Deterministic Grover search with a restricted oracle

Grover's quantum search algorithm provides a quadratic quantum advantage over classical algorithms across a broad class of unstructured search problems. The original protocol is probabilistic, returning the desired result with significant probability on each query but, in general, requiring several iterations of the algorithm. We present a modified version to return the correct result with certainty without having user control over the quantum search oracle. Our deterministic, two-parameter D2p protocol utilizes generalized phase rotations replacing the phase inversions after a standard oracle query. The D2p protocol achieves a 100% success rate in no more than one additional iteration compared to the optimal number of steps as in the original Grover's search enabling the same quadratic speedup. We also provide a visualization using the Bloch sphere for enhanced geometric intuition.

Automated summary

Grover's quantum search algorithm provides a quadratic quantum advantage over classical algorithms for unstructured search problems. We present a modified version that returns the correct result with certainty without user control over the quantum search oracle. The visualization using the Bloch sphere enhances geometric intuition.