Inverse Problems, Constraint Satisfaction, Reversible Logic, Invertible Logic and Grover Quantum Oracles for Practical Problems

Abstract

It is well-known that the “Unsorted Database” quantum algorithm by Grover gives quadratic speedup to several important combinatorial and enumerative problems, such as: SAT, Graph Coloring, Maximum Cliques, Travelling Salesman and many others. Recently, quantum programming languages such as Quipper start to be used to design, verify and simulate practical quantum algorithms for important problems in Quantum Machine Learning. So far, however, no methodologies have been created to program Grover Oracles for particular classes of problems. In contrast, such methodologies have been already created for classical Constraint Satisfaction Problems. The goal of this invited talk is to show results of some initial research towards creating systematic methodologies to program quantum computers that solve search problems in Artificial Intelligence, Logic Design and Machine Learning. Our methods are based on unified oracle blocks for such problem representations as set partition algebra, cube calculus and optimal mappings. For instance, several important problems in CAD and Machine Learning can be solved using only two basic operations on set partitions; Π1 ≤ Π2 and Π1 · Π2. Moreover, building oracles is the fundamental concept in the new approach to solve CSP proposed here and based on Invertible Logic introduced recently by Supriyo Datta and his team.