Circuits: An abstract viewpoint

Abstract

Our primary purpose is to isolate the abstract, mathematical properties of circuits — both classical Boolean circuits and quantum circuits — that are essential for their computational interpretation. A secondary purpose is to clarify the similarities and differences between the classical and quantum situations.

The general philosophy in this note is to include the mathematically es- sential aspects of circuits but to omit any of the additional structures that are usually included for convenience. We shall, however, retain the assumption that circuits are finite; this assumption does no harm to the applicability of our approach and is necessary for some of our work.

One of the endearing things about mathematicians is the extent to which they will go to avoid doing any real work.

— Matthew Pordage