Quantum lower bounds by quantum arguments

Abstract

We propose a new method for proving lower bounds on quantum query algorithms. Instead of a classical adversary that runs the algorithm with one input and then modifies the input we use a quantum adversary that runs the input with a superposition of inputs. Using this method, we prove two new Ω(√N) lower bounds on AND of ORs and inverting a permutation and also provide more uniform proofs for some known lower bounds which have been previously proven via variety of different techniques. © 2000 ACM.