Applications of Geometric Quantum Computing

Eduardo Jose Bayro-Corrochano

Kunihiko Sadakane, Noriko SUGAWARA, Takeshi Tokuyama

We discuss applications of quantum computation to geometric data processing. These applications include problems on convex hulls, minimum enclosing balls, linear programming, and intersection problems. Technically, we apply well-known Grover’s algorithm (and its variants) combined with geometric algorithms, and no further knowledge of quantum computing is required. However, revealing these applications and emphasizing potential usefulness of quantum computation in geometric data processing will promote research and development of quantum computers and algorithms.

Erik Sjöqvist, Vahid Azimi Mousolou, Carlo M. Canali

Jincheng Zhang

This paper explores the potential of geometric transformation quantum computation (GTQC) as a novel approach to quantum information processing. Traditional quantum computation relies heavily on manipulating individual quantum states, while GTQC leverages geometric transformations to encode and manipulate quantum information with enhanced precision and efficiency. This work presents a framework for achieving precise control over quantum states through the application of geometric transformations, offering a fundamentally different paradigm for quantum computation. The core mechanism focuses on utilizing geometric transformations to achieve higher fidelity in quantum state manipulations, addressing limitations in current quantum algorithms. The study investigates the design of a GTQC algorithm and its potential for practical applications, emphasizing the benefits of geometric transformations in enhancing the reliability and control of quantum information.

Seiki Akama

Jincheng Zhang

This paper introduces a novel geometric quantum computation algorithm designed to enhance the efficiency and stability of quantum computations. Traditional approaches often rely on the inherent properties of qubits, while geometric structures offer a powerful mechanism for optimizing quantum algorithms. The proposed algorithm leverages geometric properties to guide the quantum computation, leading to improved computational speed and robustness. This work explores the application of geometric principles to optimize quantum circuits, addressing key challenges in quantum algorithm design.