A Bi-directional Multi-solution Scalable Grover Search Algorithm
| Source: arXiv AI
Tags: quantum-computing, Grover-search, quantum-algorithms, Qiskit, cryptography
BMGS — a bi-directional multi-solution Grover search algorithm — achieves O(sqrt(sN)) average complexity for s solutions, outperforming Depth-First Grover Search and accepted in Quantum Information Processing (Springer Nature).
Details
Grover's algorithm offers quadratic speedup for database search, but scaling it to find multiple solutions simultaneously is computationally expensive — iterations scale with the number of solutions, limiting practical use. Konar, Hafeez, and Aggarwal propose BMGS (Bi-directional Multi-solution scalable Grover Search), which introduces a multi-segment bidirectional search tactic operating in parallel across equal database segments. The key result: BMGS achieves optimal O(sqrt(sN)) average complexity for s solutions when the depth constraint holds, requiring at most sqrt(N)(1 - sqrt(1/b^(floor(r/dk)))) iterations per solution. Benchmarked against Depth-First Grover Search (DFGS) and Partial Grover Search (PGS) on 2–20 qubit systems, BMGS requires fewer iterations for shallow quantum circuits. The Qiskit implementation is available on GitHub, making this directly testable on IBM Quantum hardware or simulators. Accepted in Quantum Information Processing (Springer Nature).