Complexity-theoretical aspects of quantum computational models

Jincheng Zhang

This paper explores the application of information theory to analyze the computational complexity of quantum algorithms. Traditional approaches to complexity analysis often rely on circuit models and gate complexity, which can be insufficient for fully characterizing the resource requirements of quantum computation. We propose utilizing information-theoretic concepts, specifically quantum entropy and mutual information, to provide a more nuanced understanding of how quantum circuits process information. This approach allows us to quantify the information-theoretic limits of quantum algorithms, providing insights into the number of qubits and gates necessary for efficient execution. We examine several key aspects, including the role of entanglement, the impact of measurement, and the relationship between quantum entropy and algorithmic complexity. The goal is to establish a framework for assessing quantum algorithms based on their fundamental information-processing capabilities, moving beyond purely circuit-based evaluations. This work contributes to a deeper theoretical understanding of quantum computation and its potential limitations.

Daowen Qiu

John Bostanci, John Watrous

This paper is concerned with complexity theoretic aspects of a general formulation of quantum game theory that models strategic interactions among rational agents that process and exchange quantum information. In particular, we prove that the computational problem of finding an approximate Nash equilibrium in a broad class of quantum games is, like the analogous problem for classical games, included in (and therefore complete for) the complexity class PPAD. Our main technical contribution, which facilitates this inclusion, is an extension of prior methods in computational game theory to strategy spaces that are characterized by semidefinite programs.

John Watrous

Marco O. Lanzagorta, Jeffrey K. Uhlmann

Jincheng Zhang

The emergence of quantum entanglement is a fundamental aspect of quantum mechanics, holding immense potential for revolutionary technological advancements. However, the inherent complexity of entangled states, particularly self-organized entanglement, presents a significant challenge to practical quantum computation. This paper explores the theoretical modeling of adaptive self-organized quantum entanglement, aiming to provide a robust framework for predicting and controlling the behavior of these systems. We propose a dynamic quantum entanglement model, leveraging the self-organizing properties of entanglement to predict distribution and stability, ultimately guiding the development of efficient and reliable quantum computing architectures. The core claim is that this model offers a significantly improved approach compared to static entanglement models, leading to more accurate predictions and facilitating the realization of complex quantum systems. Furthermore, we detail the underlying mechanism – the dynamic quantum entanglement model – and its potential impact on quantum computation.