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Nested Grover's Algorithm for Tree Search
1Department of Computer Science and Engineering, INESC-ID & Instituto Superior Técnico, University of Lisbon, 2740-122 Porto Salvo, Portugal.
Entropy (Basel, Switzerland)
|January 28, 2026
Summary
This study optimizes quantum tree search using a nested Grover Algorithm. It enhances performance by searching subsets of assignments, improving quantum artificial intelligence foundations.
Area of Science:
- Quantum Computing
- Artificial Intelligence
- Algorithm Optimization
Background:
- Traditional heuristic functions are incompatible with quantum tree search.
- Previous Grover-based methods have limitations in optimizing quantum tree search.
Purpose of the Study:
- To optimize quantum tree search algorithms using a nested Grover Algorithm.
- To enhance quantum artificial intelligence applications by improving search efficiency.
Main Methods:
- Employing a nested Grover Algorithm to expand the tree of partial assignments to a specific depth.
- Introducing the partial candidate solution to define a concatenated oracle.
- Decomposing the quantum tree search using Grover's algorithm with the concatenated oracle.
Main Results:
- The nested Grover Algorithm approach enhances results compared to previous Grover-based methods.
- The cost of Grover's algorithm is reduced from O(2m/2) to O(m·2m/4) for m partial candidate solutions with a branching factor of 2 and depth m.
Conclusions:
- The proposed method provides a foundation for advanced quantum artificial intelligence applications.
- The optimization of quantum tree search using a nested Grover Algorithm offers significant efficiency gains.
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