Quantum Mechanics, Fields and Geometry

Jincheng Zhang

The field of quantum geometry is experiencing a resurgence, driven by the desire to understand and manipulate the fundamental structure of quantum systems. This paper introduces the Phase-Field Quantum Geometry (PFQ) framework, a novel approach to representing and manipulating geometric configurations within quantum systems. PFQ leverages the concept of phase fields to dynamically construct complex geometric structures, offering a powerful tool for studying quantum phenomena and potentially enabling new quantum technologies. The core mechanism focuses on an automated "Phase Field Mapping" algorithm, which constructs intricate geometric representations from quantum data. This paper presents a detailed explanation of the PFQ framework, including its mathematical foundations, algorithm implementation, and potential applications across diverse quantum systems. The research explores the advantages of PFQ compared to existing geometric techniques and highlights its potential to unlock deeper insights into quantum mechanics.

Edoardo Ballico, Bernardi, Alessandra, Iacopo Carusotto +2 more

Lay Nam Chang, Zachary Lewis, Djordje Minić +1 more

We argue that the q=1 limit of Galois Field Quantum Mechanics, which was constructed on a vector space over the Galois Field F_q=GF(q), corresponds to its `classical limit,' where superposition of states is disallowed. The limit preserves the projective geometry nature of the state space, and can be understood as being constructed on an appropriately defined analogue of a `vector' space over the `field with one element' F_1.

Jincheng Zhang

Quantum morphic geometry offers a novel approach to geometric computation, leveraging the principles of quantum mechanics and geometry to perform complex transformations. This paper introduces a framework based on quantum morphic fields, demonstrating its potential for efficient computation through quantum algorithms. We explore the core mechanism of utilizing quantum morphic fields to simulate geometric transformations and integrate quantum algorithms for enhanced computational efficiency. The research focuses on providing a robust and scalable method for geometric manipulation, potentially revolutionizing existing computational techniques.

Ingemar Bengtsson, Carlos Herdeiro, Roger Picken