A Quantum Time-Space Lower Bound for the Counting Hierarchy

We obtain the first nontrivial time-space lower bound for quantum algorithms solving problems related to satisfiability. Our bound applies to MajSAT and MajMajSAT, which are complete problems for the first and second levels of the counting hierarchy, respectively. We prove that for every real d and every positive real there exists a real c > 1 such that either:

• Type: Journal
• Year: 2008
• Where: ECCC
• Authors: Dieter van Melkebeek, Thomas Watson
• Keywords: ECCC 2008, Quantum, Quantum Algorithm, Two-sided Error