Hardness of Pathfinding in a Welded Tree — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: Starting from the entrance of a welded tree, a quantum walk algorithm can find its exit vertex exponentially faster than any classical algorithm. However, it has been an open question whether any quantum algorithm is able to efficiently find a path from the entrance to the exit. We answer this by proving an exponential quantum query lower bound for finding such path. Specifically, for trees of height $n$, any quantum query algorithm requires at least $Ω(2^{n/24})$ queries in order to succeed with constant probability. Our proof uses the compressed permutation oracle technique in order to construct databases which track the graph information an algorithm has learned and forgotten, and show that no efficient quantum algorithm can build an entrance-to-exit path in these records. Source: http://arxiv.org/abs/2609.20651v1 (arXiv:2609.20651v1) Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Author: Caldin, Andrew Stewart
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225448442