Generating Quantum Matrix Geometry from Gauged Quantum Mechanics

• URL: http://arxiv.org/abs/2310.01051v3
• Date: Sat, 16 Dec 2023 14:09:23 GMT
• Title: Generating Quantum Matrix Geometry from Gauged Quantum Mechanics
• Authors: Kazuki Hasebe
• Abstract summary: We present a quantum-oriented non-commutative scheme for generating the matrix geometry of the coset space $G/H$. The resultant matrix geometries manifest as $itpure$ quantum Nambu geometries. We demonstrate how these quantum Nambu geometries give rise to novel solutions in Yang-Mills matrix models.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Quantum matrix geometry is the underlying geometry of M(atrix) theory. Expanding upon the idea of level projection, we propose a quantum-oriented non-commutative scheme for generating the matrix geometry of the coset space $G/H$. We employ this novel scheme to unveil unexplored matrix geometries by utilizing gauged quantum mechanics on higher dimensional spheres. The resultant matrix geometries manifest as $\it{pure}$ quantum Nambu geometries: Their non-commutative structures elude capture through the conventional commutator formalism of Lie algebra, necessitating the introduction of the quantum Nambu algebra. This matrix geometry embodies a one-dimension-lower quantum internal geometry featuring nested fuzzy structures. While the continuum limit of this quantum geometry is represented by overlapping classical manifolds, their fuzzification cannot reproduce the original quantum geometry. We demonstrate how these quantum Nambu geometries give rise to novel solutions in Yang-Mills matrix models, exhibiting distinct physical properties from the known fuzzy sphere solutions.

Related papers

• Qubit Geometry through Holomorphic Quantization [0.0]
  We develop a wave mechanics formalism for qubit geometry using holomorphic functions and Mobius transformations. This framework extends the standard Hilbert space description.
  arXiv  Detail & Related papers  (2025-04-23T05:24:43Z)
• Quantum geometric tensors from sub-bundle geometry [0.0]
  We use the differential-geometric framework of vector bundles to analyze the properties of parameter-dependent quantum states. We show that the sub-bundle geometry is similar to that of submanifolds in Riemannian geometry and is described by a generalization of the Gauss-Codazzi-Mainardi equations. This leads to a novel definition of the quantum geometric tensor, which contains an additional curvature contribution.
  arXiv  Detail & Related papers  (2025-03-21T14:08:06Z)
• Geometric monotones of violations of quantum realism [89.99666725996975]
  Quantum realism states that projective measurements in quantum systems establish the reality of physical properties, even in the absence of a revealed outcome. This framework provides a nuanced perspective on the distinction between classical and quantum notions of realism, emphasizing the contextuality and complementarity inherent to quantum systems. We derive geometric monotones of quantum realism using trace distance, Hilbert-Schmidt distance, Schatten $p$-distances, Bures, and Hellinger distances.
  arXiv  Detail & Related papers  (2024-12-16T10:22:28Z)
• Quantum geometry embedded in unitarity of evolution: revealing its impacts as quantum oscillation and dephasing in spin resonance and crystal bands [0.29127054707887967]
  We show how geometry emerges in quantum as an intrinsic consequence of unitary evolution. We exemplify geometric observables, such as oscillation, dephasing, in spin and band scenarios.
  arXiv  Detail & Related papers  (2024-06-22T13:16:51Z)
• Geometry of degenerate quantum states, configurations of $m$-planes and invariants on complex Grassmannians [55.2480439325792]
  We show how to reduce the geometry of degenerate states to the non-abelian connection $A$. We find independent invariants associated with each triple of subspaces. Some of them generalize the Berry-Pancharatnam phase, and some do not have analogues for 1-dimensional subspaces.
  arXiv  Detail & Related papers  (2024-04-04T06:39:28Z)
• A Hitchhiker's Guide to Geometric GNNs for 3D Atomic Systems [87.30652640973317]
  Recent advances in computational modelling of atomic systems represent them as geometric graphs with atoms embedded as nodes in 3D Euclidean space. Geometric Graph Neural Networks have emerged as the preferred machine learning architecture powering applications ranging from protein structure prediction to molecular simulations and material generation. This paper provides a comprehensive and self-contained overview of the field of Geometric GNNs for 3D atomic systems.
  arXiv  Detail & Related papers  (2023-12-12T18:44:19Z)
• Machine learning detects terminal singularities [49.1574468325115]
  Q-Fano varieties are positively curved shapes which have Q-factorial terminal singularities. Despite their importance, the classification of Q-Fano varieties remains unknown. In this paper we demonstrate that machine learning can be used to understand this classification.
  arXiv  Detail & Related papers  (2023-10-31T13:51:24Z)
• Vectorization of the density matrix and quantum simulation of the von Neumann equation of time-dependent Hamiltonians [65.268245109828]
  We develop a general framework to linearize the von-Neumann equation rendering it in a suitable form for quantum simulations. We show that one of these linearizations of the von-Neumann equation corresponds to the standard case in which the state vector becomes the column stacked elements of the density matrix. A quantum algorithm to simulate the dynamics of the density matrix is proposed.
  arXiv  Detail & Related papers  (2023-06-14T23:08:51Z)
• Generalized quantum geometric tensor for excited states using the path integral approach [0.0]
  The quantum geometric tensor encodes the parameter space geometry of a physical system. We first provide a formulation of the quantum geometrical tensor in the path integral formalism that can handle both the ground and excited states. We then generalize the quantum geometric tensor to incorporate variations of the system parameters and the phase-space coordinates.
  arXiv  Detail & Related papers  (2023-05-19T08:50:46Z)
• Geometrically robust linear optics from non-Abelian geometric phases [0.0]
  We construct a unified operator framework for quantum holonomies generated from bosonic systems. For a system whose Hamiltonian is bilinear in the creation and operators, we find a holonomy group determined only by a set of selected orthonormal modes.
  arXiv  Detail & Related papers  (2022-04-07T16:08:08Z)
• Weyl Geometry and Quantum Corrections [0.0]
  Weyl Geometry can be used to merge quantum theory and general relativity consistently as classical field theories. In the Weyl Geometric framework, it seems that both quantum theory and gravity can merge consistently, once quantum theory is geometrized.
  arXiv  Detail & Related papers  (2021-12-24T06:38:02Z)
• A singular Riemannian geometry approach to Deep Neural Networks I. Theoretical foundations [77.86290991564829]
  Deep Neural Networks are widely used for solving complex problems in several scientific areas, such as speech recognition, machine translation, image analysis. We study a particular sequence of maps between manifold, with the last manifold of the sequence equipped with a Riemannian metric. We investigate the theoretical properties of the maps of such sequence, eventually we focus on the case of maps between implementing neural networks of practical interest.
  arXiv  Detail & Related papers  (2021-12-17T11:43:30Z)
• Quantum Information Dimension and Geometric Entropy [0.0]
  We introduce two analysis tools, inspired by Renyi's information theory, to characterize and quantify fundamental properties of geometric quantum states. We recount their classical definitions, information-theoretic meanings, and physical interpretations, and adapt them to quantum systems via the geometric approach.
  arXiv  Detail & Related papers  (2021-11-11T18:40:49Z)
• Algebraic Compression of Quantum Circuits for Hamiltonian Evolution [52.77024349608834]
  Unitary evolution under a time dependent Hamiltonian is a key component of simulation on quantum hardware. We present an algorithm that compresses the Trotter steps into a single block of quantum gates. This results in a fixed depth time evolution for certain classes of Hamiltonians.
  arXiv  Detail & Related papers  (2021-08-06T19:38:01Z)
• Photon-mediated Stroboscopic Quantum Simulation of a $\mathbb{Z}_{2}$ Lattice Gauge Theory [58.720142291102135]
  Quantum simulation of lattice gauge theories (LGTs) aims at tackling non-perturbative particle and condensed matter physics. One of the current challenges is to go beyond 1+1 dimensions, where four-body (plaquette) interactions, not contained naturally in quantum simulating devices, appear. We show how to prepare the ground state and measure Wilson loops using state-of-the-art techniques in atomic physics.
  arXiv  Detail & Related papers  (2021-07-27T18:10:08Z)
• Quantum simulation of gauge theory via orbifold lattice [47.28069960496992]
  We propose a new framework for simulating $textU(k)$ Yang-Mills theory on a universal quantum computer. We discuss the application of our constructions to computing static properties and real-time dynamics of Yang-Mills theories.
  arXiv  Detail & Related papers  (2020-11-12T18:49:11Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.