2

I have had several opportunities to explain quantum computers to the general public, and I am always at a loss to explain S gate and T gate. Could someone please tell me if there is an origin of the names?

Incidentally, coming from a computational science background, I am always puzzled by terms like H-gate that are derived from a person's name (in computational science, for example, many terms are easy to understand, such as "quick sort"). But I can live with it as such, but S and T are the only terms I couldn't figure out even after looking them up!

Note: This question is a variant of this question, and valid answers can also be obtained from that question, but mine is a single question crystallized without group theory and other factors, focusing only on the origin of S and T.

Thanks, everyone, for the great answers! I got into quantum information from Nielsen and Chuang, so knowing some historical background before that is really helpful. I like to look up the origin of names first (e.g., the meaning of polar decomposition), so the fact that the S and T became established with Nielsen and Chuang and that they started with P (Phase) and avoided QR and went on to S, T,... is sufficient for reasoning. Thank you all for your knowledge and insight.

yasuhito
  • 91
  • 4

1 Answers1

3

Note that not all (abbreviated) names for gates are references to people, take for example the identity gate I, or the X, Y and Z gates.

That said, I don't know for certain why an S gate is called like that, but I can take an educated guess. Since the S gate is also known as the $\sqrt{Z}$ gate (see e.g. https://learn.qiskit.org/course/ch-states/single-qubit-gates), the S could simply refer to that square root.

Since S and T are related through $S = T^2$, I assume T was picked just because it was the next letter in the alphabet. Alternatively, it could have something to do with Tommaso Toffoli, after whom the Toffoli gate is also named, but then I don't know why.

Johan
  • 199
  • 2