Quantum computers can search rapidly by using almost any selective transformation

The search problem is to find a state satisfying certain properties out of a given set. Grover’s algorithm drives a quantum computer from a prepared initial state to the target state and solves the problem quadratically faster than a classical computer. The algorithm uses selective transformations to distinguish the initial state and target state from other states. It does not succeed unless the selective transformations are very close to phase inversions. Here we show a way to go beyond this limitation. An important application lies in quantum error correction, where the errors can cause the selective transformations to deviate from phase inversions. The algorithms presented here are robust to errors as long as the errors are reproducible and reversible. This particular class of systematic errors arises often from imperfections in the apparatus setup. Hence our algorithms offer a significant flexibility in the physical implementation of quantum search.