Based on Information Geometry: Optimizing Universal Quantum Algorithms

Jincheng Zhang

Published Aug 28, 2026• 0 citations

Abstract

This paper investigates a novel approach to optimizing universal quantum algorithms by leveraging the framework of information geometry. The core idea is to treat quantum algorithms as points embedded within the information geometry of a Hilbert space, specifically tailored to the underlying quantum system. We propose a methodology utilizing gradient descent, guided by the curvature of the information geometry, to identify optimal parameter settings for these algorithms. This approach contrasts with traditional, often empirically-driven, optimization techniques. We formulate the optimization problem as minimizing the quantum relative entropy between the evolved quantum state and the ideal output state, considering the algorithm's Hamiltonian and the geometric constraints imposed by information geometry. The theoretical framework presented here offers a deeper understanding of quantum algorithm optimization and potentially unlocks new avenues for enhancing their efficiency. Key mathematical concepts include the Kullback-Leibler divergence (KL divergence), the quantum relative entropy (also known as the Von Neumann entropy), and the curvature tensor of the information manifold. The primary contribution lies in the integration of these concepts to create a systematic optimization procedure.

DOI: 10.5281/zenodo.22138932

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