Running Shor's algorithm as an Aqua function

Another one of the real luminaries of quantum computing algorithms is Peter Shor's algorithm dating back to 1984, in which he proved that with a sufficiently powerful quantum computer, you can prime factorize really large integers. This is important not only from an academic point of view but also because, for example, factorizing really large (thousands of digits) numbers into constituent prime numbers is the core behind today's RSA encryption that is used to secure online transactions, from banking and social media to the computers built into your car.

At the point when these sufficiently large quantum computers enter the stage, crypto keys that would take weeks, months, years, and longer to break can theoretically be broken in a matter of minutes.

To level-set our expectations here, running Shor's algorithm on today's NISQ machines is more of an academic interest. As you will notice, the Shor circuits tend...