An unexpected moment of insightQuantum circuits are more than just abstract math. They bridge theory and hardware by turning dense unitary matrices into structured recipes that real devices can execute. Therefore, they provide an essential layer of abstraction that makes quantum computation both understandable and practical.September 17, 2025

Dear Quantum Machine Learner,

Today, I sat down to write a basic note about quantum circuits. It should be done quickly. I was wrong. It became a full-fledged post.

I thought of quantum circuits as diagrams. Some boxes and wires on which you can hang an algorithm. Useful, familiar, safe. I thought I could give a brief overview of the notation and how to construct them with Qiskit. In the end, a circuit is not the algorithm. It is a particular representation of it. So, nothing too complicated.

But when I sat down, my Nemesis hit me hard. Math came in my way. Of course, math is just another representation of a quantum algorithm. But wait, if a quantum circuit and math are two representations of the same thing, then they must be similar. To some extend.

At this point, fate took its course. Let me rephrase. The article took its own unique course. Suddenly, I asked myself: Why quantum circuits? What's their purpose anyway?

I mean, all these mathematicians and physicists use mathematics. They seem to prefer a good, complex equation to a simple diagram. Admittedly, quantum diagrams become unmanageable once they reach a certain size.

So am I the only one? Why should I stick with it? But thinking about quantum circuits all day long gave me a certain sense of relief. In fact, I strengthened my mental connections about how mathematics and quantum computing are related. I realized that a quantum circuit is actually equivalent to an equation. In fact, it is even more because it does not restrict itself to the theorist's perspective.

So, this obvious realization reinforces my belief that quantum circuits are the most powerful tools in quantum computing. Backed by math.

Enjoy reading the post

—Frank ZickertAuthor of PyQML