Non-Orientable Quantum Hilbert Space Bundle
- URL: http://arxiv.org/abs/2412.06548v1
- Date: Mon, 09 Dec 2024 14:58:26 GMT
- Title: Non-Orientable Quantum Hilbert Space Bundle
- Authors: Chia-Yi Ju, Szu-Ming Chen,
- Abstract summary: Instead of relying on hints from the Hamiltonian eigenvalues, the behavior of the fiber metric and the evolution of quantum states are analyzed.
The results reveal that the Hilbert space bundle around an exceptional point is non-orientable.
- Score: 0.0
- License:
- Abstract: This work explores the geometry of the Hilbert space bundle of a quantum system, focusing on properties related to the parameter-induced dimension. Instead of relying on hints from the Hamiltonian eigenvalues, the behavior of the fiber metric and the evolution of quantum states are analyzed directly. The results reveal that the Hilbert space bundle around an exceptional point is non-orientable. Beyond demonstrating a direct method for determining the geometry of the Hilbert space bundle, this study also offers a potential framework for constructing qubits.
Related papers
- Hilbert space geometry and quantum chaos [39.58317527488534]
We consider the symmetric part of the QGT for various multi-parametric random matrix Hamiltonians.
We find for a two-dimensional parameter space that, while the ergodic phase corresponds to the smooth manifold, the integrable limit marks itself as a singular geometry with a conical defect.
arXiv Detail & Related papers (2024-11-18T19:00:17Z) - Quantum Simulation of Large N Lattice Gauge Theories [0.0]
A Hamiltonian lattice formulation of lattice gauge theories opens the possibility for quantum simulations of QCD.
We show how the Hilbert space and interactions can be expanded in inverse powers of $N_c$.
arXiv Detail & Related papers (2024-11-14T17:43:50Z) - Non-Hermitian-Hamiltonian-induced unitarity and optional physical inner products in Hilbert space [0.0]
We show that a weakening of the isotropy of the Hilbert-space geometry can help us to enlarge the domain of the parameters at which the evolution is unitary.
The idea is tested using a simplified subset of eligible metrics and two exactly solvable models.
arXiv Detail & Related papers (2024-08-05T14:14:51Z) - Matter relative to quantum hypersurfaces [44.99833362998488]
We extend the Page-Wootters formalism to quantum field theory.
By treating hypersurfaces as quantum reference frames, we extend quantum frame transformations to changes between classical and nonclassical hypersurfaces.
arXiv Detail & Related papers (2023-08-24T16:39:00Z) - Overlapping qubits from non-isometric maps and de Sitter tensor networks [41.94295877935867]
We show that processes in local effective theories can be spoofed with a quantum system with fewer degrees of freedom.
We highlight how approximate overlapping qubits are conceptually connected to Hilbert space dimension verification, degree-of-freedom counting in black holes and holography.
arXiv Detail & Related papers (2023-04-05T18:08:30Z) - Quantum Geometry of Expectation Values [1.261852738790008]
We show that the boundary of expectation value space corresponds to the ground state, which presents a natural bound that generalizes Heisenberg's uncertainty principle.
Our approach provides an alternative time-independent quantum formulation that transforms the linear problem in a high-dimensional Hilbert space into a nonlinear algebro-geometric problem in a low dimension.
arXiv Detail & Related papers (2023-01-14T14:01:41Z) - Continuous percolation in a Hilbert space for a large system of qubits [58.720142291102135]
The percolation transition is defined through the appearance of the infinite cluster.
We show that the exponentially increasing dimensionality of the Hilbert space makes its covering by finite-size hyperspheres inefficient.
Our approach to the percolation transition in compact metric spaces may prove useful for its rigorous treatment in other contexts.
arXiv Detail & Related papers (2022-10-15T13:53:21Z) - Constraint Inequalities from Hilbert Space Geometry & Efficient Quantum
Computation [0.0]
Useful relations describing arbitrary parameters of given quantum systems can be derived from simple physical constraints imposed on the vectors in the corresponding Hilbert space.
We describe the procedure and point out that this parallels the necessary considerations that make Quantum Simulation of quantum fields possible.
We suggest how to use these ideas to guide and improve parameterized quantum circuits.
arXiv Detail & Related papers (2022-10-13T22:13:43Z) - Reformulation of Quantum Theory [0.0]
The standard quantum mechanics over a complex Hilbert space, is a Hamiltonian mechanics, regarding the Hilbert space as a linear real manifold equipped with its canonical symplectic form and restricting only to the expectation-value functions of Hermitian operators.
We reformulate the structure of quantum mechanics in the language of symplectic manifold and avoid linear structure of Hilbert space in such a way that the results can be stated for an arbitrary symplectic manifold.
arXiv Detail & Related papers (2022-01-03T17:15:35Z) - Bernstein-Greene-Kruskal approach for the quantum Vlasov equation [91.3755431537592]
The one-dimensional stationary quantum Vlasov equation is analyzed using the energy as one of the dynamical variables.
In the semiclassical case where quantum tunneling effects are small, an infinite series solution is developed.
arXiv Detail & Related papers (2021-02-18T20:55:04Z) - Hilbert-space geometry of random-matrix eigenstates [55.41644538483948]
We discuss the Hilbert-space geometry of eigenstates of parameter-dependent random-matrix ensembles.
Our results give the exact joint distribution function of the Fubini-Study metric and the Berry curvature.
We compare our results to numerical simulations of random-matrix ensembles as well as electrons in a random magnetic field.
arXiv Detail & Related papers (2020-11-06T19:00:07Z)
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.