The Bloch Sphere: Quantum’s Controversial Concept

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Kaitlin Duffey

A Controversial 2 Minutes Video

During the first months of my channel in 2019 I made a really short video about the bloch sphere. A video that turned out to be the most controversial in so far. It continuously tops the list of the most viewed and it’s the only video where my like vs. dislike ratio is as low as 20% (my channel average lays close to 85% at the time of writing)

I think this shows how overrated and misunderstood the concept is. A concept that it’s mostly only useful as a model for those working on crazy stuff such as quantum control, pulse optimization, etc.

A great example of this is the company Q-CTRL which specializes in this area. Their tools have the best bloch sphere and entanglement visualizations I’ve ever seen. And it makes total sense!

The Pitfalls of the Bloch Sphere

I have to admit it is also a great tool for beginners to learn the basics of quantum gates. It’s great to visually see how each operation maps to a specific rotation in the sphere. The sphere also complements the notion of gate matrices being seen as transformations but things get quickly messy:

  • It doesn’t help you much to understand a system with 2 qubits or more.
  • It can cause some confusion as one may wonder why is it that the states |0> and  |1> are not represented as being orthogonal.
  • It doesn’t really do a great job representing the phase of a qubit.
  • When dealing with entanglement, things get weird as you observe the state getting close to the center of the sphere (something that goes against most introductions to the tool).

To be honest, the only “aha!” moment I ever had with the bloch sphere was when I saw how a Hadamard gate evolves the state and why does it take you to |+> or |-> depending on whether you apply it to |0> or |1>. But I attribute the “aha!” feeling more to my lack of imagination when trying to grasp what it means to rotate along the X+Z axis.

When you understand it’s all about wave interference, you do realize that the bloch sphere feels a bit useless when working with algorithms.