Representation and the Quantum State

Jincheng Zhang

Quantum state representation is a cornerstone of quantum information processing, yet current methods often lack a robust, geometric framework for manipulation and analysis. This paper introduces Universal Quantum State Representation (QSR), a novel system for encoding and manipulating quantum states through a layered, dynamically evolving geometric structure. QSR leverages discrete, high-dimensional geometric transformations to provide a more intuitive and flexible approach compared to traditional methods. We demonstrate the efficacy of QSR through a series of illustrative examples, highlighting its potential to simplify complex quantum computations and facilitate deeper insights into quantum information dynamics. This work provides a foundational framework for advancing quantum state representation and enabling new algorithmic possibilities.

Olivier Brunet

Jincheng Zhang

Abstract: Quantum state representation is a fundamental concept in quantum information theory, crucial for quantum algorithms and quantum computation. Traditional state representations often rely on fixed dimensionality, limiting the expressiveness of quantum states. This paper introduces a novel quantum state representation that dynamically expands the kernel of a state space, allowing for more expressive representations. We propose a neural network-based approach to learn a dynamic kernel function, enabling a flexible and powerful representation of quantum states. This advancement offers a significant step towards more efficient quantum algorithms and a deeper understanding of quantum phenomena. The proposed method demonstrates improved performance in various quantum state comparison and manipulation tasks.

Christian DE RONDE

Richard Healey

Jincheng Zhang

This paper introduces a novel geometric representation of quantum states, termed "Geometric Quantum State Representation with Adaptive Density," designed to capture and leverage quantum information more effectively. Traditional representations often lack the ability to dynamically adapt to subtle variations in the quantum state, hindering optimal information processing. We propose a system that utilizes a geometric density adaptation algorithm, which adjusts the representation's density based on observed quantum states, offering a dynamic and adaptable framework for quantum state analysis. The core mechanism centers on the intelligent mapping of quantum states onto a geometric space, enhancing information capture and potentially enabling new functionalities. This paper details the algorithmic design, discusses the theoretical foundations, and presents preliminary results demonstrating the superior performance of this representation compared to static representations.