Geometric Criteria for Complete Mode Conversion in Detuned Systems via Piecewise-Coherent Modulation

• URL: http://arxiv.org/abs/2601.10066v1
• Date: Thu, 15 Jan 2026 04:44:28 GMT
• Title: Geometric Criteria for Complete Mode Conversion in Detuned Systems via Piecewise-Coherent Modulation
• Authors: Awanish Pandey,
• Abstract summary: Static phase detuning constrains coherent state transfer in asymmetric classical and quantum systems.<n>We introduce a Bloch-sphere formulation for piecewise-coherent modulation that recasts coupled-mode dynamics as geometric trajectories.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Static phase detuning fundamentally constrains coherent state transfer in asymmetric classical and quantum systems. We introduce a Bloch-sphere formulation for piecewise-coherent modulation that recasts coupled-mode dynamics as geometric trajectories, transforming algebraic control into path optimization. The approach reveals a cone of inaccessibility at the target pole and yields exact geodesic criteria for complete mode conversion in detuned systems. Leveraging this framework, we break time-reversal symmetry to realize a magnet-free optical isolator with near-unity contrast. Furthermore, for detuning larger than coupling between modes, we develop a recursive multi-step protocol enabling deterministic transfer for arbitrary detunings and derive a universal geometric lower bound on the required number of coupling-switching events.

Related papers

• Constructing Arbitrary Coherent Rearrangements in Optical Lattices [36.94429692322632]
  Coherent control of motional degrees of freedom of ultracold atoms in optical lattices offers a promising route towards programmable quantum dynamics with massive particles.<n>We propose and analyze a scheme for implementing coherent rearrangement of ultracold atoms, corresponding to arbitrary unitary transformations on single-particle motional states.
  arXiv  Detail & Related papers  (2026-03-04T15:57:12Z)
• Multi-level spectral navigation with geometric diabatic-adiabatic control [0.0]
  We introduce a framework for efficient few- parameter pulse optimization in multi-level quantum systems.<n>Our method interpolates smoothly between adiabatic and diabatic dynamics to minimize unwanted excitations.<n>We showcase the flexibility of our diabatic-adiabatic protocols through two examples in spin-based quantum information processing.
  arXiv  Detail & Related papers  (2026-02-16T14:01:15Z)
• WUSH: Near-Optimal Adaptive Transforms for LLM Quantization [52.77441224845925]
  Quantization to low bitwidth is a standard approach for deploying large language models.<n>A few extreme weights and activations stretch the dynamic range and reduce the effective resolution of the quantizer.<n>We derive, for the first time, closed-form optimal linear blockwise transforms for joint weight-activation quantization.
  arXiv  Detail & Related papers  (2025-11-30T16:17:34Z)
• Simulating quantum electrodynamics in 2+1 dimensions with qubits and qumodes [0.0]
  We develop a hybrid qubit-qumode framework for simulating quantum electrodynamics in 2+1 dimensions.<n>Fermionic matter fields are represented by qubits, while U(1) gauge fields are encoded in continuous-variable bosonic modes.
  arXiv  Detail & Related papers  (2025-11-18T13:52:42Z)
• Parametric resonant enhancement of motional entanglement under optimal control: an analytical study [45.88028371034407]
  We study theoretically continuous-variable entanglement between the motional degrees of freedom of optically trapped massive particles coupled via the Coulomb interaction.<n>We perform a detailed analysis of the parametric resonance induced by temporal modulation of the coupling strength, based on the system's coupled nonlinear, nonhomogeneous dynamical equations.<n>We demonstrate that a stationary nonequilibrium entangled state is realized as a result of the competition between parametric gain and decoherence.
  arXiv  Detail & Related papers  (2025-10-21T09:01:19Z)
• Convergence Rates for Gradient Descent on the Edge of Stability in Overparametrised Least Squares [33.60489399178793]
  gradient descent on neural networks is frequently performed in a large step size regime called the edge of stability"<n>We provide convergence rates for gradient descent with large learning rates in an overparametrised least squares setting.
  arXiv  Detail & Related papers  (2025-10-20T13:02:41Z)
• Implementing a Universal Set of Geometric Quantum Gates through Dressed-State assisted STA [39.27725073249277]
  We analyze the implementation of single-qubit gates in a two-level system driven by a microwave field.<n>We show how the dynamical phase can be canceled to obtain purely geometric operations.<n>We extend the protocol to construct non two-qubit gates, highlighting its feasibility for scalable quantum information processing.
  arXiv  Detail & Related papers  (2025-09-10T16:14:34Z)
• Generalized Linear Mode Connectivity for Transformers [87.32299363530996]
  A striking phenomenon is linear mode connectivity (LMC), where independently trained models can be connected by low- or zero-loss paths.<n>Prior work has predominantly focused on neuron re-ordering through permutations, but such approaches are limited in scope.<n>We introduce a unified framework that captures four symmetry classes: permutations, semi-permutations, transformations, and general invertible maps.<n>This generalization enables, for the first time, the discovery of low- and zero-barrier linear paths between independently trained Vision Transformers and GPT-2 models.
  arXiv  Detail & Related papers  (2025-06-28T01:46:36Z)
• Variational quantum algorithms with exact geodesic transport [0.0]
  Variational quantum algorithms (VQAs) are promising candidates for near-term applications of quantum computers.<n>We introduce exact-geodesic VQAs, a curvature-aware framework that enables analytic Riemannian optimization of variational quantum circuits.
  arXiv  Detail & Related papers  (2025-06-20T18:00:10Z)
• Bandstructure of a coupled BEC-cavity system: effects of dissipation and geometry [36.136619420474766]
  We present a theoretical model for a Bose-Einstein condensate coupled to an optical cavity.<n>We focus on the interplay between different coherent couplings, which can trigger a structural phase transition.<n>We find non-Hermitian phenomena such as the coalescence of crossing precursor modes.
  arXiv  Detail & Related papers  (2025-04-24T16:43:45Z)
• The multi-state geometry of shift current and polarization [44.99833362998488]
  We employ quantum state projectors to develop an explicitly gauge-invariant formalism.<n>We provide a simple expression for the shift current that resolves its precise relation to the moments of electronic polarization.<n>We demonstrate its power with applications to non-linear optics and the theory of electronic polarization.
  arXiv  Detail & Related papers  (2024-09-24T18:00:02Z)
• Action formalism for geometric phases from self-closing quantum trajectories [55.2480439325792]
  We study the geometric phase of a subset of self-closing trajectories induced by a continuous Gaussian measurement of a single qubit system. We show that the geometric phase of the most likely trajectories undergoes a topological transition for self-closing trajectories as a function of the measurement strength parameter.
  arXiv  Detail & Related papers  (2023-12-22T15:20:02Z)
• A self-consistent field approach for the variational quantum eigensolver: orbital optimization goes adaptive [52.77024349608834]
  We present a self consistent field approach (SCF) within the Adaptive Derivative-Assembled Problem-Assembled Ansatz Variational Eigensolver (ADAPTVQE) This framework is used for efficient quantum simulations of chemical systems on nearterm quantum computers.
  arXiv  Detail & Related papers  (2022-12-21T23:15:17Z)
• Accelerating the computation of quantum brachistochrone [7.899140236856746]
  An alternative set of differential equations are derived for an optimal quantum control of single or multiple qubits with or without interaction. A relaxation technique is designed for numerically detecting optimal paths involving entanglement. In the 'ground state' solution among the set of optimal paths, the time-reversal symmetry of the system shows up.
  arXiv  Detail & Related papers  (2020-11-25T10:39:53Z)

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.