A question pertaining to Shor’s discovery

The recently published interview “Peter Shor on the genesis of Shor’s algorithm ” (Physics Today, April 2025, page 34), conducted by David Zierler and adapted and annotated by Ryan Dahn, was fascinating. I was interested in Shor’s discovery that there is a polynomial-time quantum computer factoring algorithm that violates the Church–Turing thesis, which in Shor’s words, says “basically, anything any computer can do in polynomial time, a Turing machine can do in polynomial time.” The presentation of the social aspects around this discovery provides an excellent view into the topic’s history. Of course, the now well-known implications are also discussed, but in so doing, the article also highlights, by omission, something missing in the field of theoretical computing.

Since the Turing machine is classical, I am left with an obvious but unaddressed question: Is it possible that there is also a quantum Turing machine? I wonder if someone is studying this, but perhaps it is too much to expect that they would make themselves available to discuss it with Dahn for publication in Physics Today. That would only bring unwanted attention and competition to the issue.