Luke Schaeffer: Classification of Reversible Bit Operations

Wednesday, October 7, 2015 - 4:00pm to 5:00pm
Luke Schaeffer

Abstract:  We present a complete classification of all possible sets of classical reversible gates acting on bits,in terms of which reversible transformations they generate, assuming swaps and ancilla bits are available for free.

Our classification can be seen as the reversible-computing analogue of Post's lattice, a central result in mathematical logic from the 1940s. It is a step toward the ambitious goal of classifying all possible quantum gate sets acting on qubits.

This is joint work with Scott Aaronson and Daniel Grier.