance.

Agreed. We need to get this PR finished in Terra so we can talk about different bases more directly, and restore them to their former importance.

[frankharkins]

Just because it is a digression does not mean it is important, it just means that discussing it deviates from the topic of single qubit gates. I felt this was an appropriate place to discuss measuring in different bases as it consolidates what we learnt about the H-gate. I agree that having the pauli measurements will be a useful teaching tool.

Everything else should hopefully be fixed in commit a48c2dd1505cfa8ae48ed831a86cecb8c3098803

[nonhermitian]

Yes, but a digression need not be important. And may give a feeling that this can be skipped. So if there is a way to incorporate it without singling it out then that is ideal.

[shil-m]

Hi, is this completely fixed or something need to be updated? I would like to do it if yes. :)