Unit-probability quantum search for all solutions

The objective of Grover's quantum algorithm is to efficiently identify a single solution within a search space. However, there are search problems that require finding all possible solutions. A direct, repeated application of Grover's algorithm is unsuitable for these problems, as it lacks an internal mechanism to avoid rediscovering previous solutions. Here we introduce a quantum algorithm that efficiently and deterministically discovers all solutions by preparing special initial states of the index register, a step accomplished by leveraging knowledge from solutions obtained during execution. We experimentally demonstrate our algorithm on a superconducting quantum processor. This work provides quantum examples for search scenarios with some knowledge about solutions.