Kenneth W. Regan – Abstract

Kenneth W. Regan,

University at Buffalo

 

Combinatorial Invariants and Quantum Circuits
(joint work with Chaowen Guan, University of Cincinnati)

Abstract
The study of polynomial invariants of graphs, matroids, and other combinatorial structures has seen great success in recent years. We apply these techniques and methods of algebra to quantum circuits.  Results include faster algorithms for strong simulation of the tractable class of stabilizer circuits and for the basic problem of solving quadratic equations modulo 2.  This leads to a new class of polynomials that arise as quasi-specializations of Oxley-Whittle rank-generating polynomials and behave as generalized Tutte-Grothendieck invariants.  The methods aim to capture hardness properties of apparently classically intractable classes of quantum circuits.