Tree search and quantum computation

Abstract

Traditional tree search algorithms supply a blueprint for modeling problem solving behaviour. A diverse spectrum of problems can be formulated in terms of tree search. Quantum computation, namely 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 concepts 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.

Analisis Metode Quantum untuk Optimalisasi Algoritma Best First Search

“…Berbagai spektrum masalah dapat dirumuskan dalam istilah dari pencarian pohon. Komputasi kuantum, khususnya algoritma Grover, telah membangkitkan sangat menarik karena memungkinkan percepatan kuadrat diperoleh dalam pencarian Prosedur [11].…”

Quantum Iterative Deepening with an Application to the Halting Problem

“…By employing our proposal we are able to develop a quantum computational model with an inherent speedup relatively to its classical counterparts. Notice that this speedup is only obtained when searching through a search space with a branching factor of at least 2 (please refer to [37] [36]). In addition, if the set of goal states is defined to be the set of halt states, then we are able to use our algorithm to circumvent the halting problem.…”

A quantum production model

“…This approach differs from other strategies of hierarchical search, namely Tarrataca and Wichert [34] and [35], who, respectively, (1) evaluate a superposition of all possible tree paths up to a depth-level d in order to determine if a solution is present and (2) present an hierarchical decomposition of the quantum search space through entanglement detection schemes.…”

“…However, if |R| is a power of 2, then the use of the ceiling functions is no longer required and it is possible to conclude that p 1 = p 2 = p. For that reason, the number of bits m required by our current proposition will always be bigger than p, since m = n + p + 1. This implies that the number of Grover iterations to apply in [34], respectively, O( √ 2 p ) will also be less than the O( √ 2 n+ p+1 ) time required with this method. If a ratio is performed between both procedures then we are able to verify that they differ by a factor of √ 2 p √ 2 n+ p+1 = 1 2 n+1 in favor of [34].…”

“…This implies that the number of Grover iterations to apply in [34], respectively, O( √ 2 p ) will also be less than the O( √ 2 n+ p+1 ) time required with this method. If a ratio is performed between both procedures then we are able to verify that they differ by a factor of √ 2 p √ 2 n+ p+1 = 1 2 n+1 in favor of [34]. However, despite loosing in performance terms, our model differs significantly in nature.…”