Saved in:
Bibliographic Details
Main Authors: Grillo, Sebastian Alberto, Dávalos, Bernardo Daniel, Torres, Rodney Fabian Franco, Marquezino, Franklin de Lima, Pezoa, Edgar López
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2602.04700
Tags: Add Tag
No Tags, Be the first to tag this record!
Table of Contents:
  • The analysis of the computational power of single-query quantum algorithms is important because they must extract maximal information from one oracle call, revealing fundamental limits of quantum advantage and enabling optimal, resource-efficient quantum computation. This paper proposes a formulation of single-query quantum decision trees as weighted graphs. This formulation has the advantage that it facilitates the analysis of the $L_1$ spectral norm of the algorithm output. This advantage is based on the fact that a high $L_1$ spectral norm of the output of a quantum decision tree is a necessary condition to outperform its classical counterpart. We propose heuristics for maximizing the $L_{1}$ spectral norm, show how to combine weighted graphs to generate sequences with strictly increasing norm, and present functions exhibiting exponential quantum advantage. Finally, we establish a necessary condition linking single-query quantum advantage to the asymptotic growth of measurement projector dimensions.