Sevag Gharibian: Hardness of approximation for quantum problems

Sevag Gharibian, Institute for Quantum Computing (IQC)

Abstract

The polynomial hierarchy plays a central role in classical complexity theory. Here, we define a quantum generalization of the polynomial hierarchy, and initiate its study. We show that not only are there natural complete problems for the second level of this quantum hierarchy, but that these problems are in fact strongly hard to approximate. Our work thus yields the first known hardness of approximation results for a quantum complexity class. Our approach is based on the use of dispersers, and is inspired by the classical results of Umans regarding hardness of approximation for the second level of the classical polynomial hierarchy [Umans, FOCS 1999]. Joint work with Julia Kempe.