Tree search and quantum computation

Andreas Wichert

Abstract. Traditional tree search algorithms supply a blueprint for modeling prob-lem solving behaviour. A diverse spectrum of problems can be formulated in terms of tree search. Quantum computation, in particular Grover’s algorithm, has aroused a great deal of interest since it allows for a quadratic speedup to be obtained in search procedures. In this work we consider the impact of incorporating classical search con-cepts alongside Grover’s algorithm into a hybrid quantum search system. Some of the crucial points examined include: (1) the reverberations of contemplating the use of non-constant branching factors; (2) determining the consequences of incorporating an heuristic perspective into a quantum tree search model.

Weng-Long Chang, Athanasios V. Vasilakos

T. Hema, Micheal Olaolu Arowolo

Quantum computing is an emerging field of study and gains importance due to the fact that with the introduction of quantum computers, many challenges and changes are presented for the existing algorithms. The main reason for this is the exponential speed of such computers. This study analyzes some of the benefits and implications of quantum computing on geometrical problems such as the multidimensional search for window queries with R-Trees. A review of the window query on R-Trees in classical computing is done to consider its adaptability to quantum computers by applying the Grover's quantum search algorithm from a theoretical point of view. Thereby, the query time complexity in worst-case scenarios could be improved to quadratic search time.

Uwe Schöning, Randall J. Pruim

Mingjie Hu, Jian-Qiang Hu, Enlu Zhou

Recent advances in quantum computing are opening new opportunities for computationally intensive decision problems. This paper studies how quantum computing can improve Monte Carlo tree search (MCTS) in the fixed-confidence setting, where the goal is to identify a near-optimal move in a given game tree with high probability while minimizing query complexity. We first formulate MCTS under a quantum oracle model. We then develop a quantum MCTS algorithm (QMCTS) that combines threshold-based elimination on the search tree with quantum Monte Carlo estimation to reduce the cost of evaluating stochastic leaf values. We establish an instance-dependent lower bound on the query complexity and derive a corresponding upper bound for QMCTS. The lower-bound analysis introduces a new quantum phase-testing result that may also be useful beyond MCTS. We validate the theoretical results through simulation experiments and further demonstrate the feasibility of QMCTS on real quantum hardware.

Christoph Dürr, xb b b