Optimized General Uniform Quantum State Preparation

Abstract: Quantum algorithms for unstructured search problems rely on the preparation of a uniform superposition, traditionally achieved through Hadamard gates. However, this incidentally creates an auxiliary search space consisting of nonsensical answers that do not belong in the search space and reduce the efficiency of the algorithm due to the need to neglect, un-compute, or destructively interfere with them. Previous approaches to removing this auxiliary search space yielded large circuit depth and required the use of ancillary qubits. We have developed an optimized general solver for a circuit that prepares a uniform superposition of any N states while minimizing depth and without the use of ancillary qubits. We show that this algorithm is efficient, especially in its use of two wire gates, and that it has been verified on an IonQ quantum computer and through application to a quantum unstructured search algorithm.